Incorrect expression of force calculation relationship
Publish: 2021-04-20 01:04:47
1. The computing power of CPU is related to the number of CPU cores, the frequency of core and the ability of single clock cycle of core
the ability of double precision floating-point computing is commonly used to measure the scientific computing ability of CPU, that is, the ability to process 64 bit floating-point data
the processor supporting avx2 can perform 16 floating-point operations in one core and one clock cycle, Also known as 16flops
CPU power = number of cores x frequency of cores x 16flops
processors supporting avx512 can perform 32 floating-point operations in one core and one clock cycle, also known as 32flops
CPU power = number of cores x frequency of cores x 32flops
the ability of double precision floating-point computing is commonly used to measure the scientific computing ability of CPU, that is, the ability to process 64 bit floating-point data
the processor supporting avx2 can perform 16 floating-point operations in one core and one clock cycle, Also known as 16flops
CPU power = number of cores x frequency of cores x 16flops
processors supporting avx512 can perform 32 floating-point operations in one core and one clock cycle, also known as 32flops
CPU power = number of cores x frequency of cores x 32flops
2. The history of computer
the birth and development of modern computer before the advent of modern computer, the development of computer has gone through three stages: mechanical computer, electromechanical computer and electronic computer
as early as the 17th century, a group of European mathematicians began to design and manufacture digital computers that perform basic operations in digital form. In 1642, Pascal, a French mathematician, made the earliest decimal adder by using a gear transmission similar to clocks and watches. In 1678, Leibniz, a German mathematician, developed a computer to further solve the multiplication and division of decimal numbers
British mathematician Babbage put forward an idea when he made the model of difference machine in 1822. One arithmetic operation at a time will develop into a certain complete operation process automatically. In 1884, Babbage designed a program-controlled universal analyzer. Although this analyzer has described the rudiment of the program control computer, it can not be realized e to the technical conditions at that time< During the more than 100 years since Babbage's idea was put forward, great progress has been made in electromagnetics, electrotechnics and electronics, and vacuum diodes and vacuum triodes have been successively invented in components and devices; In terms of system technology, wireless telegraph, television and radar were invented one after another. All these achievements have prepared technical and material conditions for the development of modern computer< At the same time, mathematics and physics are developing rapidly. In the 1930s, all fields of physics experienced the stage of quantification. The mathematical equations describing various physical processes, some of which were difficult to solve by classical analysis methods. As a result, numerical analysis has been paid attention to, and various numerical integration, numerical differentiation, and numerical solutions of differential equations have been developed. The calculation process has been reced to a huge amount of basic operations, thus laying the foundation of modern computer numerical algorithm
the urgent need for advanced computing tools in society is the fundamental driving force for the birth of modern computers. Since the 20th century, there have been a lot of computational difficulties in various fields of science and technology, which has hindered the further development of the discipline. Especially before and after the outbreak of the Second World War, the need for high-speed computing tools in military science and technology is particularly urgent. During this period, Germany, the United States and the United Kingdom started the research of electromechanical computer and electronic computer almost at the same time<
Giuseppe in Germany was the first to use electrical components to make computers. The fully automatic relay computer Z-3, which he made in 1941, has the characteristics of modern computer, such as floating-point counting, binary operation, instruction form of digital storage address and so on. In the United States, the relay computers mark-1, mark-2, model-1, model-5 and so on were made successively from 1940 to 1947. However, the switching speed of the relay is about one hundredth of a second, which greatly limits the computing speed of the computer
the development process of electronic computer has experienced the evolution from making components to whole machine, from special machine to general machine, from "external program" to "stored program". In 1938, the Bulgarian American scholar atanasov first made the computing unit of the electronic computer. In 1943, the communications office of the British Foreign Office made the "giant" computer. This is a special cryptanalysis machine, which was used in the Second World War< In February 1946, ENIAC, a large-scale electronic digital integrator computer, was developed by Moore College of the University of Pennsylvania in the United States. At first, ENIAC was also specially used for artillery trajectory calculation. Later, it was improved many times and became a general-purpose computer capable of various scientific calculations. This computer, which uses electronic circuit to perform arithmetic operation, logic operation and information storage, is 1000 times faster than relay computer. This is the first electronic computer in the world. However, the program of this kind of computer is still external, the storage capacity is too small, and it has not fully possessed the main characteristics of modern computer
the new breakthrough was completed by a design team led by mathematician von Neumann. In March 1945, they published a new general electronic computer scheme of stored program - electronic discrete variable automatic computer (EDVAC). Then in June 1946, von Neumann and others put forward a more perfect design report "preliminary study on the logical structure of electronic computer devices". From July to August of the same year, they taught a special course "theory and technology of electronic computer design" for experts from more than 20 institutions in the United States and Britain at Moore college, which promoted the design and manufacture of stored program computers< In 1949, the Mathematics Laboratory of Cambridge University in England took the lead in making EDSAC; The United States made the eastern standard automatic computer (SFAC) in 1950. At this point, the embryonic period of the development of electronic computer came to an end, and the development period of modern computer began
at the same time of creating digital computer, we also developed another kind of important computing tool analog computer. When physicists summarize the laws of nature, they often use mathematical equations to describe a process; On the contrary, the process of solving mathematical equations may also adopt the physical process simulation method. After the invention of logarithm, the slide rule made in 1620 has changed multiplication and division into addition and subtraction for calculation. Maxwell skillfully transformed the calculation of integral (area) into the measurement of length, and made the integrator in 1855< Fourier analysis, another great achievement of mathematical physics in the 19th century, played a direct role in promoting the development of simulators. In the late 19th century and the early 20th century, a variety of analytical machines for calculating Fourier coefficients and differential equations were developed. However, when trying to popularize the differential analysis machine to solve partial differential equations and use the simulator to solve general scientific calculation problems, people graally realize the limitations of the simulator in the aspects of universality and accuracy, and turn their main energy to the digital computer
after the advent of electronic digital computer, analog computer still continues to develop, and hybrid computer is proced by combining with digital computer. Simulators and mixers have become special varieties of modern computers, that is, efficient information processing tools or simulation tools used in specific fields
since the middle of the 20th century, the computer has been in a period of high-speed development. The computer has developed from a hardware only system to a computer system which includes three subsystems: hardware, software and firmware. The performance price ratio of computer system is increased by two orders of magnitude every 10 years. The types of computers have been divided into microcomputers, minicomputers, general-purpose computers (including giant, large and medium-sized computers), and various special computers (such as various control computers and analog-to-digital hybrid computers)
computer devices, from electron tubes to transistors, from discrete components to integrated circuits to microprocessors, have made three leaps in the development of computers< In the period of electron tube computer (1946-1959), computers were mainly used for scientific calculation. Main memory is the main factor that determines the appearance of computer technology. At that time, the main memory included mercury delay line memory, cathode ray oscilloscope electrostatic memory, magnetic drum and magnetic core memory, which were usually used to classify computers.
the birth and development of modern computer before the advent of modern computer, the development of computer has gone through three stages: mechanical computer, electromechanical computer and electronic computer
as early as the 17th century, a group of European mathematicians began to design and manufacture digital computers that perform basic operations in digital form. In 1642, Pascal, a French mathematician, made the earliest decimal adder by using a gear transmission similar to clocks and watches. In 1678, Leibniz, a German mathematician, developed a computer to further solve the multiplication and division of decimal numbers
British mathematician Babbage put forward an idea when he made the model of difference machine in 1822. One arithmetic operation at a time will develop into a certain complete operation process automatically. In 1884, Babbage designed a program-controlled universal analyzer. Although this analyzer has described the rudiment of the program control computer, it can not be realized e to the technical conditions at that time< During the more than 100 years since Babbage's idea was put forward, great progress has been made in electromagnetics, electrotechnics and electronics, and vacuum diodes and vacuum triodes have been successively invented in components and devices; In terms of system technology, wireless telegraph, television and radar were invented one after another. All these achievements have prepared technical and material conditions for the development of modern computer< At the same time, mathematics and physics are developing rapidly. In the 1930s, all fields of physics experienced the stage of quantification. The mathematical equations describing various physical processes, some of which were difficult to solve by classical analysis methods. As a result, numerical analysis has been paid attention to, and various numerical integration, numerical differentiation, and numerical solutions of differential equations have been developed. The calculation process has been reced to a huge amount of basic operations, thus laying the foundation of modern computer numerical algorithm
the urgent need for advanced computing tools in society is the fundamental driving force for the birth of modern computers. Since the 20th century, there have been a lot of computational difficulties in various fields of science and technology, which has hindered the further development of the discipline. Especially before and after the outbreak of the Second World War, the need for high-speed computing tools in military science and technology is particularly urgent. During this period, Germany, the United States and the United Kingdom started the research of electromechanical computer and electronic computer almost at the same time<
Giuseppe in Germany was the first to use electrical components to make computers. The fully automatic relay computer Z-3, which he made in 1941, has the characteristics of modern computer, such as floating-point counting, binary operation, instruction form of digital storage address and so on. In the United States, the relay computers mark-1, mark-2, model-1, model-5 and so on were made successively from 1940 to 1947. However, the switching speed of the relay is about one hundredth of a second, which greatly limits the computing speed of the computer
the development process of electronic computer has experienced the evolution from making components to whole machine, from special machine to general machine, from "external program" to "stored program". In 1938, the Bulgarian American scholar atanasov first made the computing unit of the electronic computer. In 1943, the communications office of the British Foreign Office made the "giant" computer. This is a special cryptanalysis machine, which was used in the Second World War< In February 1946, ENIAC, a large-scale electronic digital integrator computer, was developed by Moore College of the University of Pennsylvania in the United States. At first, ENIAC was also specially used for artillery trajectory calculation. Later, it was improved many times and became a general-purpose computer capable of various scientific calculations. This computer, which uses electronic circuit to perform arithmetic operation, logic operation and information storage, is 1000 times faster than relay computer. This is the first electronic computer in the world. However, the program of this kind of computer is still external, the storage capacity is too small, and it has not fully possessed the main characteristics of modern computer
the new breakthrough was completed by a design team led by mathematician von Neumann. In March 1945, they published a new general electronic computer scheme of stored program - electronic discrete variable automatic computer (EDVAC). Then in June 1946, von Neumann and others put forward a more perfect design report "preliminary study on the logical structure of electronic computer devices". From July to August of the same year, they taught a special course "theory and technology of electronic computer design" for experts from more than 20 institutions in the United States and Britain at Moore college, which promoted the design and manufacture of stored program computers< In 1949, the Mathematics Laboratory of Cambridge University in England took the lead in making EDSAC; The United States made the eastern standard automatic computer (SFAC) in 1950. At this point, the embryonic period of the development of electronic computer came to an end, and the development period of modern computer began
at the same time of creating digital computer, we also developed another kind of important computing tool analog computer. When physicists summarize the laws of nature, they often use mathematical equations to describe a process; On the contrary, the process of solving mathematical equations may also adopt the physical process simulation method. After the invention of logarithm, the slide rule made in 1620 has changed multiplication and division into addition and subtraction for calculation. Maxwell skillfully transformed the calculation of integral (area) into the measurement of length, and made the integrator in 1855< Fourier analysis, another great achievement of mathematical physics in the 19th century, played a direct role in promoting the development of simulators. In the late 19th century and the early 20th century, a variety of analytical machines for calculating Fourier coefficients and differential equations were developed. However, when trying to popularize the differential analysis machine to solve partial differential equations and use the simulator to solve general scientific calculation problems, people graally realize the limitations of the simulator in the aspects of universality and accuracy, and turn their main energy to the digital computer
after the advent of electronic digital computer, analog computer still continues to develop, and hybrid computer is proced by combining with digital computer. Simulators and mixers have become special varieties of modern computers, that is, efficient information processing tools or simulation tools used in specific fields
since the middle of the 20th century, the computer has been in a period of high-speed development. The computer has developed from a hardware only system to a computer system which includes three subsystems: hardware, software and firmware. The performance price ratio of computer system is increased by two orders of magnitude every 10 years. The types of computers have been divided into microcomputers, minicomputers, general-purpose computers (including giant, large and medium-sized computers), and various special computers (such as various control computers and analog-to-digital hybrid computers)
computer devices, from electron tubes to transistors, from discrete components to integrated circuits to microprocessors, have made three leaps in the development of computers< In the period of electron tube computer (1946-1959), computers were mainly used for scientific calculation. Main memory is the main factor that determines the appearance of computer technology. At that time, the main memory included mercury delay line memory, cathode ray oscilloscope electrostatic memory, magnetic drum and magnetic core memory, which were usually used to classify computers.
3.
At the end of 2017, digital currency experienced explosive growth and Waterloo like decline in 2018, and now it tends to be stable. During this period, a large number of investors poured into the currency circle, and all kinds of digital currencies need to be bought and sold through exchanges or digital currency wallets. However, in 2018, there were frequent incidents of exchange digital currency theft, so more and more traders chose to store digital assets in digital currency wallets, Sort out the five most well-known digital currency wallets and let's get to know them
Bitpai (score: 8.5)
bitpai is a comprehensive blockchain asset service proct based on HD wallet. Its main functions include: sending and receiving, buying and selling, accelerating transaction, etc. The user controls the private key, and the coin after the transaction is completed is directly kept by the user. At present, the currencies it supports mainly include BTC, BTC, ETH, some erc2.0 tokens, qtum, HSR, dash, safe, LTC, LCH, Zec, etc and Doge
advantages: the balance of the current digital currency can be displayed at the top of the front page of the wallet, and the upper left corner can be switched to other digital currencies, and the currency balance can also be switched from quantity to legal currency value. There are many functions in the middle, such as issuing currency, receiving currency, one click trading, etc. the broadcast of each transfer transaction is displayed below, and the completed transaction can also be queried in the transaction record. After leaving the bitpai app interface for a period of time, you need to unlock it when you re-enter, which improves the security of the wallet
deficiency: Only Mainstream currencies are supported, other small currencies are not supported, and the number of currencies is 10 +. The page setting is not user-friendly, and various parameters make it difficult for users to use. In addition, the security is worrying: Recently, there is a problem with bitpai IOS version, and the application can't be opened, and the official said: if you unload it carelessly, the assets in your wallet may not be recovered! It's still in Apple communication
download address: bitpie.com
2. Geek wallet (rating: 8.2)
geek wallet is a simple and convenient light wallet, which supports the storage and management of mainstream digital currency assets such as bitcoin (BTC), lightcoin (LTC), Ethereum (ETH), EOS, usdt, etc
advantages: high security factor, using local private key security mechanism, as well as mobile phone and computer al backup strategy, supporting the current mainstream currency, the platform has a jump market, which can carry out token trading of physical assets on the chain
deficiency: usdt transaction must use 0.0001 BTC as transaction handling fee, does not support some small currencies, page optimization is good, but the function is less
download address: www.geekwallet.org 、 www.geekwallet.cn
3. Imtoken (score: 8)
imtoken is a mobile light wallet app, which supports Eth and Ethereum erc2.0 standard tokens (such as EOS, DGD, SNT, qtum), and is a necessary wallet for Ethereum series of digital currencies
advantages: as a light wallet of Ethereum series, mtoken supports all the tokens of Ethereum erc2.0 standard, can control the miner's fee of each coin, can set the amount of collection, and has convenient transaction record query, refreshing interface, simple operation, so it is suitable for ICO investors who need to receive a variety of erc2.0 standard tokens and do not trade frequently
The "discovery" mole of wallet is not intuitive enough. 2. The tokens that can only be stored on the Ethereum platform, such as BTC and Neo, can't be stored. At the same time, the bifurcations of bitcoin can't be storeddownload address: token. Im
4. Kcash (score: 7.8)
kcash is also a light wallet, which currently supports BTC, ETH, LTC, etc, act and digital currency based on Ethereum and achain smart contract platform. Kcash has cross chain and cross contract technology, and the supported currencies are still increasing
advantages: as a Multi Chain Wallet, kcash supports multiple types of digital currencies and is very friendly to users who invest in multiple series of digital currencies. In addition, kcash also has the function of sending red packets, and in the future, it will launch currency transaction, bank card connection and other functions
deficiency: too many features lead to poor usability. In addition, there are some problems with the compatibility of Android versions. Some Android models will flash back when they open the app
download address: kcash.com
5. Cobo (rating: 7.8)
Cobo is a professional digital asset management wallet, which can help you store assets safely, and the unique POS gain can help you increase the value of assets. It supports more than 20 kinds of digital assets including eth, EOS, TRX, and more than 500 kinds of tokens
advantages: Cobo security is in the lead in the same level, using multiple security verification, hot and cold separation storage, HSM multi signature, Cobo provides you with stable income through intelligent voting, dpos vote pool, POS mining digital asset gain matrix
deficiency: the page optimization is poor, the function is complex, it's a little difficult to get started, and there is also a flash back problem of Android version
download address: cobo.com
4. The research of this problem should be based on experiments. You can find some people to do experiments, let one group calculate the same problem with pen, and the other group calculate the same problem with calculator. Look at the speed results of the two, calculate more problems, and find more people to expand the sample size and increase the reliability of the test results
intuitively, it seems that using a calculator is bound to improve the user's computing ability, but in fact, the result is not certain. I remember that when I was in the second grade of junior high school, I competed with my classmates for a series of continuous calculations. I used a pen and they used a calculator to see who would finish the calculation first. As a result, I finished the calculation first, but my classmates pressed the wrong number keys on the calculator many times, And the calculator display is not intuitive enough, leading to repeated rework, but slower than my calculation. It can be seen that whether a calculator can improve a person's computing ability is related to the accuracy and speed of key pressing of the calculator, the contrast between them and the user's written calculation ability, and the complexity of the problem itself
Senior Two students should have learned the least square method. You can establish the corresponding regression line for research, such as establishing the regression relationship between a person's computing speed and his proficiency in using the calculator. Of course, the specific research steps still need to be designed by yourself.
intuitively, it seems that using a calculator is bound to improve the user's computing ability, but in fact, the result is not certain. I remember that when I was in the second grade of junior high school, I competed with my classmates for a series of continuous calculations. I used a pen and they used a calculator to see who would finish the calculation first. As a result, I finished the calculation first, but my classmates pressed the wrong number keys on the calculator many times, And the calculator display is not intuitive enough, leading to repeated rework, but slower than my calculation. It can be seen that whether a calculator can improve a person's computing ability is related to the accuracy and speed of key pressing of the calculator, the contrast between them and the user's written calculation ability, and the complexity of the problem itself
Senior Two students should have learned the least square method. You can establish the corresponding regression line for research, such as establishing the regression relationship between a person's computing speed and his proficiency in using the calculator. Of course, the specific research steps still need to be designed by yourself.
5. No, the larger the hard disk, the more data it stores
the stronger the computing power of CPU, the stronger the computing power.
the stronger the computing power of CPU, the stronger the computing power.
6. 1、 Symbol is the language of mathematics. It is a tool for people to express, calculate, reason, communicate and solve problems“ The sense of symbol is mainly manifested in the following aspects: it can abstract the quantitative relationship and the law of change from the specific situation, and express them with symbols; Understanding the quantitative relationship and change law of symbols can transform the symbols; Be able to choose appropriate proceres and methods to solve problems expressed by symbols. " 1. No matter in which period, students should be encouraged to express the quantitative relationship and change law in specific situations in their own unique way, which is the decisive factor in the development of students' sense of symbol“ The development of "symbolic sense" needs a solid foundation of experience. We should promote students to share their rich experience in the process of communication and sharing, learn various ways of symbolization, and graally realize the advantages of symbolizing practical problems with numbers and shapes. 2、 The introction of letter representation is an important step in learning mathematical symbols and learning to use symbols to express the implied quantitative relationship and change law in specific situations. It's an important step in learning mathematical symbols to use letters to represent numbers starting from the second paragraph. It should be introced from practical problems as far as possible, so that students can feel the meaning of letters. First, use letters to express the operation rules, operation laws and calculation formulas. This generalization is algorithmic and often begins with the logarithm in arithmetic. The generalization of the algorithm deepens and develops the understanding of logarithm. Second, letters are used to represent various quantitative relationships in the real world and various disciplines. For example, the relationship between velocity V, time t and distance s in uniform motion is s = vt. Thirdly, using letters to express numbers is convenient for abstracting quantitative relations and changing rules from specific situations and expressing them accurately, which is concive to further solving problems with mathematical knowledge. For example, we use letters to represent the unknowns in practical problems, and use the equality relations in the problems to list the equations. For the "standard" said that "can abstract the quantitative relationship and change law from the specific situation, and use symbols to express" should be understood from the following aspects. First, this kind of representation usually starts from the exploration and discovery of laws and inctive reasoning, and then expresses them in algebraic form. Second, the relationship or law expressed by letters is usually used to calculate (or predict) an unknown or difficult to intuitively obtain value. Thirdly, the relationship or law expressed in letters can also be used to judge or prove a certain conclusion. Using algebraic expression is a process from special to general, and evaluating by algebraic expression and using mathematical formula is a process from general to special, so that students can further understand the significance of letter expressing number. In addition, letters and expressions have different meanings in different situations. For example: 5 = 2x + 1 represents a condition that x satisfies. In fact, X only occupies a special number, so its value can be found by solving the equation; Y = 2x denotes the relationship between variables, X is an independent variable and can take any number in the domain, y is a dependent variable and Y changes with the transformation of X A + b) (a-b) = A-B represents a generalized algorithm and an identity; If a and B represent the length and width of the rectangle respectively, and s represents the area of the rectangle, then s = AB represents the formula for calculating the area of the rectangle, and also represents that the area of the rectangle varies with the length and width. 1、 Symbol is the language of mathematics. It is a tool for people to express, calculate, reason, communicate and solve problems. 3、 Understand the quantitative relationship and change law represented by symbols. First, enable students to understand the meaning of symbols and explain the meaning of algebraic expressions in real situations. Second, the relationship between variables is represented by relation, table and image. Thirdly, it can obtain the required information from the relationships among variables represented by relational expressions, tables and images. 4、 There is a conversion between symbols. Here, the transformation between symbols mainly refers to the transformation between tabular method, relational method, image method and language representation. From the perspective of mathematical psychology, different forms of thinking, their transformation and expression are the core of mathematical learning. 5、 Be able to choose appropriate proceres and methods to solve problems expressed by symbols. The first step to solve the problem is to use symbols to represent the problem, that is, to symbolize it. The second step is to select the algorithm for symbol operation. For example, we express a practical problem as a quadratic equation of one variable, and then according to the equation, we choose the formula method to solve it. It's also important to do symbolic operations. 6、 To cultivate students' sense of symbols, we should help students understand symbols, expressions and relational meanings in practical problem situations, and develop students' sense of symbols in solving practical problems. In the teaching of symbolic calculus, we should try our best to avoid the students' mechanical practice and memory, and should increase the actual background, exploration process, geometric explanation, etc. to help students understand According to the standard, it is necessary to train the symbolic operations and carry out a certain number of symbolic operations properly and in stages. However, it is not advocated to carry out complicated formal operation training. The development of students' sense of symbol can not be completed overnight, but should run through the whole process of mathematics learning, and graally develop with the improvement of students' mathematical thinking.
7. Of course not, the calculation ability tests your whole understanding of the problem, and the calculation ability is the process ability to solve the problem
8. To a large extent, the inaccuracy of understanding and memorizing concepts, formulas and rules is e to the lack of deep understanding of basic concepts, the lack of thorough grasp of basic formulas and rules, and the lack of proficiency in their application. In teaching, it is essential for students to firmly grasp the concepts, properties, formulas, rules and theorems needed by operation. We should focus on improving students' memory ability, teach them memory methods, and firmly grasp some commonly used data, formulas and rules. We should go through the process from concrete to abstract, from perceptual to rational, naturally form concepts, derive formulas and rules, pay attention to the lack of knowledge reflected in students' operations, and do not simply attribute the causes of solving problems to carelessness, or methods and skills. Only by mastering the relevant knowledge, can we make the direction of operation clear and provide reliable basis for operation, which is the premise of correct operation. Therefore, it is essential for students to learn the basic knowledge of operation< Second, we should strengthen the teaching of the occurrence, development and formation of formulas and theorems. Ignoring the preconditions of formulas and theorems and abusing formulas and theorems are the main reasons for students' low computational ability. There are many factors, but they are not comprehensive enough, or the methods are not right, and they are not in harmony with students' cognitive rules, It has a lot to do with it. Therefore, we should make great efforts in designing problems and organizing contents, let students experience the occurrence, development and formation process of knowledge, make dead knowledge alive, follow students' cognitive rules, and deepen students' knowledge and understanding of knowledge, instead of cramming, so that they will not take out of context. The focus of classroom teaching is not only on the main body of formulas and theorems, but also on the error prone areas such as the conditions of formulas and theorems and special situations< In high school, many mathematical knowledge often use simple numerical operation, but numerical operation is just the weakness of high school students. In fact, as long as our teachers can give proper guidance, flexibly use formulas and draw inferences from one instance, we can improve students' computing ability. In order to enable students to master the correct algorithm, teachers should often infiltrate modern mathematical thinking methods, and carry out some contrast exercises on students' easily confused problems. Encourage students to dare to innovate, strengthen the training of "one problem with multiple solutions" and "simple algorithm". In order to improve students' computing ability, it is necessary for them to master the theory and algorithm. Only by making clear the characteristics, methods and influencing factors of calculation, can they improve their computing ability better. Algorithm research helps to simplify the thinking process, get effective problem-solving strategies, strengthen practice, use various forms, and make students form skills
1. Intensive training, practice makes perfect
an important way to improve the speed of operation is to practice diligently, often and repeatedly. Only through certain intensive training, can students achieve the goal of "practice makes perfect". Therefore, we should carefully organize the training, whether in class or out of class, in addition to the requirements of quantity and quality, we should also have certain requirements for the speed of problem solving. In the classroom, we should arrange some limited time operation training and more hierarchical and targeted problem group training, so that different types of students can complete the appropriate training tasks in a certain period of time, so as to improve the efficiency of classroom teaching and improve the rate of reaching the standard in class< It is not enough to grasp the general rules of mathematical operation, but also to form skilled skills. Without the formation of skilled skills, it is impossible to complete the operation simply and quickly. Therefore, we should consciously discover and summarize some skills and techniques through operation practice. Such as "substitution method", "combination of number and shape", "1" transformation and the choice of coordinate system in analytic geometry, etc. In addition, the following points should be achieved:
first, master the general principles of operation. The general rule of general method is not only beneficial to the operation orientation, but also to improve the speed of operation. Therefore, we should master the transformation of basic number form and form some basic skills. For example, the multiplication formula is used to simplify the number calculation; The root of square is obtained by decomposing the quality factor; Using the rational method of denominator to find the value of root formula. In order to cultivate students' correct and rapid computing ability, it is very necessary for them to master certain skills
Second, be familiar with some methods and skills of mental calculation and quick calculation. Mental arithmetic is a form of calculation. It is a kind of calculation without writing. It is a sign of "familiarity" and can strengthen students' thinking inspiration. In teaching, whether it is to find solutions to problems, or to carry out the operation process, we should strengthen the training of mental calculation, and teach some methods of quick calculation, which is a very effective way to improve the operation speed
thirdly, memorize some common data and important conclusions. Such as the square number of one or two digits, trigonometric function value of special angle, some common mathematical propositions, etc. So as to expand the capacity of knowledge, increase the span of thinking, improve the agility of thinking
3. Tempering thinking and fast operation
infiltrating thinking training into operation training is an effective measure to improve operation speed. Because good thinking quality is a powerful guarantee to improve the computing ability. In teaching, we need to strengthen the training of mathematical methods and thinking methods, such as mastering some common mathematical methods: collocation method, substitution method, undetermined coefficient method, mathematical inction method, parameter method, elimination method, etc; Familiar with some common mathematical logic methods: analysis, synthesis, reverse, inction, dection, etc; Master the common mathematical thinking methods: observation and analysis, generalization and abstraction, analysis and synthesis, special and general, analogy, inction and dection, etc; Master common mathematical ideas: function and equation, combination of number and shape, classified discussion, transformation, etc. It is necessary to strengthen the thinking training of students in reverse, divergence, entirety, structure and intuition, so as to provide guarantee for finding a simple and fast way of operation from the aspects of thinking method, problem-solving ideas and problem-solving strategies< The teachers in vocational schools agree that the students in vocational schools are not solid in their junior middle school learning, and they do not have a firm grasp of basic knowledge and methods. They should keep some fixed knowledge and methods in mind and ask them to use them to solve problems. It is true that the fixed way of thinking has a positive side in operation, but it also has a negative impact. When students master a certain kind of knowledge (method), they often use conventional methods to solve problems when they encounter problems. In this way, they will inevitably have the inertia of thinking and lack the consciousness of thinking from multiple directions and angles, which is not concive to the improvement of students' operation speed. What's more, students in vocational schools are active in thinking and just want to find a simpler and faster method of calculation so that they can have more time to do other things. Therefore, the fixed way of thinking will affect the speed of students' operation, make the operation process cumbersome, and thus cause students' aversion to mathematics learning. In my teaching, I often guide students to think about problems from various aspects and angles, and strive to cultivate their observation ability, association ability and comparative consciousness, so as to seek the best way to solve problems< It can not exist alone without specific mathematical knowledge, nor can it develop independently without other abilities. It permeates with memory ability, observation ability, understanding ability, association ability and expression ability, and supports each other with mathematical abilities such as logical thinking ability. Therefore, the problem of improving computing power is a comprehensive problem. In the process of teaching, only when we often summarize the rules, constantly guide and graally accumulate, can we really improve the computing ability< It is an important factor to cultivate students' good study habits. Because of its strict characteristics, mathematics does not allow students to be careless and careless. Students' mistakes in calculation are partly caused by their bad study habits. In teaching, teachers should let students form the good habits of careful examination, careful observation and writing standard before doing questions. In the process of learning mathematics, students can be asked not to rely on calculators when they encounter simple calculation problems, so that they can form the judgment of the calculation results in mental calculation, oral calculation and written calculation. Good calculation habit is the guarantee of improving calculation ability. In calculation, students are required to do one look, two think, three calculate and four check. A look: before doing a question, first look at the question completely, see each number and each operation symbol, and make a preliminary perception. Second, on the basis of clearly understanding the topic, we should make clear the relationship between the characteristics of the clearing form and each operation, choose a reasonable method according to the specific situation, and determine the operation steps. Third calculation: after determining the operation steps and methods, calculate carefully. Four checks: we should "look back" in time to check whether the algorithm is reasonable, whether the operation symbol is copied wrong, whether the minus sign is missed, and whether the calculation result is wrong
be patient in calculation, and never give up until you finish a problem. Students are required to write carefully, because only when they write carefully can they concentrate their attention, so the accuracy of calculation is improved. Over time, students will be able to develop good calculation habits< In a word, China's mathematics ecation has a tradition of paying attention to the training of basic knowledge, basic skills and ability training, which should be carried forward in senior high school mathematics curriculum in the new century. Teaching practice shows that it is a complex system engineering and a long-term task to improve students' computing ability. As long as we cherish every training opportunity, carry out long-term infiltration in a planned, targeted and conscious way, and enable students to graally understand the essence of operation ability, it will inevitably promote students to develop the habit of correct, reasonable and fast operation, and finally achieve the purpose of improving students' operation ability.
1. Intensive training, practice makes perfect
an important way to improve the speed of operation is to practice diligently, often and repeatedly. Only through certain intensive training, can students achieve the goal of "practice makes perfect". Therefore, we should carefully organize the training, whether in class or out of class, in addition to the requirements of quantity and quality, we should also have certain requirements for the speed of problem solving. In the classroom, we should arrange some limited time operation training and more hierarchical and targeted problem group training, so that different types of students can complete the appropriate training tasks in a certain period of time, so as to improve the efficiency of classroom teaching and improve the rate of reaching the standard in class< It is not enough to grasp the general rules of mathematical operation, but also to form skilled skills. Without the formation of skilled skills, it is impossible to complete the operation simply and quickly. Therefore, we should consciously discover and summarize some skills and techniques through operation practice. Such as "substitution method", "combination of number and shape", "1" transformation and the choice of coordinate system in analytic geometry, etc. In addition, the following points should be achieved:
first, master the general principles of operation. The general rule of general method is not only beneficial to the operation orientation, but also to improve the speed of operation. Therefore, we should master the transformation of basic number form and form some basic skills. For example, the multiplication formula is used to simplify the number calculation; The root of square is obtained by decomposing the quality factor; Using the rational method of denominator to find the value of root formula. In order to cultivate students' correct and rapid computing ability, it is very necessary for them to master certain skills
Second, be familiar with some methods and skills of mental calculation and quick calculation. Mental arithmetic is a form of calculation. It is a kind of calculation without writing. It is a sign of "familiarity" and can strengthen students' thinking inspiration. In teaching, whether it is to find solutions to problems, or to carry out the operation process, we should strengthen the training of mental calculation, and teach some methods of quick calculation, which is a very effective way to improve the operation speed
thirdly, memorize some common data and important conclusions. Such as the square number of one or two digits, trigonometric function value of special angle, some common mathematical propositions, etc. So as to expand the capacity of knowledge, increase the span of thinking, improve the agility of thinking
3. Tempering thinking and fast operation
infiltrating thinking training into operation training is an effective measure to improve operation speed. Because good thinking quality is a powerful guarantee to improve the computing ability. In teaching, we need to strengthen the training of mathematical methods and thinking methods, such as mastering some common mathematical methods: collocation method, substitution method, undetermined coefficient method, mathematical inction method, parameter method, elimination method, etc; Familiar with some common mathematical logic methods: analysis, synthesis, reverse, inction, dection, etc; Master the common mathematical thinking methods: observation and analysis, generalization and abstraction, analysis and synthesis, special and general, analogy, inction and dection, etc; Master common mathematical ideas: function and equation, combination of number and shape, classified discussion, transformation, etc. It is necessary to strengthen the thinking training of students in reverse, divergence, entirety, structure and intuition, so as to provide guarantee for finding a simple and fast way of operation from the aspects of thinking method, problem-solving ideas and problem-solving strategies< The teachers in vocational schools agree that the students in vocational schools are not solid in their junior middle school learning, and they do not have a firm grasp of basic knowledge and methods. They should keep some fixed knowledge and methods in mind and ask them to use them to solve problems. It is true that the fixed way of thinking has a positive side in operation, but it also has a negative impact. When students master a certain kind of knowledge (method), they often use conventional methods to solve problems when they encounter problems. In this way, they will inevitably have the inertia of thinking and lack the consciousness of thinking from multiple directions and angles, which is not concive to the improvement of students' operation speed. What's more, students in vocational schools are active in thinking and just want to find a simpler and faster method of calculation so that they can have more time to do other things. Therefore, the fixed way of thinking will affect the speed of students' operation, make the operation process cumbersome, and thus cause students' aversion to mathematics learning. In my teaching, I often guide students to think about problems from various aspects and angles, and strive to cultivate their observation ability, association ability and comparative consciousness, so as to seek the best way to solve problems< It can not exist alone without specific mathematical knowledge, nor can it develop independently without other abilities. It permeates with memory ability, observation ability, understanding ability, association ability and expression ability, and supports each other with mathematical abilities such as logical thinking ability. Therefore, the problem of improving computing power is a comprehensive problem. In the process of teaching, only when we often summarize the rules, constantly guide and graally accumulate, can we really improve the computing ability< It is an important factor to cultivate students' good study habits. Because of its strict characteristics, mathematics does not allow students to be careless and careless. Students' mistakes in calculation are partly caused by their bad study habits. In teaching, teachers should let students form the good habits of careful examination, careful observation and writing standard before doing questions. In the process of learning mathematics, students can be asked not to rely on calculators when they encounter simple calculation problems, so that they can form the judgment of the calculation results in mental calculation, oral calculation and written calculation. Good calculation habit is the guarantee of improving calculation ability. In calculation, students are required to do one look, two think, three calculate and four check. A look: before doing a question, first look at the question completely, see each number and each operation symbol, and make a preliminary perception. Second, on the basis of clearly understanding the topic, we should make clear the relationship between the characteristics of the clearing form and each operation, choose a reasonable method according to the specific situation, and determine the operation steps. Third calculation: after determining the operation steps and methods, calculate carefully. Four checks: we should "look back" in time to check whether the algorithm is reasonable, whether the operation symbol is copied wrong, whether the minus sign is missed, and whether the calculation result is wrong
be patient in calculation, and never give up until you finish a problem. Students are required to write carefully, because only when they write carefully can they concentrate their attention, so the accuracy of calculation is improved. Over time, students will be able to develop good calculation habits< In a word, China's mathematics ecation has a tradition of paying attention to the training of basic knowledge, basic skills and ability training, which should be carried forward in senior high school mathematics curriculum in the new century. Teaching practice shows that it is a complex system engineering and a long-term task to improve students' computing ability. As long as we cherish every training opportunity, carry out long-term infiltration in a planned, targeted and conscious way, and enable students to graally understand the essence of operation ability, it will inevitably promote students to develop the habit of correct, reasonable and fast operation, and finally achieve the purpose of improving students' operation ability.
9. First of all, we need to find out the cause of the calculation error, whether the operation method is not grasped or the careless operation is wrong
secondly, to avoid making the same mistakes next time, you can do more exercises, strengthen training, or read more wrong questions
finally, you can check it after you finish, and correct any mistakes.
secondly, to avoid making the same mistakes next time, you can do more exercises, strengthen training, or read more wrong questions
finally, you can check it after you finish, and correct any mistakes.
10. Shame. It is also conditional to calculate work after calculating force. After that, this work has a lot to do with energy. Energy consumption. The relationship among force, work and energy: 1. The relationship between work and energy (1) work is a measure of energy transformation, that is, how much work is done must be accompanied by how much energy is transformed; On the contrary, how much energy is transformed must be done at the same time 2) All kinds of forms of energy can be transformed into each other under certain conditions, and the total energy is conserved in the process of transformation, which conforms to the law of energy transformation and conservation. Its specific meaning can be understood as: ① the decrease of one form of energy must be equal to the increase of other forms of energy. ② The energy rection of one object (or part of an object) must be equal to the energy increase of other objects (or other parts of an object). 2. The characteristics of friction work: (1) the characteristics of static friction work: (1) static friction can do positive work, negative work and no work. ② In the process of work done by static friction, there is only mutual transfer of mechanical energy (static friction plays the role of transferring mechanical energy), but no mechanical energy is transformed into other forms of energy. ③ In a system of mutual friction, the total work done by a pair of static friction forces is equal to zero 2) The characteristics of work done by sliding friction are as follows: (1) sliding friction can do positive work, negative work and no work on objects. (for example, when wood blocks move on a fixed table, the sliding friction on the table does not work on the table.). ② In the process of work done by sliding friction, there are two kinds of energy changes: one is the transfer of part of mechanical energy between the friction objects; Second, a part of mechanical energy is transformed into internal energy. ③ The total work (or net work) of a pair of sliding friction forces on the system is always negative, and its absolute value is equal to the proct of sliding friction force and relative displacement (independent of the selection of reference object, in which the work of a certain friction force is related to the selection of reference object), which is just equal to the mechanical energy lost by the system. This part of mechanical energy is converted into the internal energy of the system, that is, FS phase = Q.
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