ISBN:97873022354 15
Author: Department of Mathematics, Beijing Union University
Pricing: 32 yuan
Release date: 20 10-8- 1
Publishing House: Tsinghua University Publishing House, on the basis of summarizing the experience in the teaching process of 1 version, and focusing on the basic teaching requirements in the latest syllabus, arranges the knowledge points by chapters. The whole book *** 13. Chapter 1~ 12 includes function and limit, derivative and differential, differential mean value theorem and derivative application, indefinite integral, definite integral application, ordinary differential equation, vector algebra and spatial analytic geometry, differential method of multivariate function and its application, multiple integral and so on. Infinite series. Each chapter includes knowledge points, typical examples, self-test questions and answers. Some chapters are followed by the introduction of mathematicians, the history of mathematics and examples of mathematical applications. 13 chapter introduces the problem of learning advanced mathematics with Mathematica. The content of this book is arranged in consideration of the current teaching material order, as well as interest and application.
This book can be used as an exercise book or self-study reference book for undergraduates and students majoring in general engineering economics and management in colleges and universities, and can also be used as a reference for teachers of related courses in colleges and universities. Chapter 65438 +0 Functions and Restrictions
1. 1 function
1. 1. 1
A typical example of 1. 1.2
1.2 limit concept limit operation
1.2. 1 knowledge point
1.2.2 Typical example
1.3 Continuity of infinitesimal comparison function
1.3. 1 knowledge point
1.3.2 Typical example
Self-test 1
History of mathematics
1. Extreme thoughts-importance and development stage
2. Liu Hui and "circumcision"
Chapter II Derivative and Differential
2. The concept and operation of1derivative
2. 1. 1 knowledge points
2. 1.2 Typical example
2.2 Higher derivative and differential
2.2. 1 knowledge points
Typical example
Self-test 2
Mathematical application paradigm
1. Related rate of change problem
2. The application of differentiation in approximate calculation
3. The application of derivatives in economics
Chapter III Differential Mean Value Theorem and Application of Derivative
3. 1 differential mean value theorem lobida rule
3. 1. 1 knowledge points
3. 1.2 Typical example
3.2 Application of Derivatives
3.2. 1 knowledge points
Typical example
Self-test question 3
Introduction to mathematicians
1. Raul
2. Lagrange
3. Cauchy
4. Taylor
5. L'H?pital
catalogue
catalogue
The fourth chapter indefinite integral
4. The concept and properties of1indefinite integral
4. 1. 1 knowledge points
4. 1.2 Typical example
4.2 Substitution integration method for indefinite integral and partial integral
4.2. 1 knowledge points
Typical example.
Self-test question 4
The fifth chapter definite integral
5. The concept, properties and basic calculus formula of1definite integral
5. 1. 1 knowledge points
5. 1.2 Typical example
5.2 method of substitution, integration by parts and improper integral method of definite integral.
5.2. 1 knowledge points
Typical example.
Self-test question 5
Mathematical application paradigm
1. Find the variation from the known variation rate.
2. Application in economics
3. Storage capacity of lubricating oil (application example of improper integral)
Introduction to mathematicians
1. Newton
2.leibniz
History of Mathematics Newton and Leibniz founded calculus.
Chapter VI Application of Definite Integral
6. 1 knowledge points
6.2 Typical examples
Self-test question 6
Functions and problems of continuous variables in mathematical application examples
On the History of Mathematics: Finding Area by Exhaustive Method
Chapter VII Ordinary Differential Equations
7. 1 first order differential equation
7. 1. 1 knowledge points
7. 1.2 Typical example
7.2 Higher order differential equation Second order linear differential equation
7.2. 1 knowledge points
Typical example
Self-test question 7
Preliminary study on differential equation model of mathematical application examples
Pendulum, catenary and Bernoulli brothers in the history of mathematics
Chapter 8 Vector Algebra and Spatial Analytic Geometry
8. 1 vector algebra
8. 1. 1 knowledge points
8. 1.2 Typical example
8.2 Curves and surfaces
8.2. 1 knowledge points
Typical example
8.3 Plane and straight line
8.3. 1 knowledge points
Typical example
Self-test question 8
Introduction to mathematician Descartes
Chapter 9 Differential method of multivariate function and its application
9. The concept of1multivariate function differential method, partial derivative and total differential.
9. 1. 1 knowledge points
9. 1.2 Typical example
9.2 the difference between multivariate composite function and implicit function
9.2. 1 knowledge points
Typical example
9.3 Geometric application, directional derivative and gradient of multivariate function differential calculus,
Extreme value of multivariate function
9.3. 1 knowledge points
Typical example
Self-test question 9
How to determine the deepest part of Taihu Lake through mathematical application examples
Chapter 10 Multiple Integral
10. 1 double integral
10. 1. 1
10. 1.2 Typical example
10.2 triple integral
10.2. 1 knowledge point
10.2.2 typical example
The application of 10.3 multiple integral
10.3. 1 knowledge point
10.3.2 typical example
Self-test questions 10
1 1 chapter curve integral and surface integral
1 1. 1 curve integral
11.1.1knowledge point
1 1. 1.2 typical example
1 1.2 conditions for path-independent curve integration on the plane of green's formula
1 1.2. 1 knowledge point
1 1.2.2 Typical example
1 1.3 surface integral
1 1.3. 1 knowledge point
1 1.3.2 Typical example
Self-test 1 1
Mathematical application paradigm
1. Area change of the island between high tide and low tide
2. Coverage area of communication satellites
Introduction to mathematician Gauss
Chapter 12 Infinite Series
12. 1 constant term series
12. 1. 1 knowledge point
12. 1.2 Typical example
12.2 power series
12.2. 1 knowledge point
12.2.2 typical example
The function 12.3 is expanded into a power series.
12.3. 1 knowledge point
12.3.2 typical example
Self-test questions 12
Mathematical application paradigm
1. Achilles problem
2. Use series to estimate the value of π.
3. Series solution of differential equation
4. Represents a special function
Chapter 13 uses Mathematica to study advanced mathematics problems.
13. 1 getting started
13. 1. 1 Start and exit
13.1.2 Working interface of Mathematica 7.0
Input, output and operation of13.10.3 Mathematica 7.0
Numerical types and mathematical constants in 13. 1.4 system
13. 1.5 built-in function (built-in? Functionally)
13. 1.6 variable
13. 1.7 expression
Call the package before 13. 1.87.0.
Online help system of Mathematica13.1.9
Tips for beginners
Two-dimensional graphic limit of 13.2 function
13.2. 1 user-defined function
13.2.2 2D graphics
13.2.3 limit
13.3 differential calculus of unary function
derivation
13.3.2 Find the minimum value of the function.
13.4 unary function integral calculus
13.4. 1 calculation of integral
13.4.2 Calculation of improper integral
13.4.3 numerical integration
13.5 3D graphics
13.5. 1 3D drawing command
13. 5. 2 3D drawing example
Calculus operation of 13.6 multivariate function
13.6. 1 Find the partial derivative
13.6.2 Total difference found
13.6.3 Multiple Integral
13.7 infinite series
13.7. 1
13.7.2 Expand the function into a power series.
Remove the remaining items.
13.8 ordinary differential equation
13.8. 1 Solve the general solution of differential equation
13.8.2 Solving initial value problems of differential equations
13.8.3 Solving differential equations
Answers and tips to self-test questions