introduce
Chapter 1 Functions and limitations
1. 1 function
1. Constant and variable 2. Functional concept 3. Example 4 of establishing a functional relationship. basic elementary function
The limit of 1.2 function
1. Definition of function limit 2. Four algorithms of limit 3. Two criteria for the existence of limit and two important limits 4. Infinitesimal quantity and its comparison.
Continuity of 1.3 function
1. Definition of continuity of function 2. Properties of continuous functions on closed interval 3. Finding the root of cubic equation by dichotomy.
Chapter 2 Differential calculus of univariate function
2. 1 the concept of wechat business
1. A few examples 2. The concept of wechat business 3. Geometric significance of wechat service iv. Wechat service with several basic primary functions.
2.2 WeChat business algorithm and formula
1. Four algorithms of WeChat business II. The compound function law of wechat business iii. Exponential function and power function law of wechat business 4. Implicit function and anti-trigonometric function law of wechat business.
2.3 rate of change
2.4 higher derivative
2.5 Application of WeChat service
1. Differential mean value theorem 2. Monotonicity of function 3. Maximum (minimum) value and maximum (minimum) value of function 4. functional diagram
2.6 differences
1. The concept of differential 2. The operation of differentiation and its basic formula and rule III. The application of differentiation.
Chapter III Integral calculus
3. The concept and simple properties of1indefinite integral
3. 1 substitution integration method
1. Alternative method 2 of the first category. The second kind of substitution method.
3.3 parts integration
3.4 Integral of Rational Fraction
1. Indefinite integral of several simple fractions 2? Partial fraction method of true fraction
3.5 Use of Integral Table
3.6 Definition, properties and calculation method of definite integral
1. The concept of definite integral 2. Properties of definite integral 3. Calculation of definite integral 4. Approximate calculation of definite integral.
3.7 Application of definite integral
1. Plane area Figure 2. The volume of the rotating body 3. The solid volume of the parallel cross-sectional area 4 is known. Arc length 5. Op 6. Calculation of flow 7. The average value of the function.
3.8 generalized integral
Integral of continuous function on 1. infinite interval 2. Integral of unbounded function
Chapter IV Ordinary Differential Equations
4. 1 Basic concepts
4.2 First order differential equation
1. Differential equation of separable variables 2. linear first-order differential equation
4.3 Second Order Linear Homogeneous Equation with Constant Coefficients
4.4 Second-order linear nonhomogeneous equation with constant coefficients
4.5 Application of Differential Equation
1. Application in dynamics II. Application in reversible chemical reaction. Application in electronics.
Chapter V Probability Theory and Mathematical Statistics
Appendix Ⅰ Simple Integral Table
Appendix Ⅱ Plane Analytic Geometry
Appendix Ⅲ Determinants and Linear Equations
Appendix IV Arrangement and Combination
attached table
Second book
catalogue
Chapter VI Infinite Series
6. Several terms of1series
The concept of 1. series and its convergence and divergence II. Necessary condition of series convergence 3. Basic properties of sequence 4. Convergence judgment of positive series 5. Staggered series and its convergence judgment 6. Absolute convergence and conditional convergence.
6.2 Power Series Expansion of Functions
Convergence radius of 1. power series 2. Power series operation
6.3 Power Series Expansion of Functions
1. Taylor series 2. Power series expansion of several elementary functions 3. Euler formula
6.4 Application of Function Power Series Expansion
Approximate calculation of 1. function value 2. Approximate calculation of definite integral iii. Power series solution of differential equation
Chapter 7 Vector Algebra and Spatial Analytic Geometry
7. 1 space rectangular coordinate system
1. Cartesian coordinates of space point 2. The distance between two points in space.
7.2 vector
1. Vector concept 2. Addition and subtraction of vectors and multiplication of vectors 3. Coordinate representation of vector. Multiplication of vectors.
7.3 Plane and space straight line
The equation of 1 .2 plane. Spatial linear equation
7.4 Simple surfaces and spatial curves
1 .quadric surface 2. Spatial curve equation
Chapter 8 Differential calculus of multivariate functions
8. General concept of1multivariate function
1. The concept of multivariate function 2. Concepts of Limit and Continuity of Binary Functions
8.2 Some WeChat services
1. The concept of partial WeChat service 2. Geometric significance of binary function part wechat service 3. High-order partial wechat service.
8.3 Total variance
1. The concepts of total differential and partial differential 2. Application of total differential in approximate calculation and error estimation.
8.4 Composite functions of some WeChat services
1. Chain rule 2. Wechat service or part of WeChat service of implicit function.
8.5 Application of Geometry
The tangent plane and normal plane of 1. space curve 2. Tangent plane and normal plane of surface
8.6 Direction WeChat service and gradient
1. Direction WeChat business 2. gradient
8.7 Extreme value of multivariate function
1. Extreme value 2 of binary function. Conditional extremum-Lagrange multiplier rule
Chapter 9 Integral calculus of multivariate functions
9. The concept and properties of1double integral
1. The concept of double integral 2. Properties of double integral
9.2 Calculation of Double Integral
1. Change the double integral into the second integral. 2. Calculate the double integral with polar coordinates.
9.3 Definition and calculation of triple integral
1. The definition and calculation formula of triple integral 2. Calculate triple integral by using cylindrical coordinates and spherical coordinates.
9.4 Application of Multiple Integrals
1 .surface area 2. Center of gravity 3. rotary inertia
9.5 curve integral
1. The first kind of curve integral 2. The second kind of curve integral 3. The second kind of curve integral has nothing to do with straight lines.
Chapter 10 Preliminary Study on Fourier Series and Partial Differential Equations
10. 1 Fourier series
Fourier expansion of 1. function 2. Complex form of Fourier series
10.2 Fourier integral
10.3 Fourier transform and convolution
1 .fourier transform 2. hover
A preliminary study on the partial differential equation of 10.4
1. Wave Equation 2. Heat conduction equation 3. Laplace equation 4. Schrodinger equation.