1. 1 function
1. 1. 1 set and interval
1. 1.2 function
1. 1.3 elementary function
Limit of 1.2 sequence
1.2. 1 series
1.2.2 Definition of limit of sequence
1.2.3 Some conclusions about the limit of sequence.
The limit of 1.3 function
1.3. 1 the limit of the function when the independent variable tends to infinity.
1.3.2 the limit of the function when the independent variable tends to a finite value
Properties of 1.3.3 Function Limit
1.4 Infinite and Infinite
1.4. 1 infinitesimal
1.4.2 Infinite quantity
Operational properties of 1.4.3 infinitesimal
Algorithm of 1.5 limit
Two Important Limits of 1.6
1.6. 1 pinch theorem
1.6.2 Important limits:
Convergence criteria of 1.6.3 sequence
1.6.4 Important limits:
1.7 comparison of infinitesimals
Continuity and Discontinuity of 1.8 Function
1.8. 1 continuity of function
Breakpoint of 1.8.2 function
1.8.3 Operation of continuous function
1.8.4 Continuity of elementary functions
Properties of continuous functions on 1.9 closed interval
Summary of this chapter
Review questions 1
Chapter II Derivative and Differential
2. The concept of1derivative
2. Two examples of1.1
2. Definition of1.2 derivative
2. 1.3 derivation example
2. Geometric Significance of1.4 Derivative
2. The relationship between derivability and continuity of1.5 function
2.2 Function Derivation Rules
2.2. Derivation rules of sum, difference, product and quotient of1function
Derivative of inverse function
2.2.3 derivative of composite function
2.2.4 Derivative of elementary function
2.3 higher derivative
2.4 Implicit functions and derivatives of functions determined by parametric equations
2.4. 1 derivative of implicit function
2.4.2 Derivative of the function determined by the parametric equation
2.4.3 Correlation change rate
2.5 differential function and its application
2.5. 1 difference concept
2.5.2 the geometric meaning of differential
Differential operation
2.5.4 Application of Differential in Approximate Calculation
Summary of this chapter
Review question 2
Chapter III Application of Mean Value Theorem and Derivative
3. 1 mean value theorem
3. 1. 1 Rolle Theorem
3. 1.2 Lagrange mean value theorem
3. 1.3 Cauchy mean value theorem
3.2 Laws of L'H?pital
3.3 Monotonicity of Function and Extreme Value of Function
3.3. Monotonicity of1function
Extreme value of function
3.3.3 Maximum and Minimum Problems
3.4 Curve's Concave-convex, Inflexion and Function Drawing
3.4. 1 Curve Bump and Its Judgment Method
functional diagram
3.5 Taylor formula
Taylor formula
3.5.2 McLaughlin Formula of Several Common Functions
3.6 Arc Differential and Curvature
3.6. 1 arc difference
3.6.2 Curvature and its calculation formula
Curvature circle
3.7 Approximate solution of the equation
3.7. 1 dichotomy
tangents method
Summary of this chapter
Review question 3
The fourth chapter indefinite integral
4. The concept and properties of1indefinite integral
4. The concept of1.1indefinite integral
4. Properties of1.2 Indefinite Integral
4. 1.3 basic integral table
4.2 Alternative integration method
4.2. 1 First alternative method
4.2.2 Second alternative method
4.3 parts integration
4.4 Integrals of Two Kinds of Functions
4.4. 1 rational function integral
4.4.2 Integral of rational formula of trigonometric function
4.5 Use of Integral Table
Summary of this chapter
Review question 4
The fifth chapter definite integral and its application
5. The concept of1definite integral
5. 1. 1 Two Practical Problems
5. 1.2 concept of definite integral
5.2 Properties of definite integral
5.3 Basic Calculus Formula
5.3. 1 variable upper bound definite integral
5.3.2 Basic calculus formula
5.4 Substitution integration method for definite integral and partial integral
5.4. 1 definite integral by substitution integral method.
5.4.2 Partial integration of definite integral
5.5 Approximate calculation of definite integral
5.5. 1 rectangle method
keystoning
Parabolic method
5.6 generalized integral
5.6. 1 infinite generalized integral
5.6.2 Generalized Integrals of Unbounded Functions
5.7 Application of definite integral
5.7. 1 definite integral method
Geometric application
5.7.3 Practical application of definite integral
Summary of this chapter
Review question 5
Chapter VI Vector Algebra and Spatial Analytic Geometry
6. 1 space rectangular coordinate system
6. 1. 1 space rectangular coordinate system
6. 1.2 distance formula between two points
6.2 the concept of vector
6.2. 1 vector concept
6.2.2 Addition and subtraction of vectors
6.3 Coordinate Expression of Vector
6.3. 1 vector coordinates
6.3.2 Modulus and direction cosine of vector
6.4 Quantity product and cross product
6.4. 1 Quantity product of two vectors
6.4.2 Cross product of two vectors
6.5 Space Curved Surface and Curve Equation
6.5. 1 surface equation
6.5.2 space curve equation
6.6 space plane equation
6.6. Point normal equation of1plane
General equation of plane
6.7 space linear equation
6.7. 1 general equation of space line
6.7.2 Standard equation of spatial straight line
6.7.3 Linear Parameter Equation
6.8 Common quadric graphics
6.8. 1 ellipsoid
hyperboloid
paraboloid
6.8.4 Quadratic cone
Summary of this chapter
Review question 6
Chapter 7 Differential method of multivariate function and its application
7. Basic concept of1multivariate function
7. 1. 1 region
7. The concept of1.2 multivariate function
7. 1.3 Limit of Binary Function
7. 1.4 Continuity of Binary Functions
7.2 partial derivative
7.2. Definition and calculation method of1partial derivative
Higher order partial derivative
7.3 Total differential and its application
7.3. 1 total difference concept
7.3.2 Application of Total Differential in Approximate Calculation
7.4 Differential method of multivariate function
7.4. Derivation rule of1multivariate composite function
7.4.2 Derivation formula of implicit function
7.5 Geometric Application of Partial Derivatives
7.5. 1 Tangent and normal plane of space curve
7.5.2 tangent plane and surface normal
7.6 Directional derivatives and gradients
7.6. 1 directional derivative
gradient
7.7 Extreme value of multivariate function
7.7. 1 Extreme value, maximum value and minimum value of multivariate function
Conditional extremum
Summary of this chapter
Review question 7
Chapter VIII Multiple Integrals
8. The concept and properties of1double integral
8. The concept of1.1double integral
8. Properties of1.2 Double Integral
8.2 Calculation method of double integral
8.2. Calculation Method of Double Integral in1Cartesian Coordinate System
8.2.2 Calculation method of double integral in polar coordinates
8.3 Application example of double integral
8.3. 1 geometry application example
Examples of physical applications
8.4 The concept and calculation method of triple integral
8.4. The concept of1triple integral
8.4.2 Calculation of Triple Integral in Cartesian Coordinate System
8.4.3 Calculation of Triple Integral in Cylindrical Coordinate System
8.4.4 Calculate the triple integral in the spherical coordinate system.
Summary of this chapter
Review question 8
Chapter 9 Curve Integral and Surface Integral
9. Curve integral of1arc length
Concept and properties of arc length curve 9. 1. 1 integral
9. 1.2 Calculation method of arc length curve integral
9.2 Curve Integration of Coordinates
9.2. Concept and properties of1coordinate curve integral
9.2.2 Calculation method of coordinate curve integral
9.2.3 Relationship between Two Kinds of Curve Integrals
9.3 Green's Formula
9.3. 1 Green formula
9.3.2 Conditions for Curve Integration Independent of Path
9.4 surface integral
Surface integral of area
9.4.2 Coordinate surface integration
9.4.3 Relationship between Two Kinds of Surface Integrals
gauss formula
Summary of this chapter
Review question 9
Chapter 65438 +00 series
10. 1 series terms
Convergence and divergence of 10. 1. 1 infinite series
Properties of 10. 1.2 infinite series
Necessary conditions for convergence of series 10. 1.3
10.2 constant term series convergence method
Convergence method of 10.2. 1 positive series
Convergence method of 10.2.2 staggered series
10.2.3 Absolute Convergence and Conditional Convergence
10.3 power series
The concept of 10.3. 1 power series
Convergence of 10.3.2 power series
Operation of 10.3.3 power series
The function of 10.4 is expanded into Taylor series.
Taylor series 10.4. 1
10.4.2 Expand the function into a power series.
Application example of power series expansion of * 10.4.3 function
10.4.4 Euler formula
10.5 Fourier series
10.5. 1 Fourier series of a function with a period of 2π
10.5.2 defines the Fourier series of the function on [-π, π] or [0, π].
10.5.3 Fourier series of function with period 2l.
Summary of this chapter
Review questions 10
Chapter 1 1 differential equation
1 1. 1 Basic concepts of differential equations
11.1.1differential equation
1 1. 1.2 differential equation
The solution of 1 1. 1.3 differential equation
1 1.2 Differential equation with separable variables
1 1.3 first order linear differential equation
1 1.3. 1 Solution of General Solution of First Order Homogeneous Linear Equation
1 1.3.2 the solution of the general solution of the first-order nonhomogeneous linear equation
1 1.4 reducible second-order differential equation
Differential equation11.4.1y "= f (x)
1 1.4.2 y "= f (x, y') type differential equation
1 1.4.3 y "= f (y, y') type differential equation
1 1.5 second-order homogeneous linear differential equation with constant coefficients
1 1.5. 1 Properties of Solutions of Second Order Homogeneous Linear Differential Equations with Constant Coefficients
1 1.5.2 Solutions of second-order homogeneous linear differential equations with constant coefficients
1 1.6 Second-order non-homogeneous linear differential equation with constant coefficients
1 1.6. 1 Properties of Solutions of Second Order Nonhomogeneous Linear Differential Equations with Constant Coefficients
1 1.6.2 Solutions of second-order non-homogeneous linear differential equations with constant coefficients
Summary of this chapter
Review questions 1 1
Appendix A Several Common Plane Curves and Their Equations
Appendix b integral table
Appendix c preliminary field theory
Practice reference answers