CalculusⅡ
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Welcome to the homepage of Calculus Ⅱ !
Tips:
多元函数藏天地，偏微各剖玄机。
分峰测谷寻临界点，全微分万象，叠积分拾级。
雅可比式明变换，经纬换大地。
梯度指归极向处，高斯拓界开新域。
算尽人间曲直，浑然正道无睽。
Course Introduction
Course number: 00010011B Credit: 5
The teaching content of this course is as follows:
| Section | Content |
| 1. Space Analytic Geometry | - Equations of planes and lines in space
- Space surfaces
- Space curves
|
| 2. Multivariable Differential Calculus | - Definition, limits, and continuity of multivariable functions
- Partial derivatives, higher-order partial derivatives, total differential
- Partial derivatives of composite and implicit functions
- Taylor's formula for functions of two variables
- Multivariable vector functions, directional derivatives
- Applications of partial derivatives in geometry
- Extrema and constrained extrema of multivariable functions
|
| 3. Multiple Integrals | - Double integrals: definition, properties, computation, applications
- Triple integrals: definition, properties, computation, applications
|
| 4. Vector Calculus | - Line integrals (first/second kind): definition, properties, computation
- Surface integrals (first/second kind): definition, properties, computation
- Green's formula, Stokes' formula, Gauss's formula
|
| 5. Series | - Convergence/divergence of numerical series, properties of convergent series
- Convergence tests for positive-term series
- Convergence tests for arbitrary series
- Convergence of function series
- Power series: convergence radius/domain, sum function, function expansion
- Fourier series: definition, Fourier expansion of functions
|
| 6. Improper Integrals | - Convergence and divergence of improper integrals
|
| 7. Ordinary Differential Equations (ODEs) | - Basic concepts of ODEs
- Solution methods for first-order ODEs
- Solution methods for special higher-order ODEs
- General solution of linear nonhomogeneous ODEs with constant coefficients
|
Course Resourse
Textbook of CalculusⅡ
Textbook1
Textbook2.
All rights reserved by 科学出版社.
Courseware of CalculusⅠ
Courseware(Part1).
Courseware(Part2).
Courseware(Part3).
Courseware(Part4).
Courseware(Part5).
All rights reserved by Professer Lu Hong.
Midterm of CalculusⅡ
Midterm.
Final of CalculusⅡ
Final.
Notes of CalculusⅡ
Notes(Part1, Handwrite Version)
Notes(Part2, Handwrite Version)
by Xipingo, there is no LaTeX version of it.
Tips of CalculusⅡ
All you need to do is also 刷题 !
