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**Course Code**: B11005Y-A01

**Course Name**: Calculus III-A

**Credits**: 4.0

**Level**: Undergraduate

**Pre-requisite**: Calculus I and II

**Lecture Time**: 20 weeks, 2 sessions/week, 2 hours/session 80 hours

**Instructors**: Null

**Course Description**

This course is the foundation of numerousfuture courses such as differential equation, differential geometry, complex function, real function, probability, physics, and theoretical mechanics. In addition, it is also an important course in which instructors can teach undergraduate students basic mathematical skills and ways of thinking. It plays a key role in students’ future study and research.

**Topics and Schedule **

- Differential calculus of multivariable function

1.1.Differential

1.2.Differential characteristics of composite functions

1.3.Directional derivatives and gradient

1.4.Taylor formula and extreme point problem

- Implicit function theorem and its application

2.1.Implicit function

2.2.Implicit function groups

2.3.Geometric application

2.4.Conditional extreme

- Integral with parameter

3.1.Proper integration with parameter

3.2.Improper integration with parameter

3.3.Euler integration

- Curve integrals

4.1. Curve integrals of differential 1-forms

4.2. Curve integrals of differential 2-forms

- Multiple integration

5.1. The definition of double-integral of functions

5.2. The computation of double-integral of functions in Cartesian coordinate system

5.3. Green formula, curve integrals and path independent

5.4. Change of variables of double-integral of functions

5.5. Multiple integral

5.6. Change of variables of multiple integration

5.7. Improper double-integral of functions

- Surface integrals

12.1.Surface integrals of differential 1-forms

12.2.Surface integrals of differential 2-forms

12.3.Gauss and Tomas formula

- Differential of vector function

7.1.Vector function

7.2.Differential of vector function

7.3.Integral formula in filed theory

7.4. Potential field

- Asymptotic expansion method

8.1.Asymptotic formula and series

8.2.Asymptotic integrals

**Grading**

The grades include midterm examination, final examination and assignmentsof weekly homework

**Textbook**

B.A. Zorich, Mathematical analysis, higher education press, 2005 (Chinese version)

**References**

[1]School of mathematical sciences, Huadong Normal university, Mathematical analysis(4^{th} edition), higher education Press, 2010

[2]R. Courant, F. John, Introduction to Calculus and mathematical analysis (translators: Honglin Zhang and Minqiang Zhou), Science Press, 2001

**Course Website**

To be added