### Calculus Ⅱ-A

Course Code: B11004Y-A01

Course Name: Calculus -A

Credits: 4.0

Pre-requisite: CalculusI

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

Instructors:Null

Course Description

This course is designed for undergraduate students from all majors. The requirements for students in this course are to learn fundamentals and methods of calculus and related knowledge about calculus. The category A of this course is based on theoretical proof which is not only suitable for students who decide  to choose the mathematics, physics, computer science and etc., but also suitable for students in other majors. The basic requirements are that students should have fundamental knowledge of multivariable calculus with good understanding of related definitions and methods. In addition, students should know how to think by using calculus. The course is aimed at laying the foundation for Calculus III and other courses.

Topics and Schedule

1. The limits and continuity in multivariable function

1.1.N-dimensional space and its characteristics

1.2.The limits in multivariable function

1.3.The continuity in multivariable function

1. Leibniz notation of multivariable function

2.1.Derivative of multivariable function

2.2.Fundamental theorem of derivative methods

2.3.The characteristics of multivariable function

1. Implicit function theorem and its applications

3.1.Implicit function

3.2.Implicit function groups

3.3.Geometric application

3.4.Conditional extreme

1. Multiple integration

4.1.The Riemann integral of a function defined over an arbitrary bounded n-dimensional set

4.2.Integral of a function defined over a set

4.3.Properties of integration

4.4.Multiple integrals and iterated integrals

4.5.Change of variables

4.6.Improper multiple integration

1. Surfaces in n-dimensional real space and its differential forms

5.1.Surfaces in n-dimensional real space

5.2.Orientation of surfaces

5.3.The boundary of surfaces and its orientation

5.4.The dimensions of surfaces in Euclidean space

5.5.Differential forms

1. Curve integrals and surface integrals

6.1.Integrals of differential forms

6.2.Volume forms

6.3.Integrals of differential 1-forms

6.4.Integrals of differential 2-forms

6.5.Integral equations in analysis

The grades include midterm examination, final examination and assignments of 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(4th 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

[3]W. Rudin,, The principle for mathematical analysis (translators: Cigeng Zhao, Yi Jiang), China Machine Press.2012(Chinese Version)

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