​Mathematical Analysis I
Date: 2018-10-24 Views: 21

Mathematical Analysis I

Course No.:SMG1151201    Credit(s): 5

Course Description

Mathematical Analysis I is a course in the first semesterwhich is a foundational course of majors of mathematics, statistics and other natural sciences. It is the transition from elementarymathematics to advance mathematics, and will develop the students' qualities of modern mathematics and lay a solid foundation for students to continue to learn subsequent courses.

By studying Mathematical Analysis I, students can master theories of limitation and concepts and methods of single variable differential calculus. Meanwhile, they have the ability of strictly logical deduction, and can pithily and clearly use mathematical formulas and language to calculate quickly and flexibly.

Course Learning Outcomes

The student learning outcomes are what student would be able to know and to do on the completion of this course. In details are:

1. Understand the fundamental concepts and methods of differential calculus of single variable, e.g. limit, derivative, integral, etc.

2. Be able to develop some skills in working with the fundamental concepts and theorems.

3. Apply differentiation and integration to solve some economic problems.

Relationship to Other Courses

The prerequisites for this course are high school algebra and trigonometry.

Textbook and Reading Lists

Textbook:

Yulian Liu, Notes of Mathematical analysis (5th edition). Higher Education Press, 2011.

Suggested reading lists:

Department of Mathematics of EastChinaNormalUniversity, Mathematical Analysis (4th edition). Higher Education Press, 2010.

Yulian Liu, Study Guide of Notes of Mathematical analysis (2nd edition). Higher Education Press, 2003.

  

Course Assessment

Activities

Weighting (%)

Daily Performance and Homework

20%

Midterm Exam

0%

Final Exam

80%

  

Course Schedule

Week

Topics

Text

4

Lecture   1 Functions

1.Functions

2.Four   Types of Special Functions

3.Composite   Functions and Inverse Functions

Chapter 1

5-7

Lecture   2 Limit

1.Limit   of Sequences

2.Convergent   Sequences

3.Limit   of Functions

4.Limit   Theorem of Functions

Chapter 2

8

Lecture   3 Continuous Functions

1.  Continuous Functions

 2.  Properties of Continuous Function

Chapter 3

9

Lecture   4 Continuityof Real Numbers

1.Poof   of the Whole Property of Continuous Functions Defined on Closed Interval

Chapter 4

10-11

Lecture   5 Derivative and Differentiation

1.Derivatives

2.Derivative   Rules and Formulas

3.Implicit   Functions and Its Derivatives

4.Differentiation

5.Derivatives   and Differentiation of Higher Order

Chapter 5

12-13

Lecture   6 Basic theorem of calculus and its applications

1.Mean Value Theorems

2.L'Hôspital's Rules

3.Taylor's   Theorem

4.Applications of Properties   of Functions

Chapter 6

14-15

Lecture   7 Indefinite integrals

1.Indefinite   Integrals

2.Integration   by Parts and Changing of Variables

3.Integration   of Rational Functions

4.Integration   of Simple Irrational Functions and TrigonometricFunctions

Chapter 7

16-17

Lecture   8 Definite integrals

1.Definite Integrals

2.Criteria of Integrability   

3.Properties of Definite Integrals

4. Calculations of Definite Integrals

5.   Applications of Definite Integrals

Chapter 8

18

Lecture 9 Review

Chapters 1-8

19

Final   Exam