Mathematical Analysis I
Course No.:SMG1151201 Credit(s): 5
Course Description
Mathematical Analysis I is a course in the first semester，which 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 | |
