《Economic Mathematics I》Syllabus

Course Number:           2109031903

Course Name:               Economic Mathematics I

Instructors:                    Du Shude

Required Text:              ZHAO Shuyan. Fundamentals of Applied Mathematics in Economics (I) (Calculus) (Fifth Edition) [M]. Beijing: Chinese University Press, 2021.

Course Description:     Economic Mathematics is a compulsory course for undergraduate engineering majors in colleges and universities, which requires students to master basic mathematical theories and thinking methods, and is a basic course for cultivating mathematical literacy required by economic and management talents. Through the study of this course, students will master the basic concepts, basic theories and basic calculation skills of unary function calculus, and lay the necessary mathematical foundation for the study of subsequent courses. It enables students to obtain training in mathematical logic and rigor, cultivate and improve students' ability of abstract thinking and logical reasoning, so that students initially have the ability to use mathematical knowledge to solve some simple economic problems.

                                                                                                   Credits/Teaching Hours

Outline of UG CPC Topics Covered in this Course:           (3 credits/48 lecture hours)

Chapter 1 Functions                                      4 Teaching Hours

Section 1 Collection

Section 2 Set of Real Numbers

Section 3 Functional Relationships

Section 4 Piecewise Functions

Section 5 Example Problems for Establishing Functional Relationships

Section 6 Several Simple Properties of Functions

Section 7 Inverse Functions and Composite Functions

Section 8 Elementary Functions

Chapter 2 Limits and Continuity                            8 Teaching Hours

Section 1 The Limits of the Sequence                                                                   

Section 2 Limits of Functions

Section 3 Limits of Variables

Section 4 Infinitesimal and Infinitesimal Quantities

Section 5 Algorithms of Limits

Section 6 Two Important Limits

Section 7 Finding the Limit by Equivalent Infinitesimal Substitution

Section 8 Continuity of Functions

Chapter 3 Derivatives and Differentiation                    12 Teaching Hours

Section 1 Example problems that lead to the concept of derivatives

Section 2 The Concept of Derivatives

Section 3 Basic Formulas and Algorithms for Derivatives

Section 4 Higher-order derivatives

Section 5 Differentiation                                                                                        

Chapter 4 The Median Value Theorem and the Application of Derivatives

12 Teaching Hours

Section 1 Median Value Theorem

Section 2 The Law of Lobida

Section 3 Increment and Decrease of Functions

Section 4 Extrema of Functions

Section 5 Application of Maximum, Minimum and Extremum

Section 6 Concave and inflection points of curves

Section 7 Practices for Function Graphs

Chapter 5 Indefinite Integrals                                        12 Teaching Hours

Section 1: The Concept of Indefinite Integrals

Section 2 The Nature of Indefinite Integrals

Section 3 Basic Integral Formulas

Section 4 Commutation Integral Method

Section 5 Partial Integral Method

Total (Teaching Hours)                                                                         48  

Summary of UG CPC Topics Covered in this Course:       (5 Teaching Hours)