This course is an important public foundation course for all majors in the university, and the course mainly teaches the main content of calculus of single variable functions. Through learning, students can master the basic ideas and methods of differential calculus and integral theory of unary functions, be able to deal with common problems in calculus, enable students to get comparative and systematic mathematical training, improve students' scientific quality, and prepare for the next stage of learning.
Overview
Syllabus
- Chapter 1 Functions and Limits
- 1.1 The Concept of a Function
- 1.2 Operations on Functions, Composite Function and Inverse Function
- 1.3 A Catalog of Essential Functions
- 1.4 The Limit of a Function
- 1.5 The Limit Laws
- 1.6 The Squeeze Theorem
- 1.7 Continuity
- Chapter 2 Differentiation
- 2.1 Derivatives and Rates of Change
- 2.2 The Derivative as a Function
- 2.3 Differentiability and Continuity
- 2.4 Differentiation Formulas
- 2.5 Derivatives of Trigonometric Functions
- 2.6 The Chain Rule
- 2.7 Implicit Differentiation
- 2.8 Derivatives of logarithmic, Exponential function and Inverse Trigonometric Functions
- 2.9 L’Hospital’s Rule; Indeterminate Forms
- Chapter 3 Applications of Differentiation
- 3.1 The Mean Value Theorem
- 3.2 Monotonic Functions
- 3.3 Maximum and Minimum Values
- 3.4 Concavity
- 3.5 Limits at Infinity; Horizontal Asymptote
- Chapter 4 Integrals
- 4.1 The Area Problem
- 4.2 The Definite Integral
- 4.3 The Fundamental Theorem of Calculus
- 4.4 Indefinite integrals
- 4.5 The Substitution Rule
- Chapter 5 Techniques of Integration
- 5.1 Integration by Parts
- 5.2 Trigonometric Integrals
- 5.3 Trigonometric Substitution
- 5.4 Integration of Rational Functions by Partial Fractions
- 5.5 Improper Integrals
- Chapter 6 Applications of Integration
- 6.1 Areas Between Curves
- 6.2 Volumes
- 6.3 Volumes by Cylindrical Shells
- 6.4 Work
- 6.5 Average Value of a Function
- Final exam
Taught by
Lingna Li, Yali Chen, Nandy Luo, Debin Liu, and Jianhua Jin
