Calculus course focuses on the cultivation of students' ability of abstract thinking, logical reasoning, spatial imagination, experiment and observation, as well as the ability of comprehensive use of the knowledge learned to analyze and solve problems. It is also an important course to carry out mathematical quality education and cultivate the innovative spirit and ability of learners. Its content, thought and method have irreplaceable effect on training all kinds of talents' comprehensive quality.
Single Variable Calculus is the core and cornerstone of calculus theory with main contents: Preliminaries (real number, lines，curve, function), limit and continuity (function, limit and continuity), differentiation and application of single variable function (derivative, differential, median theorem, function form), integration and application of single variable function (definite integral, basic formula of calculus, indefinite integral, abnormal integral).
Calculus gives the students of science and engineering all the basics knowledge they need for calculation.
1 Preliminaries
1 Preliminaries
2 Limits and Continuity
2.1 The Limit of a Function
2.2 Calculating Limits Using the Limit Laws
2.3 The Precise Definition of a Limit
2.4 One-Sided Limits
2.5 Limits Involving Infinity; Asymptotes of Graphs
2.6 Continuity
Quiz for Chapter 2
3 Differentiation
3.1 Tangents and Derivatives
3.2 Derivative Functions
3.3 Differentiation Rules
3.4 Derivatives of Trigonometric Functions
3.5 Exponential and Logarithmic Differentiations
3.6 The chain Rule and Parametric Equations
3.7 Implicit Differentiation
3.8 Related Rates
3.9 Linearization and Differentials
Quiz for Chapter 3
4 Applications of Derivatives
4.1 Extreme Values of Functions
4.2 Mean Value Theorems
4.3 Indeterminate Forms and L\'Hopital\'s Rule
4.4 Monotonic Functions and Derivative Tests
4.5 Concavity
4.6 Graphing
4.7 Applied Optimization Problems
4.8 Newton\'s Method
4.9 Antiderivatives
Quiz for Chapter 4
5 Integration
5.1 Areas and Distances
5.2 The Definite Integral
5.3 The Fundamental Theorem of Calculus
5.4 Indefinite Integrals and the Substitution Rule
Quiz for Chapter 5
6 Applications of Definite Integrals
6.1 Areas Between Curves
6.2 Volumes by Slicing and Rotation About an Axis
6.3 Volumes by Cylindrical Shells
6.4 Lengths of Plane Curves
6.5 Areas of Surfaces of Revolution
6.6 Work and Fluid Forces
6.7 Center of Mass
Quiz for Chapter 6
7 Transcendental Function
7.1 Inverse Functions and Their Derivatives
7.2 Natural Logarithms
7.3 The Exponential Function
7.4 a^x and log_a(x)
7.5 Relative Rates of Growth
7.6 Inverse Trigonometric Functions
Quiz for Chapter 7
8 Techniques of Integration
8.1 Basic Integration Formulas
8.2 Integration by Parts
8.3 Integration of Rational Functions by Partial Fractions
8.4 Trigonometric Integrals
8.5 Trigonometric Substitutions
8.6 Numerical Integration
8.7 Improper Integrals
Quiz for Chapter 8
