The First Week: 1 Introduction

1.1 Why study Calculus?

1.2 What is Calculus?

1.3 Why in English?

1.4 How to study Calculus?

The First Week: 2 Limits and Continuity

2.1 Rate of change and tangents to curves

2.2 Limit of a Function

2.3 Limit Laws

2.4 How  to Find Limits

The Second Week: 2 Limits and Continuity

2.6 The Precise Definition of Limit: A Example

2.5 The Precise Definition of Limit

The Second Week: 2 Limits and Continuity

2.7 One-sided Limits

2.8 Limit Involving sinx/x

2.9 Continuity

2.10 The Intermediate Value Theorem

2.11 Limits Involving Infinity

Unit Test-CH2

The Third Week: 3 Differentiation

3.1 Tangents of a curve

3.2 Derivative at a point

The Fourth Week: 3 Differentiation

3.3 Derivative as a function

3.4 Differentiable on an interval

3.5 When does a function not have a derivative

3.6 Differentiability implies continuity

The Fifth Week: 3 Differentiation

3.7 Differentiation rules I

3.8 Differentiation rules II

3.9 Derivatives of trigonometric functions

3.10 The Chain Rule

The Sixth Week: 3 Differentiation

3.11 L'Hopital's Law

3.12 Implicit differentiation

3.13 Linearization

3.14 Differential

Unit Test-CH3

The Seventh Week: 4 Applications of Derivatives

4.1 The extreme value

4.2 Where extreme values are located

4.3 Rolle's Theorem

4.4 Mean Value Theorem

4.5 Corollaries of Mean Value Theorem

The Eighth Week: 4 Applications of Derivatives

4.6 Monotonicity

4.7 Concavity

4.8 Curve sketching

4.9 Newton's method

4.10 Antiderivative and Indefinite integral

Unit Test-CH4

The Ninth Week: 5 Integration

5.1 Area and estimating by finite sum

5.2 Sigma notation

5.3 Limit of finite sum

5.4 Riemann sum and definite integral

The Tenth Week: 5 Integration

5.5  Integrable and nonintegrable functions

5.6 Area under curve

5.7 Mean Value Theorem of definite integral

5.8 Fundamental Theorem of Calculus-Part 1

5.9 Fundamental Theorem of Calculus-Part 2

The Eleventh Week: 6 Applications of Definite Integral

6.1 Cross-section method for volume

6.2 Disk method for volume

6.3 Washer method for volume

The Eleventh Week: 5 Integration

5.10 Relation between differentiation and integration

5.11 Total area

5.12 Substitution method for indefinite integral

5.13 Substitution method for definite integral

Unit Test-CH5

The Twelfth Week: 6 Applications of Definite Integral

6.4 Cylindrical shells for volume

6.5 Arc Length

6.6 Areas of surfaces of revolution

The Twelfth Week: 7 Transcendental Functions

7.1 Inverse function and its derivative

7.2 Natural Logarithm

7.3 Exponential function

7.4 Indeterminate Forms

7.5 Relative rate of growth

Unit Test-CH6,7

The Thirteenth Week: 8 Techniques of Integration

8.1 Integration by parts

8.2 Trigonometric integrals

8.3 Trigonometric substitution

8.4 Integration of rational functions

8.5 Improper integrals I

8.6 Improper integrals II

Unit Test-CH8

The Fourteenth Week: 9 Ordinary Differential Equations

9.1 General first-order differential equations and solutions

9.2 Separable differential equations

9.3 First-order linear differential equations

9.4 Bernoulli equations

9.5 Second-order linear differential equations-homogenous I

9.6 Second-order linear differential equations-homogenous II

9.7  Nonhomogenous differential equations

9.8 Euler equations

Unit Test-CH9