1 Introduction

1.4 How to study calculus?

1.1 Why study calculus?

1.3 Why in English?

1.2 What is calculus?

2 Limits and Continuity

Unit Test 1

2.3 Limit laws

2.1 Rate of change and tangents to curves

2.4 How to find limits

2.6 Limit involving sinx/x

2.9 Limits involving infinity

2.2 Limit of a function

2.7 Continuity

2.5 One-sided limits

2.8 The intermediate value theorem

Finding limits

Finding limits and understanding continuity

3 Differentiation

3.7 Differentiation rules

3.1 Tangents of a curve

3.13 Differentials

3.11 Implicit differentiation

3.6 Differentiability implies continuity

3.12 Linearization

3.2 Derivative at a point

3.4 Differentiable on an interval

3.5 When does a function not have a derivative

3.9 The Chain rule

3.10 The L'Hopital's law

3.3 Derivative as a function

3.8 Derivatives of trigonometric functions

Unit Test 2

4 Applications of derivatives

4.2 Where extreme values are located

4.4 Mean Value Theorem

4.6 Monotonicity

4.7 Concavity

4.9 Newton's method

4.5 Corollaries of Mean Value Theorem

4.3 Rolle's Theorem

4.10 Antiderivatives and Indefinite integrals

4.8 Curve sketching

4.1 The extreme value theorem

5 Integration

5.11 Total area

5.2 Sigma notations

5.5 Integrable and nonintegrable functions

5.4 Riemann sum and definite integral

5.7 Mean value theorem of definite integral

5.8 Fundamental theorem of Calculus 1

5.3 Limit of finite sums

5.12 Substitution method for indefinite integral

5.13 Substitution method for definite integral

5.1 Area and estimating with finite sums

5.6 Area under curve

5.10 Relation between differentiation and integration

5.9 Fundamental theorem of Calculus 2