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Introduction to Calculus

Begin calculus with functions, angles and radians, trigonometry, exponentials, logarithms, inequalities, limits, continuity, derivatives, antiderivatives, and integrals. Explore interactive graphs and work through the original exercises. Chapters 1–5 are available in English and Chinese.

Table of Contents

Chapter 1: Functions

1.2 Angles, Degrees, and Radians

1.3 Trigonometric Functions

1.4 Special Triangles and Trigonometric Identities

1.5 Exponential Functions

1.6 Logarithmic Functions and Equations

Chapter 2: Inequalities

2.1 Piecewise Functions

2.2 Absolute Value Functions

2.3 Intervals and Solving Inequalities

2.4 The Case Method

2.5 The Number Line Method

Chapter 3: Limits and Continuity

3.1 Basic Limits

3.2 Continuity and Discontinuity

3.3 Evaluating Indeterminate Limits

3.4 The Fundamental Sine Limit

3.5 Limits at Infinity

Chapter 4: Derivatives

4.1 The First Principles

4.2 Differentiability and Continuity

4.3 Basic Derivative Rules

4.4 Combining Derivative Rules

4.5 Chain Rule and Higher Derivatives

4.6 Implicit Differentiation

4.7 Related Rates

4.8 Logarithmic Differentiation

4.9 Differential Approximation

Chapter 5: Antiderivatives and Integrals

5.1 The Indefinite Integral

5.2 Basic Antiderivative Rules

5.3 Trigonometric and Exponential Integrals

5.4 Chain Rule in Reverse

5.5 The Method of Substitution

5.6 Riemann Sum

5.7 Definite Integral

5.8 Area Under a Curve

SUITABLE AUDIENCE

Beginning calculus learners who want to build their understanding of functions.

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