1 Limits

1.1 The Definition of Limit

1.2 Infinitesimals

2 Derivative And Differential

2.1 The Definition of Derivative

2.2 Rules of Finding Derivatives

2.3 The Definition of Differential

2.4 Implicit Function

2.5 First Order Linear Differential equations

2.6 Higher-Order Derivative And Taylor Series

3 Integration

3.1 The Definition of Integral

3.2 Riemann Sum and Definite Integrals

3.3 First Fundamental Theorem of Calculus

3.4 Second Fundamental Theorem of Calculus

3.5 Integral Techniques

3.5.1 Integrals of Trig Functions

3.5.2 Integrals of Radical Functions

3.5.3 Integrals of Rational Functions

3.6 Improper Integrals

3.7 Applications of the Integral

4 Infinite Series

4.1 The Definition of Infinite Series

4.2 Important Infinite Series

4.3 The Test of Positive Series

4.4 The Test of Ordinary Series

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Calculus

This notebook is about the 9th edition of Dale Varberg's Calculus.

The first 4 chapters (until infinite series) are talking about the single variable calculus, then we expand the theme to multiple variable calculus.

Between the two parts, the conics and the polar coordinates are needed as the preliminaries for multiple variable calculus, which also helps in the single one.

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