ESSENTIAL
CALCULUS

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1.1 Functions and Their Representations

1.2 A Catalog of Essential Functions

1.3 The Limit of a Function

1.4 Calculating Limits

1.6 Limits Involving Infinity

2.1 Derivatives and Rates of Change

2.2 The Derivative as a Function

2.3 Basic Differentiation Formulas

2.4 The Product and Quotient Rules

2.6 Implicit Differentiation

3.1 Maximum and Minimum Values

3.3 Derivatives and the Shapes of Graphs

3.4 Curve Sketching

3.6 Newton's Method

3.7 Antiderivatives

4.2 The Definite Integral

4.2 The Mean Value Theorem

4.3 Evaluating Definite Integrals

4.5 The Substitution Rule

5.1 Inverse Functions

5.2 The Natural Logarithmic Function

5.3 The Natural Exponential Function

5.5 Exponential Growth and Decay

5.6 Inverse Trigonometric Functions

6.2 Trigonometric Integrals and Substitutions

6.3 Partial Fractions

6.6 Improper Integrals

7.1 Areas Between Curves

7.5 Area of a Surface of Revolution

7.6 Applications to Physics and Engineering

7.7 Differential Equations

8.1 Sequences

8.3 The Integral and Comparison Tests

8.7 Taylor and Maclaurin Series

9.1 Parametric Curves

9.2 Calculus with Parametric Curves

9.3 Polar Coordinates

10.1 Three-Dimensional Coordinate Systems

10.5 Equations of Lines and Planes

10.6 Cylinders and Quadric Surfaces

10.8 Arc Length and Curvature

11.7 Maximum and Minimum Values

12.1 Double Integrals over Rectangles

12.3 Double Integrals in Polar Coordinates

12.6 Triple Integrals in Cylindrical Coordinates

12.7 Triple Integrals in Spherical Coordinates