**Content of APEX Calculus, Version 3.0**

APEX Calculus comprises 13 chapters; each chapter and section is listed below. This text was written to have the same basic organization as most traditional calculus textbooks.

The whole text is 850+ pages long. For multiple reasons (lower cost per semester, lower weight per semester, increased likelihood of students bringing their text to class, etc.), APEX Calculus has been broken up into 3 overlapping volumes, roughly along traditional "Calc 1, 2 & 3" lines, as follows:

- Calculus 1: Chapters 1 through 6.1
- Limits through Integration by Substitution

- Calculus 2: Chapters 5 through 8
- Integration through Sequences and Series

- Calculus 3: Chapters 9 through 13
- Curves in the Plane through Multiple Integration

If this division does not match up well with your department's division of Calculus material:

- Tell me so I know what people are most interested in,
- Consider editing the source files at GitHub to create your own version, and/or
- Consider "just making it work as is"; while not ideal, the book is still a great text at a great price.

- Limits
- An introduction to Limits
- Epsilon-Delta Definition of a Limit
- Finding Limits Analytically
- One-Sided Limits
- Continuity
- Limits Involving Infinity

- Derivatives
- Instantaneous Rates of Change: The Derivative
- Interpretations of the Derivative
- Basic Differentiation Rules
- The Product and Quotient Rules
- The Chain Rule
- Implicit Differentiation
- Derivatives of Inverse Functions

- The Graphical Behavior of Functions
- Extreme Values
- The Mean Value Theorem
- Increasing and Decreasing Functions
- Concavity and the Second Derivative
- Curve Sketching

- Applications of the Derivative
- Newton's Method
- Related Rates
- Optimization
- Differentials

- Integration
- Antiderivatives and Indefinite Integration
- The Definite Integral
- Riemann Sums
- The Fundamental Theorem of Calculus
- Numerical Integration

- Techniques of Integration
- Substitution
- Integration by Parts
- Trigonometric Integrals
- Trigonometric Substitution
- Partial Fraction Decomposition
- Hyperbolic Functions
- L'Hopital's Rule
- Improper Integration

- Applications of Integration
- Area Between Curves
- Volume by Cross-Sectional Area: Disk and Washer Methods
- The Shell Method
- Arc Length and Surface Area
- Work
- Fluid Forces

- Sequences and Series
- Sequences
- Infinite Series
- Integral and Comparison Tests
- Ratio and Root Tests
- Alternating Series and Absolute Convergence
- Power Series
- Taylor Polynomials
- Taylor Series

- Curves in the Plane
- Conic Sections
- Parametric Equation
- Calculus and Parametric Equations
- Introduction to Polar Coordinates
- Calculus and Polar Functions

- Vectors
- Introduction to Cartesian Coordinates in Space
- An Introduction to Vectors
- The Dot Product
- The Cross Product
- Lines
- Planes

- Vector-Valued Functions
- Vector-Valued Functions
- Calculus and Vector-Valued Functions
- The Calculus of Motion
- Unit Tangent and Normal Vectors
- The Arc Length Parameter and Curvature

- Functions of Several Variables
- An Introduction to Multivariable Functions
- Limits and Continuity of Multivariable Functions
- Partial Derivatives
- Differentiability and the Total Differential
- The Multivariable Chain Rule
- Directional Derivatives
- Tangent Lines, Normal Lines, and Tangent Planes
- Extreme Values

- Multiple Integration
- Iterated Integration and Area
- Double Integration and Volume
- Double Integration with Polar Coordinates
- Center of Mass
- Surface Area
- Volume Between Surfaces and Triple Integration

- (Coming Soon) Vector Calculus
- Introduction to Line Integrals
- Vector Fields
- Line Integrals over Vector Fields
- Flow, Flux, Green's Theorem and the Divergence Theorem
- Parametrized Surfaces and Surface Area
- Surface Integrals
- The Divergence Theorem and Stokes' Theorem

- Appendix:
- Solutions to Odd Numbered Exercises
- Index
- Useful formulas