Table of Contents
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Chapter 1 • Vectors
- Components of a Vector
- Graphical Operations on Vectors
- Magnitude of a 2D Vector
- Vector Operations in 2D
- Scalar Multiplication and Unit Vectors
- Vectors in terms of Fundamental Unit Vectors
- Polar Form of a Vector
- Dot Product in 2D
- Points, Midpoints, and Distances in Space
- Vector Operations in 3D
- Dot Product in 3D
- Cross Product in 3D
- Angle between Two Vectors in Space
- Chapter 2 • Polar Coordinates and Complex Numbers
- Chapter 3 • Probability and Statistics
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Chapter 4 • Limits and Differentiation
- Limits from Tables and Graphs
- One-Sided Limits
- Limits at Infinity
- Limits by Direct Substitution
- Evaluating Limits Using Algebraic Techniques
- Definition of the Derivative
- Combining the Product, Quotient, and Chain Rules
- Critical Points and Local Extrema of a Function
- The Product Rule
- The Quotient Rule
- Riemann Sums
- Indefinite Integrals: The Power Rule
- The Fundamental Theorem of Calculus: Functions Defined by Integrals
- The Fundamental Theorem of Calculus: Evaluating Definite Integrals