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Algebra and Trigonometry
High school to first-year college
Functions, exponentials, logarithms, the unit circle and trigonometry in full. It covers most of Math for Physics, one chapter at a time.
Contents
- Preface
2Equations and Inequalities
3Functions
5Polynomial and Rational Functions
- Introduction to Polynomial and Rational Functions
- 5.1Quadratic Functions
- 5.2Power Functions and Polynomial Functions
- 5.3Graphs of Polynomial Functions
- 5.4Dividing Polynomials
- 5.5Zeros of Polynomial Functions
- 5.6Rational Functions
- 5.7Inverses and Radical Functions
- 5.8Modeling Using Variation
Chapter Review
Exercises
6Exponential and Logarithmic Functions
- Introduction to Exponential and Logarithmic Functions
- 6.1Exponential Functions
- 6.2Graphs of Exponential Functions
- 6.3Logarithmic Functions
- 6.4Graphs of Logarithmic Functions
- 6.5Logarithmic Properties
- 6.6Exponential and Logarithmic Equations
- 6.7Exponential and Logarithmic Models
- 6.8Fitting Exponential Models to Data
Chapter Review
Exercises
7The Unit Circle: Sine and Cosine Functions
9Trigonometric Identities and Equations
- Introduction to Trigonometric Identities and Equations
- 9.1Verifying Trigonometric Identities and Using Trigonometric Identities to Simplify Trigonometric Expressions
- 9.2Sum and Difference Identities
- 9.3Double-Angle, Half-Angle, and Reduction Formulas
- 9.4Sum-to-Product and Product-to-Sum Formulas
- 9.5Solving Trigonometric Equations
Chapter Review
Exercises
10Further Applications of Trigonometry
- Introduction to Further Applications of Trigonometry
- 10.1Non-right Triangles: Law of Sines
- 10.2Non-right Triangles: Law of Cosines
- 10.3Polar Coordinates
- 10.4Polar Coordinates: Graphs
- 10.5Polar Form of Complex Numbers
- 10.6Parametric Equations
- 10.7Parametric Equations: Graphs
- 10.8Vectors
Chapter Review
Exercises
11Systems of Equations and Inequalities
- Introduction to Systems of Equations and Inequalities
- 11.1Systems of Linear Equations: Two Variables
- 11.2Systems of Linear Equations: Three Variables
- 11.3Systems of Nonlinear Equations and Inequalities: Two Variables
- 11.4Partial Fractions
- 11.5Matrices and Matrix Operations
- 11.6Solving Systems with Gaussian Elimination
- 11.7Solving Systems with Inverses
- 11.8Solving Systems with Cramer's Rule
Chapter Review
Exercises
13Sequences, Probability, and Counting Theory
- AProofs, Identities, and Toolkit Functions
- Index