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Precalculus
The bridge to calculus
The same ground as Algebra and Trigonometry at a brisker pace, ending with limits and derivatives. Read it before a first calculus course.
Contents
- Preface
1Functions
3Polynomial and Rational Functions
- Introduction to Polynomial and Rational Functions
- 3.1Complex Numbers
- 3.2Quadratic Functions
- 3.3Power Functions and Polynomial Functions
- 3.4Graphs of Polynomial Functions
- 3.5Dividing Polynomials
- 3.6Zeros of Polynomial Functions
- 3.7Rational Functions
- 3.8Inverses and Radical Functions
- 3.9Modeling Using Variation
Chapter Review
Exercises
4Exponential and Logarithmic Functions
- Introduction to Exponential and Logarithmic Functions
- 4.1Exponential Functions
- 4.2Graphs of Exponential Functions
- 4.3Logarithmic Functions
- 4.4Graphs of Logarithmic Functions
- 4.5Logarithmic Properties
- 4.6Exponential and Logarithmic Equations
- 4.7Exponential and Logarithmic Models
- 4.8Fitting Exponential Models to Data
Chapter Review
Exercises
7Trigonometric Identities and Equations
- Introduction to Trigonometric Identities and Equations
- 7.1Solving Trigonometric Equations with Identities
- 7.2Sum and Difference Identities
- 7.3Double-Angle, Half-Angle, and Reduction Formulas
- 7.4Sum-to-Product and Product-to-Sum Formulas
- 7.5Solving Trigonometric Equations
- 7.6Modeling with Trigonometric Functions
Chapter Review
Exercises
8Further Applications of Trigonometry
9Systems of Equations and Inequalities
- Introduction to Systems of Equations and Inequalities
- 9.1Systems of Linear Equations: Two Variables
- 9.2Systems of Linear Equations: Three Variables
- 9.3Systems of Nonlinear Equations and Inequalities: Two Variables
- 9.4Partial Fractions
- 9.5Matrices and Matrix Operations
- 9.6Solving Systems with Gaussian Elimination
- 9.7Solving Systems with Inverses
- 9.8Solving Systems with Cramer's Rule
Chapter Review
Exercises
11Sequences, Probability and Counting Theory
- ABasic Functions and Identities
- Index