Precalculus

This precalculus textmap is intended for college-level Precalculus students and is a comprehensive book that covers more ground than an instructor could likely cover in a typical one- or two-semester course; but instructors should find, almost without fail, that the topics they wish to include in their syllabus are covered in the text.

Precalculus Mathematics

Tác giả: Jay Abramson
Nhà xuất bản: OpenStax
Nguồn: LibreTexts
Giấy phép: CC BY
Ngôn ngữ: EN
Danh mục: Khoa học cơ bản

Đọc trực tuyến Tải PDF (nguồn mở)

Mục lục· 197 mục

01: Functions
1.01: Introduction to Functions
1.02: Functions and Function Notation
1.03: Domain and Range
1.04: Rates of Change and Behavior of Graphs
1.05: Composition of Functions
1.06: Transformation of Functions
1.07: Absolute Value Functions
1.08: Inverse Functions
1.09: Chapter Review
1.9.01: Key Terms
1.9.02: Key Equations
1.9.03: Key Concepts
1.10: Exercises
1.10.01: Review Exercises
1.10.02: Practice Test
02: Linear Functions
2.01: Introduction to Linear Functions
2.02: Linear Functions
2.03: Graphs of Linear Functions
2.04: Modeling with Linear Functions
2.05: Fitting Linear Models to Data
2.06: Chapter Review
2.6.01: Key Terms
2.6.02: Key Equations
2.6.03: Key Concepts
2.07: Exercises
2.7.01: Review Exercises
2.7.02: Practice Test
03: Polynomial and Rational Functions
3.01: Introduction to Polynomial and Rational Functions
3.02: Complex Numbers
3.03: Quadratic Functions
3.04: Power Functions and Polynomial Functions
3.05: Graphs of Polynomial Functions
3.06: Dividing Polynomials
3.07: Zeros of Polynomial Functions
3.08: Rational Functions
3.09: Inverses and Radical Functions
3.10: Modeling Using Variation
3.11: Chapter Review
3.11.01: Key Terms
3.11.02: Key Equations
3.11.03: Key Concepts
3.12: Exercises
3.12.01: Review Exercises
3.12.02: Practice Test
04: Exponential and Logarithmic Functions
4.01: Introduction to Exponential and Logarithmic Functions
4.02: Exponential Functions
4.03: Graphs of Exponential Functions
4.04: Logarithmic Functions
4.05: Graphs of Logarithmic Functions
4.06: Logarithmic Properties
4.07: Exponential and Logarithmic Equations
4.08: Exponential and Logarithmic Models
4.09: Fitting Exponential Models to Data
4.10: Chapter Review
4.10.01: Key Terms
4.10.02: Key Equations
4.10.03: Key Concepts
4.11: Exercises
4.11.01: Review Exercises
4.11.02: Practice Test
05: Trigonometric Functions
5.01: Introduction to Trigonometric Functions
5.02: Angles
5.03: Unit Circle - Sine and Cosine Functions
5.04: The Other Trigonometric Functions
5.05: Right Triangle Trigonometry
5.06: Chapter Review
5.6.01: Key Terms
5.6.02: Key Equations
5.6.03: Key Concepts
5.07: Exercises
5.7.01: Review Exercises
5.7.02: Practice Test
06: Periodic Functions
6.01: Introduction to Periodic Functions
6.02: Graphs of the Sine and Cosine Functions
6.03: Graphs of the Other Trigonometric Functions
6.04: Inverse Trigonometric Functions
6.05: Chapter Review
6.5.01: Key Terms
6.5.02: Key Equations
6.5.03: Key Concepts
6.06: Exercises
6.6.01: Review Exercises
6.6.02: Practice Test
07: Trigonometric Identities and Equations
7.01: Introduction to Trigonometric Identities and Equations
7.02: Solving Trigonometric Equations with Identities
7.03: Sum and Difference Identities
7.04: Double-Angle Half-Angle and Reduction Formulas
7.05: Sum-to-Product and Product-to-Sum Formulas
7.06: Solving Trigonometric Equations
7.07: Modeling with Trigonometric Functions
7.08: Chapter Review
7.8.01: Key Terms
7.8.02: Key Equations
7.8.03: Key Concepts
7.09: Exercises
7.9.01: Review Exercises
7.9.02: Practice Test
08: Further Applications of Trigonometry
8.01: Introduction to Further Applications of Trigonometry
8.02: Non-right Triangles - Law of Sines
8.03: Non-right Triangles - Law of Cosines
8.04: Polar Coordinates
8.05: Polar Coordinates - Graphs
8.06: Polar Form of Complex Numbers
8.07: Parametric Equations
8.08: Parametric Equations - Graphs
8.09: Vectors
8.10: Chapter Review
8.10.01: Key Terms
8.10.02: Key Equations
8.10.03: Key Concepts
8.11: Exercises
8.11.01: Review Exercises
8.11.02: Practice Test
09: Systems of Equations and Inequalities
9.01: Introduction to Systems of Equations and Inequalities
9.02: Systems of Linear Equations - Two Variables
9.03: Systems of Linear Equations - Three Variables
9.04: Systems of Nonlinear Equations and Inequalities - Two Variables
9.05: Partial Fractions
9.06: Matrices and Matrix Operations
9.07: Solving Systems with Gaussian Elimination
9.08: Solving Systems with Inverses
9.09: Solving Systems with Cramer's Rule
9.10: Chapter Review
9.10.01: Key Terms
9.10.02: Key Equations
9.10.03: Key Concepts
9.11: Exercises
9.11.01: Review Exercises
9.11.02: Practice Test
10: Analytic Geometry
10.01: Introduction to Analytic Geometry
10.02: The Ellipse
10.03: The Hyperbola
10.04: The Parabola
10.05: Rotation of Axes
10.06: Conic Sections in Polar Coordinates
10.07: Chapter Review
10.7.01: Key Terms
10.7.02: Key Equations
10.7.03: Key Concepts
10.08: Exercises
10.8.01: Review Exercises
10.8.02: Practice Test
10.8.3: Answers to Questions
11: Sequences Probability and Counting Theory
11.01: Introduction to Sequences Probability and Counting Theory
11.02: Sequences and Their Notations
11.03: Arithmetic Sequences
11.04: Geometric Sequences
11.05: Series and Their Notations
11.06: Counting Principles
11.07: Binomial Theorem
11.08: Probability
11.09: Chapter Review
11.9.01: Key Terms
11.9.02: Key Equations
11.9.03: Key Concepts
11.10: Exercises
11.10.01: Review Exercises
11.10.02: Practice Test
12: Introduction to Calculus
12.01: Introduction to Calculus
12.02: Finding Limits - Numerical and Graphical Approaches
12.03: Finding Limits - Properties of Limits
12.04: Continuity
12.05: Derivatives
12.06: Chapter Review
12.6.01: Key Terms
12.6.02: Key Equations
12.6.03: Key Concepts
12.07: Exercises
12.7.01: Review Exercises
12.7.02: Practice Test
13: Appendix
13.01: Basic Functions and Identities
13.02: Answer Key
13.2.01: Chapter 1
13.2.02: Chapter 2
13.2.03: Chapter 3
13.2.04: Chapter 4
13.2.05: Chapter 5
13.2.06: Chapter 6
13.2.07: Chapter 7
13.2.08: Chapter 8
13.2.09: Chapter 9
13.2.10: Chapter 10
13.2.11: Chapter 11
13.2.12: Chapter 12