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· 129 mục

01: Functions
1.00: Prelude to Functions
1.01: Functions and Function Notation
1.02: Domain and Range
1.03: Rates of Change and Behavior of Graphs
1.04: Composition of Functions
1.05: Transformation of Functions
1.06: Absolute Value Functions
1.07: Inverse Functions
1.E: Functions (Exercises)
1.R: Functions (Review)
02: Linear Functions
2.00: Prelude to Linear Functions
2.01: Linear Functions
2.02: Graphs of Linear Functions
2.03: Modeling with Linear Functions
2.04: Fitting Linear Models to Data
2.E: Linear Functions(Exercises)
2.R: Linear Functions(Review)
03: Polynomial and Rational Functions
3.00: Prelude to Polynomial and Rational Functions
3.01: Complex Numbers
3.02: Quadratic Functions
3.03: Power Functions and Polynomial Functions
3.04: Graphs of Polynomial Functions
3.05: Dividing Polynomials
3.06: Zeros of Polynomial Functions
3.07: Rational Functions
3.08: Inverses and Radical Functions
3.09: Modeling Using Variation
3.E: Polynomial and Rational Functions(Exercises)
3.R: Polynomial and Rational Functions(Review)
04: Exponential and Logarithmic Functions
4.00: Prelude to Exponential and Logarithmic Functions
4.01: Exponential Functions
4.02: Graphs of Exponential Functions
4.03: Logarithmic Functions
4.04: Graphs of Logarithmic Functions
4.05: Logarithmic Properties
4.06: Exponential and Logarithmic Equations
4.07: Exponential and Logarithmic Models
4.08: Fitting Exponential Models to Data
4.E: Exponential and Logarithmic Functions (Exercises)
05: Trigonometric Functions
5.00: Prelude to Trigonometric Functions
5.01: Angles
5.02: Unit Circle - Sine and Cosine Functions
5.03: The Other Trigonometric Functions
5.04: Right Triangle Trigonometry
5.E: Trigonometric Functions (Exercises)
5.R: Trigonometric Functions (Review)
06: Periodic Functions
6.00: Prelude to Periodic Functions
6.01: Graphs of the Sine and Cosine Functions
6.02: Graphs of the Other Trigonometric Functions
6.03: Inverse Trigonometric Functions
6.E: Periodic Functions (Exercises)
6.R: Periodic Functions (Review)
07: Trigonometric Identities and Equations
7.00: Prelude to Trigonometric Identities and Equations
7.01: Solving Trigonometric Equations with Identities
7.02: Sum and Difference Identities
7.03: Double-Angle Half-Angle and Reduction Formulas
7.04: Sum-to-Product and Product-to-Sum Formulas
7.05: Solving Trigonometric Equations
7.06: Modeling with Trigonometric Equations
7.E: Trigonometric Identities and Equations (Exercises)
7.R: Trigonometric Identities and Equations (Review)
08: Further Applications of Trigonometry
8.00: Prelude to Further Applications of Trigonometry
8.01: Non-right Triangles - Law of Sines
8.02: Non-right Triangles - Law of Cosines
8.03: Polar Coordinates
8.04: Polar Coordinates - Graphs
8.05: Polar Form of Complex Numbers
8.06: Parametric Equations
8.07: Parametric Equations - Graphs
8.08: Vectors
8.E: Further Applications of Trigonometry (Exercises)
8.R: Further Applications of Trigonometry (Review)
09: Systems of Equations and Inequalities
9.00: Prelude to Systems of Equations and Inequalities
9.01: Systems of Linear Equations - Two Variables
9.02: Systems of Linear Equations - Three Variables
9.03: Systems of Nonlinear Equations and Inequalities - Two Variables
9.04: Partial Fractions
9.05: Matrices and Matrix Operations
9.06: Solving Systems with Gaussian Elimination
9.07: Solving Systems with Inverses
9.08: Solving Systems with Cramer's Rule
9.E: Systems of Equations and Inequalities (Exercises)
9.R: Systems of Equations and Inequalities (Review)
10: Analytic Geometry
10.00: Prelude to Analytic Geometry
10.01: The Ellipse
10.02: The Hyperbola
10.03: The Parabola
10.04: Rotation of Axes
10.05: Conic Sections in Polar Coordinates
10.E: Analytic Geometry (Exercises)
10.R: Analytic Geometry (Review)
11: Sequences Probability and Counting Theory
11.00: Prelude to Sequences Probability and Counting Theory
11.01: Sequences and Their Notations
11.02: Arithmetic Sequences
11.03: Geometric Sequences
11.04: Series and Their Notations
11.05: Counting Principles
11.06: Binomial Theorem
11.07: Probability
11.E: Sequences Probability and Counting Theory (Exercises)
11.R: Sequences Probability and Counting Theory (Review)
12: Introduction to Calculus
12.00: Prelude to Calculus
12.01: Finding Limits - Numerical and Graphical Approaches
12.02: Finding Limits - Properties of Limits
12.03: Continuity
12.04: Derivatives
12.E: Introduction to Calculus (Exercises)
12.R: Introduction to Calculus (Review)
13: Trigonometric Functions
13.00: Prelude to Trigonometric Functions
13.01: Angles
13.02: Unit Circle - Sine and Cosine Functions
13.03: The Other Trigonometric Functions
13.04: Right Triangle Trigonometry
13.E: Trigonometric Functions (Exercises)
13.R: Trigonometric Functions (Review)
14: Appendix