Nguồn ngoài

Math 370: Precalculus

This course improves upon the foundational mathematics and critical thinking skills required in the calculus sequence for STEM majors. Course content includes a rigorous treatment of the properties of polynomial, rational, exponential, logarithmic, and trigonometric functions. Additional topics include systems of linear and non-linear equations and inequalities, conic sections, sequences and series, analytic geometry, vectors, parametric equations, and polar equations.

Mathematics

Tác giả: Carl Stitz & Jeff Zeager
Nhà xuất bản: Lakeland Community College & Lorain County Community College
Nguồn: LibreTexts
Giấy phép: CC BY-NC-SA
Ngôn ngữ: EN
Danh mục: Khoa học cơ bản

Đọc trực tuyến Tải PDF (nguồn mở)

Mục lục· 119 mục

01: Relations and Functions
1.01: Sets of Real Numbers and the Cartesian Coordinate Plane
1.1E: Exercises
1.02: Relations
1.2E: Exercises
1.03: Introduction to Functions
1.3E: Exercises
1.04: Function Notation
1.4E: Exercises
1.05: Function Arithmetic
1.5E: Exercises
1.06: Graphs of Functions
1.6E: Exercises
1.07: Transformations
1.7E: Exercises
02: Linear and Quadratic Functions
2.01: Linear Functions
2.1E: Exercises
2.02: Absolute Value Functions
2.2E: Exercises
2.03: Quadratic Functions
2.3E: Exercises
2.04: Inequalities with Absolute Value and Quadratic Functions
2.4E: Exercises
03: Polynomial Functions
3.01: Graphs of Polynomials
3.1E: Exercises
3.02: The Factor and Remainder Theorems
3.2E: Exercises
3.03: Real Zeros of Polynomials
3.3E: Exercises
3.04: Complex Zeros and the Fundamental Theorem of Algebra
3.4E: Exercises
04: Rational Functions
4.01: Introduction to Rational Functions
4.1E: Exercises
4.02: Graphs of Rational Functions
4.2E: Exercises
4.03: Rational Inequalities and Applications
4.3E: Exercises
05: Further Topics in Functions
5.01: Function Composition
5.1E: Exercises
5.02: Inverse Functions
5.2E: Exercises
5.03: Other Algebraic Functions
5.3E: Exercises
5.4: Algebraic Simplifications Necessary for Calculus
06: Exponential and Logarithmic Functions
6.01: Introduction to Exponential and Logarithmic Functions
6.1E: Exercises
6.02: Properties of Logarithms
6.2E: Exercises
6.03: Exponential Equations and Inequalities
6.3E: Exercises
6.04: Logarithmic Equations and Inequalities
6.4E: Exercises
6.05: Applications of Exponential and Logarithmic Functions
6.5E: Exercises
07: Sequences and the Binomial Theorem
7.01: Sequences
7.1E: Exercises
7.02: Summation Notation
7.2E: Exercises
7.03: Mathematical Induction
7.3E: Exercises
7.04: The Binomial Theorem
7.4E: Exercises
08: Hooked on Conics
8.01: Introduction to Conics
8.02: Circles
8.2E: Exercises
8.03: Parabolas
8.3E: Exercises
8.04: Ellipses
8.4E: Exercises
8.05: Hyperbolas
8.5E: Exercises
09: Systems of Equations and Inequalities
9.01: Systems of Linear Equations - Gaussian Elimination
9.1E: Exercises
9.02: Systems of Linear Equations - Augmented Matrices
9.2E: Exercises
9.03: Systems of Non-Linear Equations and Inequalities
9.3E: Exercises
10: Foundations of Trigonometry
10.01: Angles and their Measure
10.1E: Exercises
10.02: The Unit Circle - Cosine and Sine
10.2E: Exercises
10.03: The Six Circular Functions and Fundamental Identities
10.3E: Exercises
10.04: Trigonometric Identities
10.4E: Exercises
10.05: Graphs of the Trigonometric Functions
10.5E: Exercises
10.06: The Inverse Trigonometric Functions
10.6E: Exercises
10.07: Trigonometric Equations and Inequalities
10.7E: Exercises
11: Applications of Trigonometry
11.01: Applications of Sinusoids
11.1E: Exercises
11.02: The Law of Sines
11.2E: Exercises
11.03: The Law of Cosines
11.3E: Exercises
11.04: Polar Coordinates
11.4E: Exercises
11.05: Graphs of Polar Equations
11.5E: Exercises
11.06: Hooked on Conics Again
11.6E: Exercises
11.07: Polar Form of Complex Numbers
11.7E: Exercises
11.08: Vectors
11.8E: Exercises
11.09: Parametric Equations
11.9E: Exercises