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Math 372: College Algebra for Calculus

This course provides a rigorous treatment of college-level algebra and its applications for STEM majors. Topics include polynomial, rational, radical, exponential, absolute value, and logarithmic functions, the graphs of these functions, and solving equations involving these functions; systems of equations; the theory of polynomial equations; analytic geometry including conics; sequences and series; and mathematical induction. Emphasis is given to analytical reasoning and problem-solving.

Mathematics

Tác giả: Roy Simpson
Nhà xuất bản: Cosumnes River College
Nguồn: LibreTexts
Ngôn ngữ: EN
Danh mục: Khoa học cơ bản

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Mục lục· 99 mục

01: Refining Function Knowledge
1.01: The Domain of a Function
1.1E: Exercises
1.02: Function Arithmetic and the Difference Quotient
1.2E: Exercises
1.03: Graphical Properties of Functions
1.3E: Exercises
1.04: Graphing Functions Using Transformations
1.4.01: Exercises
02: Linear and Quadratic Functions
2.01: Linear Functions
2.1.01: Exercises
2.02: Absolute Value Functions
2.2.01: Exercises
2.03: Quadratic Functions
2.3.01: Exercises
03: Polynomial Functions
3.01: Graphs of Polynomials
3.1.01: Exercises
3.02: The Factor and Remainder Theorems
3.2.01: Exercises
3.03: Real Zeros of Polynomials
3.3.01: Exercises
3.04: Complex Zeros and the Fundamental Theorem of Algebra
3.4.01: Exercises
04: Rational Functions
4.01: Introduction to Rational Functions
4.1.01: Exercises
4.02: Graphs of Rational Functions
4.2.01: Exercises
4.03: Rational Inequalities and Applications
4.3.01: Exercises
05: Further Topics in Functions
5.01: Function Composition
5.1.01: Exercises
5.02: Inverse Functions
5.2.01: Exercises
5.03: Other Algebraic Functions
5.3.01: Exercises
5.04: Algebraic Simplifications Necessary for Calculus
06: Exponential and Logarithmic Functions
6.01: Introduction to Exponential and Logarithmic Functions
6.1.01: Exercises
6.02: Properties of Logarithms
6.2.01: Exercises
6.03: Exponential Equations and Inequalities
6.3.01: Exercises
6.04: Logarithmic Equations and Inequalities
6.4.01: Exercises
6.05: Applications of Exponential and Logarithmic Functions
6.5.01: Exercises
07: Sequences and Series Mathematical Induction and the Binomial Theorem
7.01: Sequences
7.1.01: Exercises
7.02: Summation Notation
7.2.01: Exercises
7.03: Mathematical Induction
7.3.01: Exercises
7.04: The Binomial Theorem
7.4.01: Exercises
08: Hooked on Conics
8.01: Introduction to Conics
8.02: Circles
8.2.01: Exercises
8.03: Parabolas
8.3.01: Exercises
8.04: Ellipses
8.4.01: Exercises
8.05: Hyperbolas
8.5.01: Exercises
09: Systems of Equations and Inequalities
9.01: Systems of Linear Equations - Gaussian Elimination
9.1.01: Exercises
9.02: Systems of Linear Equations - Augmented Matrices
9.2.01: Exercises
9.03: Systems of Non-Linear Equations and Inequalities
9.3.01: Exercises
10: Appendix - The Language of Mathematics
10.01: Definitions
10.02: Axioms Theorems and Proofs
10.03: Operations
10.04: Simplifying
10.05: Theory versus Application
10.06: The Mathematical Mantra
11: Appendix - Prerequisite Function Material
11.01: Sets of Real Numbers and the Cartesian Coordinate Plane
11.1.01: Exercises
11.02: Relations
11.2.01: Exercises
11.03: A Brief Review of Functions
11.3.01: Exercises
11.04: Function Notation
11.4E: Exercises
11.05: Graphing Functions by Point-Plotting
11.5E: Exercises
12: Corequisite Appendix - Expressions and Equations
12.01: Quadratic Expressions and Equations
12.02: Radical Expressions and Equations
13: Corequisite Appendix - The Basics of Functions