Algebra: Form and Function / Edition 1

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More About This Textbook

Overview

Algebra: Form and Function offers a fresh approach to algebra that focuses on teaching readers how to truly understand the principles, rather than viewing them merely as tools for other forms of mathematics. Meant for a College Algebra course, Algebra: Form and Function is an introduction to one of the fundamental aspects of modern society. Algebraic equations describe the laws of science, the principles of engineering, and the rules of business. The power of algebra lies in the efficient symbolic representation of complex ideas, which also presents the main difficulty in learning it. It is easy to forget the underlying structure of algebra and rely instead on a surface knowledge of algebraic manipulations. Most students rely on surface knowledge of algebraic manipulations without understanding the underlying structure of algebra that allows them to see patterns and apply it to multiple situations: McCallum focuses on the structure from the start.

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Product Details

  • ISBN-13: 9780470226667
  • Publisher: Wiley, John & Sons, Incorporated
  • Publication date: 1/9/2008
  • Edition description: Preliminary Edition
  • Edition number: 1
  • Pages: 416
  • Product dimensions: 10.30 (w) x 8.50 (h) x 0.30 (d)

Table of Contents

(Each chapter ends with a Summary, Review Exercises, Test, and an Internet Project.)
1. Algebraic Expressions.

Real Numbers and Their Properties.
Order and Absolute Value.
Polynomials; The Binomial Theorem.
Factoring Polynomials.
Rational Expressions.
Rational Exponents.
Radical Expressions.

2. Equations and Inequalities.
Linear Equations.
Linear Applications and Modeling.
Complex Numbers.
Quadratic Equations.
Quadratic Applications and Modeling.
Other Types of Equations.
Inequalities.
Absolute Value Equations and Inequalities.

3. Relations, Functions, and Graphs.
Relations and the Rectangular Coordinate System; Circles.
Functions.
Linear Functions.
Equations of Lines; Curve Fitting.
Graphs of Relations and Functions.
General Graphing Techniques.
Operations and Composition.

4. Polynomial and Rational Functions.
Quadratic Functions; Curve Fitting.
Synthetic Division.
Zeros of Polynomial Functions.
Polynomials Functions: Graphs, Applications, and Models.
Rational Functions: Graphs, Applications, and Models.
Variation.

5. Exponential and Logarithmic Functions.
Inverse Functions.
Exponential Functions.
Logarithmic Functions.
Evaluating Logarithms and the Change-of-Base Theorem.
Exponential and LogarithmicEquations.
Applications and Models of Exponential Growth and Decay.

6. Systems of Equations and Inequalities.
Linear Systems of Equations.
Matrix Solution of Linear Systems.
Determinant Solution of Linear Systems.
Partial Fractions.
Nonlinear Systems.
Systems of Inequalities and Linear Programming.
Properties of Matrices.
Matrix Inverses.

7. Analytic Geometry.
Parabolas.
Ellipses.
Hyperbolas.
Summary of the Conic Sections.

8. Further Topics in Algebra.
Sequences and Series.
Arithmetic Sequences and Series.
Geometric Sequences and Series.
The Binomial Theorem Revisited.
Mathematical Induction.
Counting Theory.
Basics of Probability.

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