Precalculus with Limits

by Young, Cynthia Y.

• ISBN13: 9780470532027
• ISBN10: 0470532025
• Format: Hardcover
• Copyright: 2010-01-19
• Publisher: John Wiley & Sons Inc

Summary

Engineers looking for an accessible approach to calculus will appreciate Young's introduction. The book offers a clear writing style that helps reduce any math anxiety they may have while developing their problem-solving skills. It incorporates Parallel Words and Math boxes that provide detailed annotations which follow a multi-modal approach. Your Turn exercises reinforce concepts by allowing them to see the connection between the exercises and examples. A five-step problem solving method is also used to help engineers gain a stronger understanding of word problems.

Author Biography

Cynthia Young is an Associate Dean for the College of Sciences and a Professor of Mathematics. She received her B.A. in Mathematics Education from the University of North Carolina and both her M.S. in Electrical Engineering and her PhD in Applied Mathematics from the University of Washington. She went to UCF in 1997 and as an assistant professor she was selected by the Office of Naval Research for the Young Investigator Award to support her research in mathematical modeling of atmospheric effects on laser beams with interest in laser radar and laser communications systems. In addition to atmospheric propagation studies, Dr. Young leads several STEM education initiatives at UCF. From 2005-2008 Dr. Young was the NCAA Faculty Athletics Representative for UCF.?Her primary areas of responsibility as Associate Dean in the College of Sciences involve oversight of COS Assessment, External Research, and Faculty Affairs.

Table of Contents

Review: Equations and Inequalities

Linear Equations

Quadratic Equations

Other Types of Equations

Inequalities

Graphing Equations

Lines

Modeling Variation

Functions and Their Graphs

Functions

Graphs of Functions

Graphing Techniques: Transformations

Combining Functions

One-to-One Functions and Inverse Functions

Polynomial and Rational Functions

Quadratic Functions

Polynomial Functions of Higher Degree

Dividing Polynomials

The Real Zeros of a Polynomial Function

Complex Zeros: The Fundamental Theorem of Algebra

Rational Functions

Exponential and Logarithmic Functions

Exponential Functions and Their Graphs

Logarithmic Functions and Their Graphs

Properties of Logarithms

Exponential and Logarithmic Equations

Exponential and Logarithmic Models

Trigonometric Functions of Angles

Angle Measure

Right Triangle Trigonometry

Trigonometric Functions of Angles

The Law of Sines

The Law of Cosines

Trigonometric Functions of Real Numbers

Trigonometric Functions: The Unit Circle Approach

Graphs of Sine and Cosine Functions

Graphs of Other Trigonometric Functions

Analytic Trigonometry

Verifying Trigonometric Identities

Sum and Difference Identities

Double-Angle and Half-Angle Identities

Product-to-Sum and Sum-to-Product Identities

Inverse Trigonometric Functions

Trigonometric Equations

Vectors, the Complex Plane, and Polar Coordinates

Vectors

The Dot Product

Polar (Trigonometric) Form of Complex Numbers

Products, Quotients, Powers, and Roots of Complex Numbers

Polar Coordinates and Graphs of Polar Equations

Systems of Linear Equations and Inequalities

Systems of Linear Equations in Two Variables

Systems of Linear Equations in Three Variables

Systems of Linear Equations and Matrices

Matrix Algebra

The Determinant of a Square Matrix and Cramer's Rule

Partial Fractions

Systems of Linear Inequalities in Two Variables

Conics, Systems of Nonlinear Equations and Inequalities, and Parametric Equations

Conic Basics

The Parabola

The Ellipse

The Hyperbola

Systems of Nonlinear Equations

Systems of Nonlinear Inequalities

Rotation of Axes

Polar Equations of Conics

Parametric Equations and Graphs

Sequences and Series

Sequences and Series

Arithmetic Sequences and Series

Geometric Sequences and Series

Mathematical Induction

The Binomial Theorem

Limits: A Preview to Calculus 992

Introduction to Limits: Estimating Limits Numerically and Graphically

Techniques for Finding Limits

Tangent Lines and Derivatives

Limits at Infinity; Limits of Sequences

Finding the Area Under a Curve

Appendix Prerequisites: Fundamentals of Algebra

Real Numbers

Integer Exponents and Scientific Notation

Polynomials: Basic Operations

Factoring Polynomials

Rational Expressions

Rational Exponents and Radicals

Complex Numbers

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