1 FUNDAMENTALS

1 Chapter Overvıew

2 Real Numbers

13 Exponents and Radicals

25 Algebraıc Expressıons

36 Ratıonal Expressıon

45 Equatıons

59 Complex Numbers

65 Modeling with Equations

81 Inequalities

92 The Coordinate plane: Graph of Equations : Circles

106 Lines

117 Solving Equations and Inequalities Graphically

122 Modeling Variation

130 Chapter 1 Review

137 Chapter 1 Test

139 FOCUS ON MODELING Fitting Lines to Data

147 FUNCTIONS

147 Chapter Overview

148 Function

159 Graph of Functions

170 Getting Information from the Graph of a Function

183 Average Rate of Charge of a Function

190 Linear Function and Model

198 Transformations of Functions

210 Combining Functions

219 One-to-One Functions and their Inverse

229 Chapter 2 Review

235 Chapter 2 Test

237 FOCUS ON MODELING Modeling with Functions

245 POLYNOMIAL AND RATIONAL FUNCTIONS

245 Chapter Overview

246 Quadratic Functions and Models

254 Polynomial Functional and their Graphs

269 Dividing Polynomials

275 Real Zeros of Polynomials

287 Complex Zeros and the Fundamental Theorem of Algebra

295 Rational Function

311 Polynomial and Rational Inequalities

317 Chapter 3 Review

323 Chapter3 Test

325 FOCUSING ON MODELING Fitting Polynomial Curves to Data

329 EXPONENTIAL AND LOGARITHMIC FUNCTIONS

329 Chapter Overview

330 Exponential Functions

338 The Natural Exponential function

344 Logarithmic Function

354 Laws of Logarithmic

360 Exponentials and Logarithmic

370 Modeling with Exponential Functions

381 Logarithmic Scales

386 Chapter 4 Review

391 Chapter a test

392 FOCUS ON MODELING Fitting Exponential and Power Curves to Data Cumulative Review Test Chapter 2.3 and 4 (Website)

401 TRIGONOMETRIC FUNCTIONS: UNIT CIRCLE APPROACH

401 Chapter Overview

402 The Unit Circle

409 Trigonometric Functions of real Numbers

432 More Trigonometric Graphs

419 Trigonometric Graphs

439 Inverse Trigonometric Functions and Their Graphs

445 Modeling Harmonic Motion

460 Chapter 5 Review

465 Chapter 5 Test

466 FOCUS ON MODELING Fitting Sinusoidal Curves to Data

471 TRIGONOMETRIC FUNCTIONS: RIGHT TRIANGLE APPROACH

471 Chapter Overview

472 Angle Measure

482 Trigonometry of Right Triangles

491 Trigonometric Functions of Angles

501 Inverse Trigonometric Functions and Right Triangles

508 The Law of Sines

516 The Law of Cosines

524 Chapter 6 Review

531 Chapter 6

533 FOCUS ON MODELING Surveying

537 ANALYTIC TRIGONOMETRY

537 Chapter Overview

538 Trigonometric Identities

545 Addition and Subtraction Formulas

553 Double angle Half Angle and Product Sum Formulas

564 Basic Trigonometric Equations

570 More Trigonometric Equations

576 Chapter 7 Review

580 Chapter 7 Test

580 FOCUS ON MODELING Travelling and Standing Waves Cumulative Review Test; Chapter 5.6.and 7 (WEBSITE)

587 POLAR COORDINATES AND PARAMETRIC EQUATIONS

587 Chapter Overview

588 Polar Coordinates

594 Graph of Polar Equations

602 Polar Form of Complex Number De Moivres Theorem

611 Plane Curves and Parametric Equations

620 Chapter 8 Review

624 Chapter 8 Test

625 FOCUS ON MODELING The path of a projectile

629 VECTOR IN TWO AND THREE DIMENTION

629 Chapter Overview

630 Vectors in Two Dimension

639 The Dot Product

647 Three Dimensional Coordinate Geometry

653 Vector In Three Dimension

659 The Cross Product

666 Equation of Lines and Planes

670 Chapter 9 Review

675 Chapter 9 Test

676 FOCUS ON MODELING Vector Fields Cumulative Review chapter 8 and 9 (Website)

679 SYSTEMS OF EQUATIONS AND INEQUALITIES

679 Chapter Overview

680 Systems of Linear Equation in Two Variables

690 System of Linear Equation in Several Variables

699 Matrices and System of Linear Equations

734 Determinants and Cramer's Rule

745 Partial Fraction

751 Systems of Nonlinear Equation

756 Systems of Inequalities

766 Chapter 10 Review

773 Chapter 10 Test

FOCUS ON MODELING Linear Programming

781 CONIC SECTIONS

781 Chapter Overview

782 Parabolas

790 Ellipses

799 Hyperbolas

807 Shifted Conics

816 Rotation of Axes

824 Polar Equations of Conics

831 Chapter 11 Review

835 Chapter 11 Test

836 FOCUS ON MODELING Conics in Architecture Cumulative Review Test Chapter 10 and 11( website)

841 SEQUENCES AND SERIES

841 Chapter Overview

842 Sequences and Summation Notation

853 Arithmetic Sequences

858 Geometric Sequence

867 Mathematics of Finance

873 Mathematical Induction

879 The Binomial Theorem

887 Chapter 12 Review

892 Chapter 12 Test

893 FOCUS ON MODELING Modeling with Recursive Sequences

897 LIMTS: A PREVIEW OF CALCULUS

897 Chapter Overview

898 Finding Limits Numerically and Graphically

906 Finding Limits Algebraically

914 Tangent Lines and Derivatives

924 Limits at Infinity : Limits of Sequences

931 Areas

940 Chapter 13 Review

943 Chapter 13 Test

FOCUS ON MODELING Interpretation of Area Cumulative Review Test Chapters 12 and 13 (Website)

949 APPENDIX A Geometry Review APPENDIX B Calculations and Significant Figures (Website) APPENDIX C Graphing with a Graphing calculator (Website) APPENDIX D Using the TI-83/84 (Website)

A1 Answers

11 INDEX