Precalculus Mathematics for Calculus (with CD-ROM and iLrn™)

by Stewart, James; Redlin, Lothar; Watson, Saleem

• ISBN13: 9780534492779
• ISBN10: 0534492770
• Edition: 5th
• Format: Hardcover
• Copyright: 2005-10-20
• Publisher: Cengage Learning

Summary

This best selling author team explains concepts simply and clearly, without glossing over difficult points. Problem solving and mathematical modeling are introduced early and reinforced throughout, so that when students finish the course, they have a solid foundation in the principles of mathematical thinking. This comprehensive, evenly paced book provides complete coverage of the function concept and integrates substantial graphing calculator materials that help students develop insight into mathematical ideas. The authors' attention to detail and clarity, as in James Stewart's market-leading Calculus text, is what makes this text the market leader.

Table of Contents

Preface	xv
To the Student	xxiii
Calculators and Calculations	xxiv
Fundamentals	1	(145)
Chapter Overview	1	(1)
Real Numbers	2	(10)
Exponents and Radicals	12	(12)
Algebraic Expressions	24	(11)
Discovery Project: Visualizing a Formula	34	(1)
Rational Expressions	35	(9)
Equations	44	(14)
Modeling with Equations	58	(18)
Discovery Project: Equations through the Ages	75	(1)
Inequalities	76	(11)
Coordinate Geometry	87	(14)
Graphing Calculators; Solving Equations and Inequalities Graphically	101	(10)
Lines	111	(12)
Modeling Variation	123	(23)
Chapter 1 Review	130	(5)
Chapter 1 Test	135	(3)
Focus on Problem Solving: General Principles	138	(8)
Functions	146	(102)
Chapter Overview	147	(1)
What is a Function?	148	(10)
Graphs of Functions	158	(15)
Discovery Project: Relations and Functions	171	(2)
Increasing and Decreasing Functions; Average Rate of Change	173	(9)
Transformations of Functions	182	(11)
Quadratic Functions; Maxima and Minima	193	(10)
Modeling with Functions	203	(11)
Combining Functions	214	(11)
Discovery Project: Iteration and Chaos	223	(2)
One-to-One Functions and Their Inverses	225	(23)
Chapter 2 Review	233	(4)
Chapter 2 Test	237	(2)
Focus on Modeling: Fitting Lines to Data	239	(9)
Polynomial and Rational Functions	248	(78)
Chapter Overview	249	(1)
Polynomial Functions and Their Graphs	250	(15)
Dividing Polynomials	265	(7)
Real Zeros of Polynomials	272	(13)
Discovery Project: Zeroing in on a Zero	283	(2)
Complex Numbers	285	(6)
Complex Zeros and the Fundamental Theorem of Algebra	291	(8)
Rational Functions	299	(27)
Chapter 3 Review	316	(3)
Chapter 3 Test	319	(1)
Focus on Modeling: Fitting Polynomial Curves to Data	320	(6)
Exponential and Logarithmic Functions	326	(72)
Chapter Overview	327	(1)
Exponential Functions	328	(14)
Discovery Project: Exponential Explosion	341	(1)
Logarithmic Functions	342	(10)
Laws of Logarithms	352	(6)
Exponential and Logarithmic Equations	358	(11)
Modeling with Exponential and Logarithmic Functions	369	(29)
Chapter 4 Review	382	(3)
Chapter 4 Test	385	(1)
Focus on Modeling: Fitting Exponential and Power Curves to Data	386	(12)
Trigonometric Functions of Real Numbers	398	(68)
Chapter Overview	399	(1)
The Unit Circle	400	(8)
Trigonometric Functions of Real Numbers	408	(10)
Trigonometric Graphs	418	(16)
Discovery Project: Predator/Prey Models	432	(2)
More Trigonometric Graphs	434	(8)
Modeling Harmonic Motion	442	(24)
Chapter 5 Review	454	(4)
Chapter 5 Test	458	(1)
Focus on Modeling: Fitting Sinusoidal Curves to Data	459	(7)
Trigonometric Functions of Angles	466	(60)
Chapter Overview	467	(1)
Angle Measure	468	(10)
Trigonometry of Right Triangles	478	(10)
Trigonometric Functions of Angles	488	(13)
Discovery Project: Similarity	499	(2)
The Law of Sines	501	(7)
The Law of Cosines	508	(18)
Chapter 6 Review	516	(4)
Chapter 6 Test	520	(2)
Focus on Modeling: Surveying	522	(4)
Analytic Trigonometry	526	(54)
Chapter Overview	527	(1)
Trigonometric Identities	528	(7)
Addition and Subtraction Formulas	535	(6)
Double-Angle, Half-Angle, and Sum-Product Formulas	541	(9)
Inverse Trigonometric Functions	550	(11)
Discovery Project: Where to Sit at the Movies	560	(1)
Trigonometric Equations	561	(19)
Chapter 7 Review	571	(3)
Chapter 7 Test	574	(1)
Focus on Modeling: Traveling and Standing Waves	575	(5)
Polar Coordinates and Vectors	580	(54)
Chapter Overview	581	(1)
Polar Coordinates	582	(5)
Graphs of Polar Equations	587	(9)
Polar Form of Complex Numbers; DeMoivre's Theorem	596	(11)
Discovery Project: Fractals	605	(2)
Vectors	607	(10)
The Dot Product	617	(17)
Discovery Project: Sailing Against the Wind	626	(1)
Chapter 8 Review	627	(2)
Chapter 8 Test	629	(1)
Focus on Modeling: Mapping the World	630	(4)
Systems of Equations and Inequalities	634	(108)
Chapter Overview	635	(1)
Systems of Equations	636	(8)
Systems of Linear Equations in Two Variables	644	(7)
Systems of Linear Equations in Several Variables	651	(11)
Discovery Project: Best Fit versus Exact Fit	660	(2)
Systems of Linear Equations: Matrices	662	(13)
The Algebra of Matrices	675	(14)
Discovery Project: Will the Species Survive?	688	(1)
Inverses of Matrices and Matrix Equations	689	(15)
Discovery Project: Computer Graphics I	700	(4)
Determinants and Cramer's Rule	704	(11)
Partial Fractions	715	(6)
Systems of Inequalities	721	(21)
Chapter 9 Review	728	(5)
Chapter 9 Test	733	(2)
Focus on Modeling: Linear Programming	735	(7)
Analytic Geometry	742	(78)
Chapter Overview	743	(1)
Parabolas	744	(9)
Ellipses	753	(9)
Hyperbolas	762	(13)
Discovery Project: Conics in Architecture	771	(4)
Shifted Conics	775	(8)
Rotation of Axes	783	(12)
Discovery Project: Computer Graphics II	792	(3)
Polar Equations of Conics	795	(6)
Plane Curves and Parametric Equations	801	(19)
Chapter 10 Review	810	(4)
Chapter 10 Test	814	(2)
Focus on Modeling: The Path of a Projectile	816	(4)
Sequences and Series	820	(60)
Chapter Overview	821	(1)
Sequences and Summation Notation	822	(11)
Arithmetic Sequences	833	(5)
Geometric Sequences	838	(10)
Discovery Project: Finding Patterns	847	(1)
Mathematics of Finance	848	(6)
Mathematical Induction	854	(6)
The Binomial Theorem	860	(20)
Chapter 11 Review	870	(3)
Chapter 11 Test	873	(1)
Focus on Modeling: Modeling with Recursive Sequences	874	(6)
Limits: A Preview of Calculus	880
Chapter Overview	881	(1)
Finding Limits Numerically and Graphically	882	(8)
Finding Limits Algebraically	890	(8)
Tangent Lines and Derivatives	898	(10)
Discovery Project: Designing a Roller Coaster	908	(1)
Limits at Infinity: Limits of Sequences	908	(8)
Areas	916
Chapter 12 Review	925	(3)
Chapter 12 Test	928	(1)
Focus on Modeling: Interpretations of Area	929
Answers	1	(10)
Index	11
Photo Credits	1