Pre-calculus Books

Book SynopsisTrade Review"There are plenty of books about managing your wealth, but The Calculus of Happiness: How a Mathematical Approach to Life Adds Up to Health, Wealth, and Love, by Oscar Fernandez of Princeton University Press, sounds intriguing."--Matthew Partridge, Money Week "[E]ngaging... Readers are sure to get a sense of how content from algebra and precalculus can help inform us about important decisions that are almost universally relevant."--Jason M. Graham, MAA Reviews "Brilliant... Where Fernandez's book scores highly is that it goes beyond being a typical self-help manual for the numerate, by presenting example after example of how mathematical topics such as probability, game theory and exponential functions really do make sense of a world that can sometimes seem so subjective. It's also an easy-going analysis of those areas in life that get brushed under the carpet, to be attended to another day. Once you realise it all boils down to maths, you will wake up happier, wealthier and healthier tomorrow morning, and we have Oscar E. Fernandez to thank for that."Nick Smith, Engineering & TechnologyTable of ContentsPreface ix Math Topics Covered by Chapter xiii I: A Healthier You Is Just a Few Equations Away 1 1 How Many Calories Should You Eat Each Day? 3 1.1 The Linear Functions Hidden in Your Diet 4 1.2 The Mathematics of Metabolism 8 1.3 Burn Those Calories! Work Those Quads! 11 1.4 The Calories Required to Digest Food 14 2 Live Longer (and Be Healthier) by Eating the Right Foods 20 2.1 A Game of Macronutrient Musical Chairs 20 2.2 How to Eat More and Be Healthier: Energy Density 29 2.3 Live Long(er) and Prosper with theWaist-Height Ratio 34 II: A Mathematician's Guide to Managing Your Money 41 3 Dissecting Your Monthly Budget 43 3.1 The Return of the King (the Linear Function) 44 3.2 To Expenses, and Beyond! 49 3.3 How Many YearsWill It Take You to Reach Financial Independence? 62 4 How to Beat Wall Street at Its Own Game 69 4.1 How to Make 15% a Year, Guaranteed 70 4.2 The Safest Investments 71 4.3 Quantifying Investment Risk and Return 73 4.4 Stocks, Bonds, and the "All-Weather" Portfolio 77 III: Looking for Love? There May Be an Equation for That 87 5 Finding "The 1" 89 5.1 What the Search for Aliens Can Teach You about FindingYour Soulmate 89 5.2 Why Hiring a Secretary Is Like Dating 92 5.3 The Stable Matching Problem 97 6 Living Happily Ever After with "The 1" 103 6.1 Your Relationship as a Dynamical System 104 6.2 Need Help Making a Joint Decision? There's an Equation for That 108 6.3 How Psychologists Use Math to Predict Divorce 113 Epilogue 118 Acknowledgments 120 Appendix A: Background Content 121 Appendix 1 123 Appendix 2 128 Appendix 3 130 Appendix 4 141 Appendix 5 143 Appendix 6 144 Bibliography 151 Index 157

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Book SynopsisTrade Review“Surveys a wide variety of ways that mathematics can be used to improve decision making and general well-being.”—Chris Wilson, TIME.com“Readers are sure to get a sense of how content from algebra and precalculus can help inform us about important decisions that are almost universally relevant.”—Jason M. Graham, MAA Reviews“Brilliant. . . . Once you realise it all boils down to maths, you will wake up happier, wealthier and healthier tomorrow morning, and we have Oscar E. Fernandez to thank for that.”—Nick Smith, Engineering and Technology“The Calculus of Happiness . . . demonstrate[s] how mathematics can yield powerful insights into everyday life."—Helen Thomson, New Scientist“Fernandez generates such enthusiasm [for studying math] by considering topics that people do want to learn more about—food, money, other people—and skillfully weaving solid mathematical concepts within these topics.”—Sandra L. Arlinghaus, Mathematical Reviews

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Book SynopsisTable of Contents0 Review: Equations and Inequalities 1 0.1 Linear Equations 2 0.2 Quadratic Equations 17 0.3 Other Types of Equations 30 0.4 Inequalities 43 0.5 Graphing Equations 59 0.6 Lines 74 0.7 Modeling Variation 86 0.8* Linear Regression: Best Fit 0.8-1 1 Functions and Their Graphs 100 1.1 Functions 101 1.2 Graphs of Functions; Piecewise-Defined Functions; Increasing and Decreasing Functions; Average Rate of Change 118 1.3 Graphing Techniques: Transformations 138 1.4 Operations on Functions and Composition of Functions 152 1.5 One-to-One Functions and Inverse Functions 163 2 Polynomial and Rational Functions 185 2.1 Quadratic Functions 186 2.2 Polynomial Functions of Higher Degree 203 2.3 Dividing Polynomials: Long Division and Synthetic Division 219 2.4 The Real Zeros of a Polynomial Function 227 2 .5 Complex Zeros: The Fundamental Theorem of Algebra 242 2.6 Rational Functions 251 3 Exponential and Logarithmic Functions 278 3.1 Exponential Functions and Their Graphs 279 3.2 Logarithmic Functions and Their Graphs 295 3.3 Properties of Logarithms 311 3.4 Exponential and Logarithmic Equations 320 3.5 Exponential and Logarithmic Models 331 4 Trigonometric Functions of Angles 350 4.1 Angle Measure 351 4.2 Right Triangle Trigonometry 369 4.3 Trigonometric Functions of Angles 387 4.4 The Law of Sines 405 4.5 The Law of Cosines 418 5 Trigonometric Functions of Real Numbers 440 5.1 Trigonometric Functions: The Unit Circle Approach 441 5.2 Graphs of Sine and Cosine Functions 451 5.3 Graphs of Other Trigonometric Functions 481 6 Analytic Trigonometry 507 6.1 Trigonometric Identities 508 6.2 Sum and Difference Identities 519 6.3 Double-Angle and Half-Angle Identities 531 6.4 Product-to-Sum and Sum-to-Product Identities 547 6.5 Inverse Trigonometric Functions 555 6.6 Trigonometric Equations 576 7 Vectors, the Complex Plane, and Polar Coordinates 602 7.1 Vectors 603 7.2 The Dot Product 619 7.3 Polar (Trigonometric) Form of Complex 7.4 Products, Quotients, Powers, and Roots of Complex Numbers 638 7.5 Polar Coordinates and Graphs of Polar Equations 649 8 Systems of Linear Equations and Inequalities 674 8.1 Systems of Linear Equations in Two Variables 675 8.2 Systems of Linear Equations in Three Variables 691 8.3 Systems of Linear Equations and Matrices 703 8.4 Matrix Algebra 726 8.5 The Determinant of a Square Matrix and Cramer's Rule 751 8.6 Partial Fractions 765 8.7 Systems of Linear Inequalities in Two Variables 776 9 Conics and Systems of Nonlinear Equations and Inequalities 800 9.1 Conic Basics 801 9.2 The Parabola 804 9.3 The Ellipse 818 9.4 The Hyperbola 832 9.5 Systems of Nonlinear Equations 844 9.6 Systems of Nonlinear Inequalities 854 9.7 Rotation of Axes 864 9.8 Polar Equations of Conics 872 9.9 Parametric Equations and Graphs 881 10 Sequences and Series 897 10.1 Sequences and Series 898 10.2 Arithmetic Sequences and Series 909 10.3 Geometric Sequences and Series 918 10.4 Mathematical Induction 929 10.5 The Binomial Theorem 933 11 Limits: A Preview to Calculus 948 11.1 Introduction to Limits: Estimating Limits Numerically and Graphically 949 11.2 Techniques for Finding Limits 961 11.3 Tangent Lines and Derivatives 975 11.4 Limits at Infinity; Limits of Sequences 986 11.5 Finding the Area Under a Curve 995 Review 1010 Review Exercises 1012 Practice Test 1014 Cumulative Test 1015 ANSWERS TO ODD-NUMBERED EXERCISES 1016 APPLICATION INDEX 1076 SUBJECT INDEX 1080 APPENDIX (ONLINE ONLY) *online only

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Book SynopsisFranklin D. Demana Frank Demana received his master's and Ph.D. degrees in mathematics from Michigan State University. Currently, he is Professor Emeritus of Mathematics at The Ohio State University. As an active supporter of the use of technology to teach and learn mathematics, he is cofounder of the international Teachers Teaching with Technology (T3) professional development program. He has been the director or codirector of more than $10 million of National Science Foundation (NSF) and foundational grant activities, including a $3 million grant from the U.S. Department of Education Mathematics and Science Educational Research program awarded to The Ohio State University. Along with frequent presentations at professional meetings, he has published a variety of articles in the areas of computer-and calculator-enhanced mathematics instruction. Dr. Demana is also cofounder (with Bert Waits) of the annual International Conference on Technology in Collegiate MaTable of Contents Functions and Graphs Polynomial, Power, and Rational Functions Exponential, Logistic, and Logarithmic Functions Trigonometric Functions Analytic Trigonometry Applications of Trigonometry Systems and Matrices Analytic Geometry in Two and Three Dimensions Discrete Mathematics Statistics and Probability An Introduction to Calculus: Limits, Derivatives, and Integrals Algebra Review Logic Key Formulas

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Book SynopsisHelps you focus on preparing students for calculus. This book includes a brief algebra review to the core precalculus topics along with coverage of analytic geometry in three dimensions and an introduction to concepts covered in calculus.Table of Contents1. FUNCTIONS AND THEIR GRAPHS. Rectangular Coordinates. Graphs of Equations. Linear Equations in Two Variables. Functions. Analyzing Graphs of Functions. A Library of Parent Functions. Transformations of Functions. Combinations of Functions: Composite Functions. Inverse Functions. Mathematical Modeling and Variation. Chapter Summary. Review Exercises. Chapter Test. Proofs in Mathematics. P.S. Problem Solving. 2. POLYNOMIAL AND RATIONAL FUNCTIONS. Quadratic Functions and Models. Polynomial Functions of Higher Degree. Polynomial and Synthetic Division. Complex Numbers. Zeros of Polynomial Functions. Rational Functions. Nonlinear Inequalities. Chapter Summary. Review Exercises. Chapter Test. Proofs in Mathematics. P.S. Problem Solving. 3. 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. Chapter Summary. Review Exercises. Chapter Test. Cumulative Test for Chapters 1-3. Proofs in Mathematics. P.S. Problem Solving. 4. TRIGONOMETRY. Radian and Degree Measure. Trigonometric Functions: The Unit Circle. Right Triangle Trigonometry. Trigonometric Functions of Any Angle. Graphs of Sine and Cosine Functions. Graphs of Other Trigonometric Functions. Inverse Trigonometric Functions. Applications and Models. Chapter Summary. Review Exercises. Chapter Test. Proofs in Mathematics. P.S. Problem Solving. 5. ANALYTIC TRIGONOMETRY. Using Fundamental Identities. Verifying Trigonometric Identities. Solving Trigonometric Equations. Sum and Difference Formulas. Multiple-Angle and Product-to-Sum Formulas. Chapter Summary. Review Exercises. Chapter Test. Proofs in Mathematics. P.S. Problem Solving. 6. ADDITIONAL TOPICS IN TRIGONOMETRY. Law of Sines. Law of Cosines. Vectors in the Plane. Vectors and Dot Products. Trigonometric Form of a Complex Number. Chapter Summary. Review Exercises. Chapter Test. Cumulative Test for Chapters 4-6. Proofs in Mathematics. P.S. Problem Solving. 7. SYSTEMS OF EQUATIONS AND INEQUALITIES. Linear and Nonlinear Systems of Equations. Two-Variable Linear Systems. Multivariable Linear Systems. Partial Fractions. Systems of Inequalities. Linear Programming. Chapter Summary. Review Exercises. Chapter Test. Proofs in Mathematics. P.S. Problem Solving. 8. MATRICES AND DETERMINANTS. Matrices and Systems of Equations. Operations with Matrices. The Inverse of a Square Matrix. The Determinant of a Square Matrix. Applications of Matrices and Determinants. Chapter Summary. Review Exercises. Chapter Test. Proofs in Mathematics. P.S. Problem Solving. 9. SEQUENCES, SERIES, AND PROBABILITY. Sequences and Series. Arithmetic Sequences and Partial Sums. Geometric Sequences and Series. Mathematical Induction. The Binomial Theorem. Counting Principles. Probability. Chapter Summary. Review Exercises. Chapter Test. Cumulative Test for Chapters 7-9. Proofs in Mathematics. P.S. Problem Solving. 10. TOPICS IN ANALYTIC GEOMETRY. Lines. Introduction to Conics: Parabolas. Ellipses. Hyperbolas. Rotation of Conics. Parametric Equations. Polar Coordinates. Graphs of Polar Equations. Polar Equations of Conics. Chapter Summary. Review Exercises. Chapter Test. Proofs in Mathematics. P.S. Problem Solving. 11. ANALYTIC GEOMETRY IN THREE DIMENSIONS. The Three-Dimensional Coordinate System. Vectors in Space. The Cross Product of Two Vectors. Lines and Planes in Space. Chapter Summary. Review Exercises. Chapter Test. Proofs in Mathematics. P.S. Problem Solving. 12. LIMITS AND AN INTRODUCTION TO CALCULUS. Introduction to Limits. Techniques for Evaluating Limits. The Tangent Line Problem. Limits at Infinity and Limits of Sequences. The Area Problem. Chapter Summary. Review Exercises. Chapter Test. Cumulative Test for Chapters. Proofs in Mathematics. P.S. Problem Solving. APPENDIX A. Review of Fundamental Concepts of Algebra. A.1 Real Numbers and Their Properties. A.2 Exponents and Radicals. A.3 Polynomials and Factoring. A.4 Rational Expressions. A.5 Solving Equations. A.6 Linear Inequalities in One Variable. A.7 Errors and the Algebra of Calculus. APPENDIX B. Concepts in Statistics (web). B.1 Representing Data. B.2 Measures of Central Tendency and Dispersion. B.3 Least Squares Regression.

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Book SynopsisThe easy way to understand and retain all the concepts taught in pre-calculus classes Pre-Calculus All-in-One For Dummies is a great resource if you want to do you best in Pre-Calculus. Packed with lessons, examples, and practice problems in the book, plus extra chapter quizzes online, it gives you absolutely everything you need to succeed in pre-calc. Unlike your textbook, this book presents the essential topics clearly and concisely, so you can really understand the stuff you learn in class, score high on your tests (including the AP Pre-Calculus exam!), and get ready to confidently move ahead to upper-level math courses. And if you need a refresher before launching into calculus, look no furtherthis book has your back. Review what you learned in algebra and geometry, then dig into pre-calculus Master logarithms, exponentials, conic sections, linear equations, and beyond Get easy-to-understand explanations that match the methods your teaTable of ContentsIntroduction 1 Unit 1: Getting Started with Pre-Calculus 5 Chapter 1: Preparing for Pre-Calculus 7 Chapter 2: Operating with Real Numbers 25 Chapter 3: Cementing the Building Blocks of Pre-Calculus Functions 43 Chapter 4: Operating on Functions 65 Unit 2: Getting the Grip on Graphing 93 Chapter 5: Graphing Polynomial Functions 95 Chapter 6: Exponential and Logarithmic Functions 131 Chapter 7: Piece-Wise and Greatest-Integer Functions 159 Unit 3: The Essentials of Trigonometry 171 Chapter 8: Circling In on Angles 173 Chapter 9: Homing In on the Friendliest Angles 201 Chapter 10: Picturing Basic Trig Functions and Reciprocal Functions 217 Chapter 11: Graphing and Transforming Trig Functions 237 Unit 4: Identities and Special Triangles 267 Chapter 12: Identifying with Trig Identities: The Basics 269 Chapter 13: Advancing with Advanced Identities 297 Chapter 14: Getting the Slant on Oblique Triangles 327 Unit 5: Analytic Geometry 361 Chapter 15: Coordinating with Complex Numbers 363 Chapter 16: Warming Up to Polar Coordinates 379 Chapter 17: Relating Conics to Sliced Cones 399 Unit 6: Systems, Sequences, and Series 443 Chapter 18: Streamlining Systems of Equations 445 Chapter 19: Making Matrices Work 473 Chapter 20: Sequences and Series 499 Chapter 21: Expanding Binomials for the Real World 519 Unit 7: Onward to Calculus 533 Chapter 22: Lining Up the Tools 535 Chapter 23: Proceeding with Successful Procedures 557 Index 573

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Book SynopsisEach step higher in math studies is crucial to doing well at the next level. Pre-Calc is the gateway to higher level mathematics of which the best degrees and careers are built upon. The core essentials in 6 laminated pages can be used along with your text and lectures, as a review before testing, or as a memory companion that keeps key answers always at your fingertips. The most answers for your money in what students have said is 'a must have' study tool. Suggested uses: Quick Reference -- instead of digging into the textbook to find a core answer you need while studying, use the guide to reinforce quickly and repeatedly; Memory -- refreshing your memory repeatedly is a foundation of studying, have the core answers handy so you can focus on understanding the concepts; Test Prep -- no student should be cramming, but if you are, there is no better tool for that final review.

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Book SynopsisAn open textbook covering pre-calculus including trigonometry. The first portion of the book is an investigation of functions, exploring the graphical behavior of, interpretation of, and solutions to problems involving linear, polynomial, rational, exponential, and logarithmic functions. The second portion of the book introduces trigonometry. Trig is introduced through an integrated circle/triangle approach. Identities are introduced in the first chapter, and revisited throughout. Likewise, solving is introduced in the second chapter and revisited more extensively in the third chapter. An emphasis is placed on modeling and interpretation, as well as the important characteristics needed in calculus.

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