Calculus I with Precalculus

Carefully developed for one-year courses that combine and integrate material from Precalculus through Calculus I, this text is ideal for instructors who wish to successfully bring students up to speed algebraically within precalculus and transition them into calculus. The Larson Calculus texts continue to offer instructors and students new and innovative teaching and learning resources. The Calculus series was the first to use computer-generated graphics, to include exercises involving the use of computers and graphing calculators, to be available in an interactive CD-ROM format, to be offered as a complete, online calculus course, and to offer this two-semester Calculus I with Precalculus text. Every edition of the series has made the mastery of traditional calculus skills a priority, while embracing the best features of new technology and, when appropriate, calculus reform ideas. Two primary objectives guided the authors in writing this book: to develop precise, readable materials for students that clearly define and demonstrate concepts and rules of calculus and to design comprehensive teaching resources for instructors that employ proven pedagogical techniques and saves the instructor time.

Table of Contents:
Note: Each chapter concludes with Problem Solving. P. Prerequisites P.1 Solving Equations Section Project: Projectile Motion P.2 Solving Inequalities P.3 Graphical Representation of Data P.4 Graphs of Equations P.5 Linear Equations in Two Variables 1. Functions and Their Graphs 1.1 Functions 1.2 Analyzing Graphs of Functions 1.3 Shifting, Reflecting, and Stretching Graphs 1.4 Combinations of Functions 1.5 Inverse Functions 1.6 Mathematical Modeling Section Project: Hooke's Law 2. Polynomial and Rational Functions 2.1 Quadratic Functions 2.2 Polynomial Functions of Higher Degree 2.3 Polynomial and Synthetic Division 2.4 Complex Numbers Section Project: The Mandelbrot Set 2.5 The Fundamental Theorem of Algebra 2.6 Rational Functions Section Project: Rational Functions 3. Limits and Their Properties 3.1 A Preview of Calculus 3.2 Finding Limits Graphically and Numerically 3.3 Evaluating Limits Analytically 3.4 Continuity and One-Sided Limits 3.5 Infinite Limits Section Project: Graphs and Limits of Functions Progressive Summary 1: Flowchart of Calculus 4. Differentiation 4.1 The Derivative and the Tangent Line Problem 4.2 Basic Differentiation Rules and Rates of Change 4.3 The Product and Quotient Rules and Higher-Order Derivatives 4.4 The Chain Rule 4.5 Implicit Differentiation Section Project: Optical Illusions 4.6 Related Rates 5. Applications of Differentiation 5.1 Extrema on an Interval 5.2 Rolle's Theorem and the Mean Value Theorem 5.3 Increasing and Decreasing Functions and the First Derivative Test 5.4 Concavity and the Second Derivative Test 5.5 Limits at Infinity 5.6 A Summary of Curve Sketching 5.7 Optimization Problems Section Project: Connecticut River 5.8 Differentials 6. Integration 6.1 Antiderivatives and Indefinite Integration 6.2 Area 6.3 Riemann Sums and Definite Integrals 6.4 The Fundamental Theorem of Calculus Section Project: Demonstrating the Fundamental Theorem 6.5 Integration by Substitution 6.6 Numerical Integration Progressive Summary 2: Flowchart of Calculus 7. Exponential and Logarithmic Functions 7.1 Exponential Functions and Their Graphs 7.2 Logarithmic Functions and Their Graphs 7.3 Using Properties of Logarithms 7.4 Exponential and Logarithmic Equations 7.5 Exponential and Logarithmic Models Section Project: Comparing Models 8. Exponential and Logarithmic Functions and Calculus 8.1 Exponential Functions: Differentiation and Integration 8.2 Logarithmic Functions and Differentiation Section Project: An Alternate Definition of ln x 8.3 Logarithmic Functions and Integration 8.4 Differential Equations: Growth and Decay Progressive Summary 3: Flowchart of Calculus 9. Trigonometric Functions 9.1 Radian and Degree Measure 9.2 Trigonometric Functions: The Unit Circle 9.3 Right Triangle Trigonometry 9.4 Trigonometric Functions of Any Angle 9.5 Graphs of Sine and Cosine Functions Section Project: Approximating Sine and Cosine Functions 9.6 Graphs of Other Trigonometric Functions 9.7 Inverse Trigonometric Functions 9.8 Applications and Models 10. Analytic Trigonometry 10.1 Using Fundamental Trigonometric Identities 10.2 Verifying Trigonometric Identities 10.3 Solving Trigonometric Equations Section Project: Modeling a Sound Wave 10.4 Sum and Difference Formulas 10.5 Multiple-Angle and Product-to-Sum Formulas 11. Trigonometric Functions and Calculus 11.1 Limits of Trigonometric Functions Section Project: Graphs and Limits of Trigonometric Functions 11.2 Trigonometric Functions: Differentiation 11.3 Trigonometric Functions: Integration 11.4 Inverse Trigonometric Functions: Differentiation 11.5 Inverse Trigonometric Functions: Integration 11.6 Hyperbolic Functions Section Project: St. Louis Arch Progressive Summary 4: Flowchart of Calculus 12. Topics in Analytic Geometry 12.1 Introduction to Conics: Parabolas 12.2 Ellipses and Implicit Differentiation 12.3 Hyperbolas and Implicit Differentiation 12.4 Parametric Equations and Calculus 12.5 Polar Coordinates and Calculus 12.6 Graphs of Polar Equations 12.7 Polar Equations of Conics Section Project: Polar Equations of Planetary Orbits Progressive Summary 5: Flowchart of Calculus 13. Additional Topics in Trigonometry 13.1 Law of Sines 13.2 Law of Cosines 13.3 Vectors in the Plane Section Project: Adding Vectors Graphically 13.4 Vectors and Dot Products 13.5 Trigonometric Form of a Complex Number 14. Systems of Equations and Matrices 14.1 Systems of Linear Equations in Two Variables 14.2 Multivariable Linear Systems 14.3 Systems of Inequalities Section Project: Area Bounded by Concentric Circles 14.4 Matrices and Systems of Equations 14.5 Operations with Matrices 14.6 The Inverse of a Square Matrix 14.7 The Determinant of a Square Matrix Section Project: Cramer's Rule Appendices A. Proofs of Selected Theorems B. Applications of Integration C. Study Capsules 1. Graphing Algebraic Functions 2. Limits of Algebraic Functions 3. Differentiation of Algebraic Functions 4. Calculus of Algebraic Functions 5. Calculus of Exponential and Logarithmic Functions 6. Trigonometric Functions 7. Calculus of Trigonometric and Inverse Trigonometric Functions

About the Author :
Dr. Ron Larson is a professor of mathematics at The Pennsylvania State University, where he has taught since 1970. He received his Ph.D. in mathematics from the University of Colorado and is considered the pioneer of using multimedia to enhance the learning of mathematics, having authored over 30 software titles since 1990. Dr. Larson conducts numerous seminars and in-service workshops for math educators around the country about using computer technology as an instructional tool and motivational aid. He is the recipient of the 2014 William Holmes McGuffey Longevity Award for CALCULUS: EARLY TRANSCENDENTAL FUNCTIONS, the 2014 Text and Academic Authors Association TEXTY Award for PRECALCULUS, the 2012 William Holmes McGuffey Longevity Award for CALCULUS: AN APPLIED APPROACH, and the 1996 Text and Academic Authors Association TEXTY Award for INTERACTIVE CALCULUS (a complete text on CD-ROM that was the first mainstream college textbook to be offered on the Internet). Dr. Larson authors numerous textbooks including the best-selling Calculus series published by Cengage Learning. The Pennsylvania State University, The Behrend College Bio: Robert P. Hostetler received his Ph.D. in mathematics from The Pennsylvania State University in 1970. He has taught at Penn State for many years and has authored several calculus, precalculus, and intermediate algebra textbooks. His teaching specialties include remedial algebra, calculus, and math education, and his research interests include mathematics education and textbooks. Dr. Bruce H. Edwards is Professor of Mathematics at the University of Florida. Professor Edwards received his B.S. in Mathematics from Stanford University and his Ph.D. in Mathematics from Dartmouth College. He taught mathematics at a university near Bogota, Colombia, as a Peace Corps volunteer. While teaching at the University of Florida, Professor Edwards has won many teaching awards, including Teacher of the Year in the College of Liberal Arts and Sciences, Liberal Arts and Sciences Student Council Teacher of the Year, and the University of Florida Honors Program Teacher of the Year. He was selected by the Office of Alumni Affairs to be the Distinguished Alumni Professor for 1991-1993. Professor Edwards has taught a variety of mathematics courses at the University of Florida, from first-year calculus to graduate-level classes in algebra and numerical analysis. He has been a frequent speaker at research conferences and meetings of the National Council of Teachers of Mathematics. He has also coauthored a wide range of award winning mathematics textbooks with Professor Ron Larson.