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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|
|Solving Equations Section Project: Projectile Motion|
|Graphical Representation of Data|
|Graphs of Equations|
|Linear Equations in Two Variables|
|Functions and Their Graphs|
|Analyzing Graphs of Functions|
|Shifting, Reflecting, and Stretching Graphs|
|Combinations of Functions|
|Mathematical Modeling Section Project: Hooke's Law|
|Polynomial and Rational Functions|
|Polynomial Functions of Higher Degree|
|Polynomial and Synthetic Division|
|Complex Numbers Section Project: The Mandelbrot Set|
|The Fundamental Theorem of Algebra|
|Rational Functions Section Project: Rational Functions|
|Limits and Their Properties|
|A Preview of Calculus|
|Finding Limits Graphically and Numerically|
|Evaluating Limits Analytically|
|Continuity and One-Sided Limits|
|Infinite Limits Section Project: Graphs and Limits of Functions Progressive Summary 1: Flowchart of Calculus|
|The Derivative and the Tangent Line Problem|
|Basic Differentiation Rules and Rates of Change|
|The Product and Quotient Rules and Higher-Order Derivatives|
|The Chain Rule|
|Implicit Differentiation Section Project: Optical Illusions|
|Applications of Differentiation|
|Extrema on an Interval|
|Rolle's Theorem and the Mean Value Theorem|
|Increasing and Decreasing Functions and the First Derivative Test|
|Concavity and the Second Derivative Test|
|Limits at Infinity|
|A Summary of Curve Sketching|
|Optimization Problems Section Project: Connecticut River|
|Antiderivatives and Indefinite Integration|
|Riemann Sums and Definite Integrals|
|The Fundamental Theorem of Calculus Section Project: Demonstrating the Fundamental Theorem|
|Integration by Substitution|
|Numerical Integration Progressive Summary 2: Flowchart of Calculus|
|Exponential and Logarithmic Functions|
|Exponential Functions and Their Graphs|
|Logarithmic Functions and Their Graphs|
|Using Properties of Logarithms|
|Exponential and Logarithmic Equations|
|Exponential and Logarithmic Models Section Project: Comparing Models|
|Exponential and Logarithmic Functions and Calculus|
|Exponential Functions: Differentiation and Integration|
|Logarithmic Functions and Differentiation Section Project: An Alternate Definition of ln x|
|Logarithmic Functions and Integration|
|Differential Equations: Growth and Decay Progressive Summary 3: Flowchart of Calculus|
|Radian and Degree Measure|
|Trigonometric Functions: The Unit Circle|
|Right Triangle Trigonometry|
|Trigonometric Functions of Any Angle|
|Graphs of Sine and Cosine Functions Section Project: Approximating Sine and Cosine Functions|
|Graphs of Other Trigonometric Functions|
|Inverse Trigonometric Functions|
|Applications and Models|
|Using Fundamental Trigonometric Identities|
|Verifying Trigonometric Identities|
|Solving Trigonometric Equations Section Project: Modeling a Sound Wave|
|Sum and Difference Formulas|
|Multiple-Angle and Product-to-Sum Formulas|
|Trigonometric Functions and Calculus|
|Limits of Trigonometric Functions Section Project: Graphs and Limits of Trigonometric Functions|
|Trigonometric Functions: Differenti|
|Table of Contents provided by Publisher. All Rights Reserved.|