Technical Calculus with Analytic Geometry (Dover Books on Mathematics)

This well-thought-out text, filled with many special features, is designed for a two-semester course in calculus for technology students with a background in college algebra and trigonometry. The author has taken special care to make the book appealing to students by providing motivating examples, facilitating an intuitive understanding of the underlying concepts involved, and by providing much opportunity to gain proficiency in techniques and skills.
Initial chapters cover functions and graphs, straight lines and conic sections, new coordinate systems, the derivative, using the derivative, integration and using the integral. The last four chapters focus on derivatives of transcendental functions, patterns for integrations, series expansion of functions, and differential equations.
Throughout, the writing style is clear, readable and informal. Examples are abundant and have complete worked solutions. Practice problems appear in the body of the text in each section; these are relatively easy and are intended to be worked by the student as soon as they are encountered. Each new type of example in the text is followed by a practice problem that allows the student to gain immediate reinforcement in applying the problem-solving technique illustrated by the example. Answers to all practice problems are given at the back of the book, many with worked-out solutions.
Other learning aids include the division of complex problem-solving processes into a series of step-by-step tasks, numerous exercises at the end of each section and a Status Check at the end of each chapter that helps students review what they have learned. Additional review exercises and a glossary, with definitions and page references, round out the book.

Preface to the Instructor Note to the Student 1 Functions and Graphs 1.1 Functions 1.2 Types of Functions 1.3 Graphing 1.4 Distance Formula and Slope STATUS CHECK 1.5 More Exercises for Chapter 1 2 Straight Lines and Conic Sections 2.1 Why Analytic Geometry 2.2 The Straight Line 2.3 The Parabola 2.4 The Ellipse and Circle 2.5 The Hyperbola 2.6 The Second-Degree Equation STATUS CHECK 2.7 More Exercises for Chapter 2 3 New Coordinate Systems 3.1 Graphing in Three Dimensions 3.2 Polar Coordinates 3.3 Polar Graphs STATUS CHECK 3.4 More Exercises for Chapter 3 4 The Derivative 4.1 Introduction 4.2 Limits 4.3 The Definition of the Derivative 4.4 General Interpretation of the Derivative 4.5 Differentiating Polynomials 4.6 Differentiating Products and Quotients 4.7 Differentiating Powers of Functions 4.8 Higher-Order Derivatives 4.9 Implicit Differentiation 4.10 Partial Derivatives STATUS CHECK 4.11 More Exercises for Chapter 4 5 Using the Derivative 5.1 Tangents and Normals 5.2 Curve Sketching 5.3 Maxima and Minima 5.4 Motion 5.5 Related Rates 5.6 Differentials 5.7 Applications of Partial Derivatives STATUS CHECK 5.8 More Exercises for Chapter 5 6 Integration 6.1 The Indefinite Integral 6.2 Area Under a Curve; the Definite Integral 6.3 The Fundamental Theorem STATUS CHECK 6.4 More Exercises for Chapter 6 7 Using the Integral 7.1 Indefinite Integral 7.2 Area 7.3 Volume 7.4 Moments 7.5 Fluid Pressure and Force 7.6 Other Applications 7.7 Double Integrals STATUS CHECK 7.8 More Exercises for Chapter 7 8 Derivatives of Transcendental Functions 8.1 Quick Trigonometry Review 8.2 Derivative of the Sine Function 8.3 Derivatives of Other Trigonometric Functions 8.4 Inverse Trigonometric Functions and Their Derivatives 8.5 Applications 8.6 The Exponential and Logarithmic Functions 8.7 Derivatives of Logarithmic and Exponential Functions 8.8 Applications STATUS CHECK 8.9 More Exercises for Chapter 8 9 Patterns for Integration 9.1 The Power Rule 9.2 The Logarithmic Form 9.3 The Exponential Form 9.4 Basic Trigonometric Forms 9.5 Tricks for Trigonometric Integrals 9.6 Inverse Trigonometric Forms 9.7 Integration by Parts 9.8 Integration by Trigonometric Substitution 9.9 Integration by Partial Functions 9.10 Integration Tables 9.11 Approximate Methods STATUS CHECK 9.12 More Exercises for Chapter 9 10 Series Expansion of Functions 10.1 Infinite Series 10.2 Maclaurin Series 10.3 Operating with Series 10.4 Computing with Series 10.5 Taylor Series 10.6 Fourier Series STATUS CHECK 10.7 More Exercises for Chapter 10 11 Differential Equations 11.1 Differential Equations and Their Solutions 11.2 Separation of Variables 11.3 Regrouping to Advantage 11.4 First-Order Linear Differential Equations 11.5 Applications 11.6 Approximation Techniques 11.7 Second-Order Linear Homogeneous Equations 11.8 Repeated or Complex Roots 11.9 Nonhomogeneous Equations 11.10 Applications 11.11 Laplace Transforms 11.12 Differential Equations and Laplace Transforms STATUS CHECK 11.13 More Exercises for Chapter 11 Glossary Appendices 1. Table of Geometric Formulas 2. International System of Units 3. Table of Integrals Answers to Practice Problems Answers to Odd-Numbered Exercises Index