Quick Calculus: A Self-Teaching Guide

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Cover Title Page Copyright Preface Contents Chapter 1 Starting Out 1.1 A Few Preliminaries 1.2 Functions 1.3 Graphs 1.4 Linear and Quadratic Functions 1.5 Angles and Their Measurements 1.6 Trigonometry 1.7 Exponentials and Logarithms Summary of Chapter 1 1.2 Functions (frames 3–13) 1.3 Graphs (frames 14–22) 1.4 Linear and Quadratic Functions (frames 23–39) 1.5–1.6 Angles and Their Measurements; Trigonometry (frames 40–74) 1.7 Exponentials and Logarithms (frames 75–95) Chapter 2 Differential Calculus 2.1 The Limit of a Function 2.2 Velocity 2.3 Derivatives 2.4 Graphs of Functions and Their Derivatives 2.5 Differentiation 2.6 Some Rules for Differentiation 2.7 Differentiating Trigonometric Functions 2.8 Differentiating Logarithms and Exponentials 2.9 Higher‐Order Derivatives 2.10 Maxima and Minima 2.11 Differentials 2.12 A Short Review and Some Problems Conclusion to Chapter 2 Summary of Chapter 2 2.1 Limit of a Function (frames 97–115) 2.2 Velocity (frames 116–145) 2.3 Derivatives (frames 146–159) 2.4 Graphs of Functions and Their Derivatives (frames 160–169) 2.5–2.8 Differentiation (frames 170–241) 2.9 Higher‐Order Derivatives (frames 242–249) 2.10 Maxima and Minima (frames 250–263) 2.11 Differentials (frames 264–273) Chapter 3 Integral Calculus 3.1 Antiderivative, Integration, and the Indefinite Integral 3.2 Some Techniques of Integration 3.3 Area Under a Curve and the Definite Integral 3.4 Some Applications of Integration 3.5 Multiple Integrals Conclusion to Chapter 3 Summary of Chapter 3 3.1 Antiderivative, Integration, and the Indefinite Integral (frames 306–314) 3.2 Some Techniques of Integration (frames 315–334) 3.3 Area under a Curve and Definite Integrals (frames 335–367) 3.4 Some Applications of Integration (frames 368–389) 3.5 Multiple Integrals (frames 390–399) Chapter 4 Advanced Topics: Taylor Series, Numerical Integration, and Differential Equations 4.1 Taylor Series 4.2 Numerical Integration 4.3 Differential Equations 4.4 Additional Problems for Chapter 4 Summary of Chapter 4 4.1 Taylor's Theorem (frames 400–417) 4.2 Numerical Integration (frames 419–422) 4.3 Differential Equations (frames 423–437) Conclusion (frame 449) Appendix A Derivations A.1 Trigonometric Functions of Sums of Angles A.2 Some Theorems on Limits A.3 Exponential Function A.4 Proof That dy/dx = 1/dx/dy A.5 Differentiating xn A.6 Differentiating Trigonometric Functions A.7 Differentiating the Product of Two Functions A.8 Chain Rule for Differentiating A.9 Differentiating ln x A.10 Differentials When Both Variables Depend on a Third Variable A.11 Proof That if Two Functions Have the Same Derivative They Differ Only by a Constant A.12 Limits Involving Trigonometric Functions Appendix B Additional Topics in Differential Calculus B.1 Implicit Differentiation B.2 Differentiating the Inverse Trigonometric Functions B.3 Partial Derivatives B.4 Radial Acceleration in Circular Motion B.5 Resources for Further Study Frame Problems Answers Answers to Selected Problems from the Text Chapter 1: A Few Preliminaries Chapter 2: Differential Calculus Chapter 3: Integral Calculus Review Problems Chapter 1 Chapter 2 Chapter 3 Tables Table 1: Derivatives Table 2: Integrals Index Index of Symbols EULA