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 Single Variable version only includes chapters 1-11, Appendices A-C, Calculus Easy Reference, and Answers to Odd Problems. Multivariable version contains chapters 12 - 20. Chapter 1. A Library of Functions1.1. Functions and Change1.2. Exponential Functions 1.3. New Functions From Old 1.4. Logarithmic Functions 1.5. Trigonometric Functions 1.6. Powers, Polynomials, and Rational Functions 1.7. Introduction to Continuity 1.8. Limits Review Problems Check Your Understanding Projects Chapter 2. Key Concept: The Derivative2.1. How Do We Measure Speed?2.2. The Derivative at a Point 2.3. The Derivative Function 2.4. Interpretations of the Derivative 2.5. The Second Derivative 2.6. Differentiability Review Problems Check Your Understanding Projects Chapter 3. Short-Cuts to Differentiation3.1. Powers and Polynomials3.2. The Exponential Function 3.3. The Product and Quotient Rules 3.4. The Chain Rule 3.5. The Trigonometric Functions 3.6. The Chain Rule and Inverse Functions 3.7. Implicit Functions 3.8. Hyperbolic Functions 3.9. Linear Approximation and the Derivative 3.10. Theorems About Differentiable Functions Review Problems Check Your Understanding Projects Chapter 4. Using the Derivative4.1. Using First and Second Derivatives4.2. Families of Curves 4.3. Optimization 4.4. Applications of Marginality 4.5. Optimization and Modeling 4.6. Rates and Related Rates 4.7. L’Hopital’s Rule, Growth, and Dominance 4.8. Parametric Equations Review Problems Check Your Understanding Projects Chapter 5. Key Concept: The Definite Integral5.1. How Do We Measure Distance Traveled?5.2. The Definite Integral 5.3. The Fundamental Theorem and Interpretations 5.4. Theorems About Definite Integrals Review Problems Check Your Understanding Projects Chapter 6. Constructing Antiderivatives6.1. Antiderivatives Graphically and Numerically6.2. Constructing Antiderivatives Analytically 6.3. Differential Equations 6.4. Second Fundamental Theorem of Calculus 6.5. The Equation of Motion Review Problems Check Your Understanding Projects Chapter 7. Integration7.1. Integration By Substitution7.2. Integration By Parts 7.3. Tables of Integrals 7.4. Algebraic Identitites and Trigonometric Substitutions 7.5. Approximating Definite Integrals 7.6. Approximating Errors and Simpson’s Rule 7.7. Improper Integrals 7.8. Comparison of Improper Integrals Review Problems Check Your Understanding Projects Chapter 8. Using the Definite Integral8.1. Areas and Volumes8.2. Applications to Geometry 8.3. Area and Arc Length in Polar Coordinates 8.4. Density and Center of Mass 8.5. Applications to Physics 8.6. Applications to Economics 8.7. Distribution Functions 8.8. Probability, Mean, and Median Review Problems Check Your Understanding Projects Chapter 9. Sequences and Series9.1. Sequences9.2. Geometric Series 9.3. Convergence of Series 9.4. Tests for Convergence 9.5. Power Series and Interval of Convergence Review Problems Check Your Understanding Projects Chapter 10. Approximating Functions Using Series10.1. Taylor Polynomials10.2. Taylor Series 10.3. Finding and Using Taylor Series 10.4. The Error in Taylor Polynomial Approximations 10.5. Fourier Series Review Problems Check Your Understanding Projects Chapter 11. Differential Equations11.1. What is a Differential Equation?11.2. Slope Fields 11.3. Euler’s Method 11.4. Separation of Variables 11.5. Growth and Decay 11.6. Applications and Modeling 11.7. Models of Population Growth 11.8. Systems of Differential Equations 11.9. Analyzing the Phase Plane 11.10. Second-Order Differential Equations: Oscillations 11.11. Linear Second-Order Differential Equations Review Problems Check Your Understanding Projects Chapter 12. Functions of Several Variables12.1. Functions of Two Variables12.2. Graphs of Functions of Two Variables 12.3. Contour Diagrams 12.4. Linear Functions 12.5. Functions of Three Variables 12.6. Limits and Continuity Review Problems Check Your Understanding Projects Chapter 13. A Fundamental Tool: Vectors13.1. Displacement Vectors13.2. Vectors in General 13.3. The Dot Product 13.4. The Cross Product Review Problems Check Your Understanding Projects Chapter 14. Differentiating Functions of Many Variables14.1. The Partial Derivative14.2. Computing Partial Derivatives Algebraically 14.3. Local Linearity and the Differential 14.4. Gradients and Directional Derivatives in the Plane 14.5. Gradients and Directional Derivatives in Space 14.6. The Chain Rule 14.7. Second-Order Partial Derivatives 14.8. Differentiability Review Problems Check Your Understanding Projects Chapter 15. Optimization: Local and Global Extrema15.1. Local Extrema15.2. Optimization 15.3. Constrained Optimization: LaGrange Multipliers Review Problems Check Your Understanding Projects Chapter 16. Integrating Functions of Many Variables16.1. The Definite Integral of a Function of Two Variables16.2. Iterated Integrals 16.3. Triple Integrals 16.4. Double Integrals in Polar Coordinates 16.5. Integrals in Cylindrical and Spherical Coordinates 16.6. Applications of Integration to Probability 16.7. Change of Variables in a Multiple Integral Review Problems Check Your Understanding Projects Chapter 17. Parameterized Curves and Vector Fields17.1. Parameterized Curves17.2. Motion, Velocity, and Acceleration 17.3. Vector Fields 17.4. The Flow of a Vector Field 17.5. Parameterized Surfaces Review Problems Check Your Understanding Projects Chapter 18. Line Integrals18.1. The Idea of a Line Integral18.2. Computing Line Integrals Over Parameterized Curves 18.3. Gradient Fields and Path-Independent Fields 18.4. Path-Dependent Vector Fields and Green’s Theorem Review Problems Check Your Understanding Projects Chapter 19. Flux Integrals19.1. The Idea of a Flux Integral19.2. Flux Integrals for Graphs, Cylinders, and Spheres 19.3. Flux Integrals Over Parameterized Surfaces Review Problems Check Your Understanding Projects Chapter 20. Calculus of Vector Fields20.1. The Divergence of a Vector Field20.2. The Divergence Theorem 20.3. The Curl of a Vector Field 20.4. Stokes’ Theorem 20.5. The Three Fundamental Theorems Review Problems Check Your Understanding Projects Appendix A: Roots, Accuracy, and Bounds Appendix B: Complex Numbers Appendix C: Newton’s Method Appendix D: Determinants Calculus Easy Reference Answers to Odd Problems Index |