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Rogawski/Adams: Calculus 3e Single VariableChapter 1: Precalculus Review 1.1 Real Numbers, Functions, and Graphs1.2 Linear and Quadratic Functions1.3 The Basic Classes of Functions1.4 Trigonometric Functions1.5 Technology: Calculators and ComputersChapter Review Exercises
Chapter 2: Limits 2.1 Limits, Rates of Change, and Tangent Lines2.2 Limits: A Numerical and Graphical Approach2.3 Basic Limit Laws2.4 Limits and Continuity2.5 Evaluating Limits Algebraically2.6 Trigonometric Limits2.7 Limits at Infinity2.8 Intermediate Value Theorem2.9 The Formal Definition of a LimitChapter Review Exercises
Chapter 3: Differentiation3.1 Definition of the Derivative3.2 The Derivative as a Function3.3 Product and Quotient Rules3.4 Rates of Change3.5 Higher Derivatives3.6 Trigonometric Functions3.7 The Chain Rule3.8 Implicit Differentiation3.9 Related RatesChapter Review Exercises
Chapter 4: Applications of the Derivative 4.1 Linear Approximation and Applications4.2 Extreme Values4.3 The Mean Value Theorem and Monotonicity4.4 The Shape of a Graph4.5 Graph Sketching and Asymptotes4.6 Applied Optimizations4.7 Newton’s MethodChapter Review Exercises Chapter 5: The Integral5.1 Approximating and Computing Area5.2 The Definite Integral5.3 The Indefinite Integral5.4 The Fundamental Theorem of Calculus, Part I5.5 The Fundamental Theorem of Calculus, Part II5.6 Net Change as the Integral of a Rate5.7 Substitution Method Chapter Review Exercises
Chapter 6: Applications of the Integral6.1 Area Between Two Curves6.2 Setting Up Integrals: Volume, Density, Average Value6.3 Volumes of Revolution6.4 The Method of Cylindrical Shells6.5 Work and Energy Chapter Review Exercises
Chapter 7: Exponential Functions7.1 Derivative of f(x)=bx and the Number e7.2 Inverse Functions7.3 Logarithms and their Derivatives7.4 Exponential Growth and Decay7.5 Compound Interest and Present Value7.6 Models Involving y’= k(y-b)7.7 L’Hôpital’s Rule7.8 Inverse Trigonometric Functions7.9 Hyperbolic FunctionsChapter Review Exercises
Chapter 8: Techniques of Integration8.1 Integration by Parts8.2 Trigonometric Integrals8.3 Trigonometric Substitution8.4 Integrals Involving Hyperbolic and Inverse Hyperbolic Functions8.5 The Method of Partial Fractions8.6 Strategies for Integration8.7 Improper Integrals 8.8 Probability and Integration8.9 Numerical IntegrationChapter Review Exercises
Chapter 9: Further Applications of the Integral and Taylor Polynomials 9.1 Arc Length and Surface Area9.2 Fluid Pressure and Force9.3 Center of Mass9.4 Taylor PolynomialsChapter Review Exercises
Chapter 10: Introduction to Differential Equations10.1 Solving Differential Equations10.2 Graphical and Numerical Methods10.3 The Logistic Equation10.4 First-Order Linear EquationsChapter Review Exercises
Chapter 11: Infinite Series11.1 Sequences 11.2 Summing an Infinite Series11.3 Convergence of Series with Positive Terms11.4 Absolute and Conditional Convergence11.5 The Ratio and Root Tests11.6 Power Series11.7 Taylor SeriesChapter Review Exercises
Chapter 12: Parametric Equations, Polar Coordinates, and Conic Sections 12.1 Parametric Equations12.2 Arc Length and Speed12.3 Polar Coordinates12.4 Area and Arc Length in Polar Coordinates12.5 Conic SectionsChapter Review Exercises
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