Description: Chapter 1: Precalculus Review 1.1 Real Numbers, Functions, and Graphs 1.2 Linear and Quadratic Functions 1.3 The Basic Classes of Functions 1.4 Trigonometric Functions 1.5 Inverse Functions 1.6 Exponential and Logarithmic Functions 1.7 Technology Calculators and Computers Chapter 2: Limits 2.1 Limits, Rates of Change, and Tangent Lines 2.2 Limits: A Numerical and Graphical Approach2.3 Basic Limit Laws 2.4 Limits and Continuity 2.5 Evaluating Limits Algebraically 2.6 Trigonometric Limits 2.7 Limits at Infinity 2.8 Intermediate Value Theorem 2.9 The Formal Definition of a Limit Chapter 3: Differentiation 3.1 Definition of the Derivative 3.2 The Derivative as a Function 3.3 Product and Quotient Rules 3.4 Rates of Change 3.5 Higher Derivatives 3.6 Trigonometric Functions 3.7 The Chain Rule 3.8 Derivatives of Inverse Functions 3.9 Derivatives of General Exponential and Logarithmic Functions 3.10 Implicit Differentiation 3.11 Related Rates Chapter 4: Applications of the Derivative 4.1 Linear Approximation and Applications 4.2 Extreme Values 4.3 The Mean Value Theorem and Monotonicity 4.4 The Shape of a Graph 4.5 L'Hopital's Rule 4.6 Graph Sketching and Asymptotes 4.7 Applied Optimization 4.8 Newton's Method 4.9 Antiderivatives Chapter 5: The Integral 5.1 Approximating and Computing Area 5.2 The Definite Integral 5.3 The Fundamental Theorem of Calculus, Part I 5.4 The Fundamental Theorem of Calculus, Part II 5.5 Net Change as the Integral of a Rate 5.6 Substitution Method 5.7 Further Transcendental Functions 5.8 Exponential Growth and Decay Chapter 6: Applications of the Integral 6.1 Area Between Two Curves 6.2 Setting Up Integrals: Volume, Density, Average Value 6.3 Volumes of Revolution 6.4 The Method of Cylindrical Shells 6.5 Work and Energy Chapter 7: Techniques of Integration 7.1 Integration by Parts 7.2 Trigonometric Integrals 7.3 Trigonometric Substitution 7.4 Integrals Involving Hyperbolic and Inverse Hyperbolic Functions 7.5 The Method of Partial Fractions 7.6 Improper Integrals 7.7 Probability and Integration 7.8 Numerical Integration Chapter 8: Further Applications of the Integral and Taylor Polynomials 8.1 Arc Length and Surface Area 8.2 Fluid Pressure and Force 8.3 Center of Mass 8.4 Taylor Polynomials Chapter 9: Introduction to Differential Equations 9.1 Solving Differential Equations 9.2 Models Involving y' = k (y-b) 9.3 Graphical and Numerical Methods 9.4 The Logistic Equation 9.5 First-Order Linear Equations Chapter 10: Infinite Series 10.1 Sequences 10.2 Summing an Infinite Series 10.3 Convergence of Series with Positive Terms 10.4 Absolute and Conditional Convergence 10.5 The Ratio and Root Tests 10.6 Power Series 10.7 Taylor Series Chapter 11: Parametric Equations, Polar Coordinates, and Conic Sections 11.1 Parametric Equations 11.2 Arc Length and Speed 11.3 Polar Coordinates 11.4 Area and Arc Length in Polar Coordinates 11.5 Conic Sections Chapter 12: Vector Geometry 12.1 Vectors in the Plane 12.2 Vectors in Three Dimensions 12.3 Dot Product and the Angle Between Two Vectors 12.4 The Cross Product 12.5 Planes in Three-Space 12.6 A Survey of Quadric Surfaces 12.7 Cylindrical and Spherical Coordinates

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