Table of Contents:
Chapter 0: Preliminaries
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0.1 Polynomials and Rational Functions"
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0.2 Graphing Calculators and Computer Algebra Systems"
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0.3 Inverse Functions"
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0.4 Trigonometric and Inverse Trigonometric Functions"
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0.5 Exponential and Logarithmic Functions"
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0.6 Transformations of Functions"
Chapter 1: Limits and Continuity
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1.1 A Brief Preview of Calculus: Tangent Lines and the Length of a Curve
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1.2 The Concept of Limit"
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1.3 Computation of Limits"
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1.4 Continuity and Its Consequences"
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1.5 Limits Involving Infinity; Asymptotes"
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1.6 Formal Definition of the Limit"
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1.7 Limits and Loss-of-Significance Errors"
Chapter 2: Differentiation
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2.1 Tangent Lines and Velocity"
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2.2 The Derivative"
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2.3 Computation of Derivatives: The Power Rule"
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2.4 The Product and Quotient Rules"
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2.5 The Chain Rule"
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2.6 Derivatives of Trigonometric Functions"
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2.7 Derivatives of Exponential and Logarithmic Functions"
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2.8 Implicit Differentiation and Inverse Trigonometric Functions"
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2.9 The Hyperbolic Functions"
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2.10 The Mean Value Theorem"
Chapter 3: Applications of the Derivative
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3.1 Linear Approximations and Newton's Method""
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3.2 Indeterminate Forms and L'Hôpital's Rule "
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3.3 Maximum and Minimum Values"
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3.4 Increasing and Decreasing Functions"
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3.5 Concavity and the Second Derivative Test"
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3.6 Overview of Curve Sketching"
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3.7 Optimization"
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3.8 Related Rates"
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3.9 Rates of Change in Economics and the Sciences"
Chapter 4: Integration
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4.1 Antiderivatives"
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4.2 Sums and Sigma Notation"
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4.3 Area"
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4.4 The Definite Integral"
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4.5 The Fundamental Theorem of Calculus"
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4.6 Integration by Substitution"
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4.7 Numerical Integration"
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4.8 The Natural Logarithm as an Integral"
Chapter 5: Applications of the Definite Integral
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5.1 Area Between Curves"
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5.2 Volume: Slicing, Disks and Washers"
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5.3 Volumes by Cylindrical Shells"
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5.4 Arc Length and Surface Area"
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5.5 Projectile Motion"
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5.6 Applications of Integration to Physics and Engineering"
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5.7 Probability"
Chapter 6: Integration Techniques
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6.1 Review of Formulas and Techniques"
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6.2 Integration by Parts"
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6.3 Trigonometric Techniques of Integration"
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6.4 Integration of Rational Functions Using Partial Fractions"
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6.5 Integration Tables and Computer Algebra Systems"
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6.6 Improper Integrals"
Chapter 7: First-Order Differential Equations
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7.1 Modeling with Differential Equations"
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7.2 Separable Differential Equations"
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7.3 Direction Fields and Euler's Method"
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7.4 Systems of First-Order Differential Equations"
Chapter 8: Infinite Series
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8.1 Sequences of Real Numbers"
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8.2 Infinite Series"
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8.3 The Integral and Comparison Tests"
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8.4 Alternating Series"
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8.5 Absolute Convergence and the Ratio Test"
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8.6 Power Series"
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8.7 Taylor Series"
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8.8 Applications of Taylor Series"
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8.9 Fourier Series"
Chapter 9: Parametric Equations and Polar Coordinates
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9.1 Plane Curves and Parametric Equations"
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9.2 Calculus and Parametric Equations"
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9.3 Arc Length and Surface Area in Parametric Equations"
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9.4 Polar Coordinates"
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9.5 Calculus and Polar Coordinates"
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9.6 Conic Sections"
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9.7 Conic Sections in Polar Coordinates"
Chapter 10: Vectors and the Geometry of Space
Chapter 11: Vector-Valued Functions
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11.1 Vector-Valued Functions"
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11.2 The Calculus of Vector-Valued Functions"
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11.3 Motion in Space"
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11.4 Curvature"
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11.5 Tangent and Normal Vectors"
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11.6 Parametric Surfaces"
Chapter 12: Functions of Several Variables and Partial Differentiation
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12.1 Functions of Several Variables"
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12.2 Limits and Continuity"
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12.3 Partial Derivatives"
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12.4 Tangent Planes and Linear Approximations"
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12.5 The Chain Rule"
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12.6 The Gradient and Directional Derivatives"
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12.7 Extrema of Functions of Several Variables"
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12.8 Constrained Optimization and and Lagrange Multipliers"
Chapter 13: Multiple Integrals
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13.1 Double Integrals"
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13.2 Area, Volume and Center of Mass"
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13.3 Double Integrals in Polar Coordinates"
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13.4 Surface Area"
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13.5 Triple Integrals"
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13.6 Cylindrical Coordinates"
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13.7 Spherical Coordinates"
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13.8 Change of Variables in Multiple Integrals"
Chapter 14: Vector Calculus
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14.1 Vector Fields"
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14.2 Line Integrals"
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14.3 Independence of Path and Conservative Vector Fields"
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14.4 Green's Theorem"
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14.5 Curl and Divergence"
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14.6 Surface Integrals"
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14.7 The Divergence Theorem"
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14.8 Stokes' Theorem"
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14.9 Applications of Vector Calculus"
Chapter 15: Second Order Differential Equations
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15.1, Second-Order Equations With Constant Coefficients"
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15.2 Nonhomogeneous Equations: Undetermined Coefficients"
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15.3 Applications of Second-Order Equations"
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15.4 Power Series Solutions of Differential Equations"
Appendix A: Proofs of Selected Theorems
Appendix B: Answers to Odd-Numbered Exercises
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