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| Preparation for Calculus | |
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| Graphs and Models | |
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| Linear Models and Rates of Change | |
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| Functions and Their Graphs | |
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| Fitting Models to Data | |
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| Limits and Their Properties | |
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| A Preview of Calculus | |
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| Finding Limits Graphically and Numerically | |
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| Evaluating Limits Analytically | |
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| Continuity and One-Sided Limits | |
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| Infinite Limits | |
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| Section Project: Graphs and Limits of Trigonometric Functions | |
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| Differentiation | |
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| The Derivative and the Tangent Line Problem | |
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| Basic Differentiation Rules and Rates of Change | |
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| The Product and Quotient Rules and Higher-Order Derivatives | |
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| The Chain Rule | |
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| Implicit Differentiation | |
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| Section Project: Optical Illusions | |
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| Related Rates | |
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| Applications of Differentiation | |
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| Extrema on an Interval | |
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| Rolle's Theorem and the Mean Value Theorem | |
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| Increasing and Decreasing Functions and the First Derivative TeSt. Section Project: Rainbows | |
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| Concavity and the Second Derivative Test | |
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| Limits at Infinity | |
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| A Summary of Curve Sketching | |
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| Optimization Problems | |
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| Section Project: Connecticut River | |
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| Newton's Method | |
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| Differentials | |
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| Integration | |
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| Antiderivatives and Indefinite Integration | |
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| Area | |
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| Riemann Sums and Definite Integrals | |
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| The Fundamental Theorem of Calculus | |
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| Section Project: Demonstrating the Fundamental Theorem | |
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| Integration by Substitution | |
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| Numerical Integration | |
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| Logarithmic, Exponential, and Other Transcendental Functions | |
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| The Natural Logarithmic Function: Differentiation | |
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| The Natural Logarithmic Function: Integration | |
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| Inverse Functions | |
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| Exponential Functions: Differentiation and Integration | |
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| Bases Other than e and Applications | |
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| Section Project: Using Graphing Utilities to Estimate Slope | |
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| Inverse Trigonometric Functions: Differentiation | |
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| Inverse Trigonometric Functions: Integration | |
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| Hyperbolic Functions | |
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| Section Project: St. Louis Arch | |
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| Differential Equations | |
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| Slope Fields and Euler's Method | |
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| Differential Equations: Growth and Decay | |
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| Separation of Variables and the Logistic Equation | |
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| First-Order Linear Differential Equations | |
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| Section Project: Weight Loss | |
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| Applications of Integration | |
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| Area of a Region Between Two Curves | |
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| Volume: The Disk Method | |
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| Volume: The Shell Method | |
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| Section Project: Saturn | |
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| Arc Length and Surfaces of Revolution | |
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| Work | |
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| Section Project: Tidal Energy | |
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| Moments, Centers of Mass, and Centroids | |
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| Fluid Pressure and Fluid Force | |
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| Integration Techniques, L'Hopital's Rule, and Improper Integrals | |
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| Basic Integration Rules | |
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| Integration by Parts | |
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| Trigonometric Integrals | |
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| Section Project: Power Lines | |
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| Trigonometric Substitution | |
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| Partial Fractions | |
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| Integration by Tables and Other Integration Techniques | |
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| Indeterminate Forms and L'Hopital's Rule | |
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| Infinite Series | |
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| Sequences | |
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| Series and Convergence | |
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| Section Project: Cantor's Disappearing Table | |
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| The Integral Test and p-Series | |
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| Section Project: The Harmonic Series | |
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| Comparisons of Series | |
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| Section Project: Solera Method | |
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| Alternating Series | |
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| The Ratio and Root Tests | |
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| Taylor Polynomials and Approximations | |
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| Power Series | |
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| Representation of Functions by Power Series | |
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| Taylor and Maclaurin Series | |
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| Conics, Parametric Equations, and Polar Coordinates | |
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| Conics and Calculus | |
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| Plane Curves and Parametric Equations | |
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| Section Project: Cycloids | |
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| Parametric Equations and Calculus | |
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| Polar Coordinates and Polar Graphs | |
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| Section Project: Anamorphic Art | |
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| Area and Arc Length in Polar Coordinates | |
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| Polar Equations of Conics and Kepler's Laws | |
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| Vectors and the Geometry of Space | |
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| Vectors in the Plane | |
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| Space Coordinates and Vectors in Space | |
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| The Dot Product of Two Vectors | |
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| The Cross Product of Two Vectors in Space | |
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| Lines and Planes in Space | |
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| Section Project: Distances in Space | |
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| Surfaces in Space | |
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| Cylindrical and Spherical Coordinates | |
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| Vector-Valued Functions | |
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| Vector-Valued Functions | |
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| Section Project: Witch of Agnesi | |
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| Differentiation and Integration of Vector-Valued Functions | |
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| Velocity and Acceleration | |
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| Tangent Vectors and Normal Vectors | |
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| Arc Length and Curvature | |
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| Functions of Several Variables | |
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| Introduction to Functions of Several Variables | |
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| Limits and Continuity | |
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| Partial Derivatives | |
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| Section Project: Moir? Fringes | |
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| Differentials | |
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| Chain Rules for Functions of Several Variables | |
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| Directional Derivatives and Gradients | |
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| Tangent Planes and Normal Lines | |
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| Section Project: Wildflowers | |
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| Extrema of Functions of Two Variables | |
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| Applications of Extrema of Functions of Two Variables | |
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| Section Project: Building a Pipeline | |
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| Lagrange Multipliers | |
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| Multiple Integration | |
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| Iterated Integrals and Area in the Plane | |
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| Double Integrals and Volume | |
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| Change of Variables: Polar Coordinates | |
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| Center of Mass and Moments of Inertia | |
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| Section Project: Center of Pressure on a Sail | |
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| Surface Area | |
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| Section Project: Capillary Action | |
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| Triple Integrals and Applications | |
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| Triple Integrals in Cylindrical and Spherical Coordinates | |
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| Section Project: Wrinkled and Bumpy Spheres | |
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| Change of Variables: Jacobians | |
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| Vector Analysis | |
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| Vector Fields | |
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| Line Integrals | |
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| Conservative Vector Fields and Independence of Path | |
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| Green's Theorem | |
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| Section Project: Hyperbolic and Trigonometric Functions | |
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| Parametric Surfaces | |
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| Surface Integrals | |
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| Section Project: Hyperboloid of One Sheet | |
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| Divergence Theorem | |
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| Stokes's Theorem | |
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| Section Project: The Planimeter | |
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| Bonus Online Material | |
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| Additional Topics in Differential Equations (please visit URL to come) | |
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| Exact First-Order Equations | |
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| Second-Order Homogeneous Linear Equations | |
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| Second-Order Nonhomogeneous Linear Equations | |
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| Section Project: Parachute Jump | |
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| Series Solutions of Differential Equations | |
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| Book Appendices | |
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| Proofs of Selected Theorems | |
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| Integration Tables | |
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| Online Appendices | |
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| Precalculus Review (please visit URL to come) | |
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| Real Numbers and the Real Number Line | |
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| The Cartesian Plane | |
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| Review of Trigonometric Functions | |
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| Rotation and the General Second-Degree Equation (please visit URL to come) | |
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| Complex Numbers (please visit URL to come) | |
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| Business and Economic Applications (please visit URL to come) | |
