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| Functions And Limits | |
| Functions and Their Representations | |
| A Catalog of Essential Functions | |
| The Limit of a Function | |
| Calculating Limits | |
| Continuity | |
| Limits Involving Infinity | |
| Review | |
| Derivatives | |
| Derivatives and Rates of Change | |
| The Derivative as a Function | |
| Basic Differentiation Formulas | |
| The Product and Quotient Rules | |
| The Chain Rule | |
| Implicit Differentiation | |
| Related Rates | |
| Linear Approximations and Differentials | |
| Review | |
| Inverse Functions: Exponential, Logarithmic, and Inverse Trigonometric Functions | |
| Exponential Functions | |
| Inverse Functions and Logarithms | |
| Derivatives of Logarithmic and Exponential Functions | |
| Exponential Growth and Decay | |
| Inverse Trigonometric Functions | |
| Hyperbolic Functions | |
| Indeterminate Forms and l'Hospital's Rule | |
| Review | |
| Applications of Differentiation | |
| Maximum and Minimum Values | |
| The Mean Value Theorem | |
| Derivatives and the Shapes of Graphs | |
| Curve Sketching | |
| Optimization Problems | |
| Newton's Method | |
| Antiderivatives | |
| Review | |
| Integrals | |
| Areas and Distances | |
| The Definite Integral | |
| Evaluating Definite Integrals | |
| The Fundamental Theorem of Calculus | |
| The Substitution Rule | |
| Review | |
| Techniques of Integration | |
| Integration by Parts | |
| Trigonometric Integrals and Substitutions | |
| Partial Fractions | |
| Integration with Tables and Computer Algebra Systems | |
| Approximate Integration | |
| Improper Integrals | |
| Review | |
| Applications of Integration | |
| Areas between Curves | |
| Volumes | |
| Volumes by Cylindrical Shells | |
| Arc Length | |
| Applications to Physics and Engineering | |
| Differential Equations | |
| Review | |
| Series | |
| Sequences | |
| Series | |
| The Integral and Comparison Tests | |
| Other Convergence Tests | |
| Power Series | |
| Representing Functions as Power Series | |
| Taylor and Maclaurin Series | |
| Applications of Taylor Polynomials | |
| Review | |
| Parametric Equations and Polar Coordinates | |
| Parametric Curves | |
| Calculus with Parametric Curves | |
| Polar Coordinates | |
| Areas and Lengths in Polar Coordinates | |
| Conic Sections in Polar Coordinates | |
| Review | |
| Vectors and the Geometry of Space | |
| Three-Dimensional Coordinate Systems | |
| Vectors | |
| The Dot Product | |
| The Cross Product | |
| Equations of Lines and Planes | |
| Cylinders and Quadric Surfaces | |
| Vector Functions and Space Curves | |
| Arc Length and Curvature | |
| Motion in Space: Velocity and Acceleration | |
| Review | |
| Partial Derivatives | |
| Functions of Several Variables | |
| Limits and Continuity | |
| Partial Derivatives | |
| Tangent Planes and Linear Approximations | |
| The Chain Rule | |
| Directional Derivatives and the Gradient Vector | |
| Maximum and Minimum Values | |
| Lagrange Multipliers | |
| Review | |
| Multiple Integrals | |
| Double Integrals over Rectangles | |
| Double Integrals over General Regions | |
| Double Integrals in Polar Coordinates | |
| Applications of Double Integrals | |
| Triple Integrals | |
| Triple Integrals in Cylindrical Coordinates | |
| Triple Integrals in Spherical Coordinates | |
| Change of Variables in Multiple Integrals | |
| Review | |
| Vector Calculus | |
| Vector Fields | |
| Line Integrals | |
| The Fundamental Theorem for Line Integrals | |
| Green's Theorem | |
| Curl and Divergence | |
| Parametric Surfaces and Their Areas | |
| Surface Integrals | |
| Stokes' Theorem | |
| The Divergence Theorem | |
| Review | |
| Trigonometry | |
| Proofs | |
| Sigma Notation | |
| The Logarithm Defined as an Integral. | |
| Table of Contents provided by Publisher. All Rights Reserved. |
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