Table of contents for Single variable calculus : concepts and contexts / James Stewart.
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1. FUNCTIONS AND MODELS. Four Ways to Represent a Function. New Functions from Old Functions. Graphing Calculators and Computers. Parametric Curves. Laboratory Project: Families of Hypocycloids. Exponential Functions. Inverse Functions and Logarithms. Models and Curve Fitting. 2. LIMITS AND DERIVATIVES. The Tangent and Velocity Problems. The Limit of a Function. Calculating Limits Using the Limit Laws. Continuity. Limits Involving Infinity. Tangents, Velocities, and Other Rates of Change. Derivatives. Writing Project: Early Methods for Finding Tangents. The Derivative as a Function. Linear Approximations. What does f'' say about f? 3. DIFFERENTIATION RULES. Derivatives of Polynomials and Exponential Functions. The Product and Quotient Rules. Rates of Change in the Natural and Social Sciences. Derivatives of Trigonometric Functions. The Chain Rule. Laboratory Project: Bezier Curves. Applied Project: Where Should a Pilot Start Descent? Implicit Differentiation. Derivatives of Logarithmic Functions. Discovery Project: Hyperbolic Functions. Linear Approximations and Differentials. Laboratory Project: Taylor Polynomials. 4. APPLICATIONS OF DIFFERENTIATION. Related Rates. Maximum and Minimum Values. Applied Project: The Calculus of Rainbows. Derivatives and the Shapes of Curves. Graphing with Calculus and Calculators. Indeterminate Forms and l''Hospital''s Rule. Writing Project: The Origins of l''Hospital''s Rule. Optimization Problems. Applied Project: The Shape of a Can. Applications to Economics. Newton''s Method. Antiderivatives. 5. INTEGRALS. Areas and Distances. The Definite Integral. Evaluating Definite Integrals. Discovery Project: Area Functions. The Fundamental Theorem of Calculus. Writing Project: Newton, Leibniz, and the Invention of Calculus. The Substitution Rule. Integration by Parts. Integration Using Tables and Computer Algebra Systems. Discovery Project: Patterns in Integrals. Approximate Integration. Improper Integrals. 6. APPLICATIONS OF INTEGRATION. More about Areas. Volumes. Arc Length. Average Value of a Function. Applied Project: Where to Sit at the Movies. Applications to Physics. Applications to Economics and Biology. Probability. 7. DIFFERENTIAL EQUATIONS. Modeling with Differential Equations. Direction Fields. Euler''s Method. Separable Equations. Applied Project: Which is Faster, Going Up or Coming Down? Exponential Growth and Decay. Applied Project: Calculus and Baseball. The Logistic Equation. Predator-Prey Systems. Some Special Second Order Equations. 8. POLAR COORDINATES. Curves in Polar Coordinates. Laboratory Project: Families of Polar Curves. Tangents to Polar Curves. Areas and lengths in Polar Coordinates. Conic Sections in Polar Coordinates. 9. INFINITE SEQUENCES AND SERIES. Sequences. Laboratory Project: Logistic Sequences. Series. The Integral and Comparison Tests; Estimating Sums. Other Convergence Tests. Power Series. Representation of Functions as Power Series. Taylor and Maclaurin Series. Writing Project: Newton, Gregory, Taylor, and Maclaurin. The Binomial Series. Applications of Taylor Polynomials. Applied Project: Radiation from the Stars. Using Series to Solve Differential Equations. Appendix A: Intervals, Inequalities, and Absolute Values. Appendix B: Coordinate Geometry. Appendix C: Trigonometry. Appendix D: Precise Definitions of Limits. Appendix E: A Few Proofs. Appendix F: Integration of Rational Functions by Partial Fractions. Appendix G: Complex Numbers. Appendix H: Answers to Odd-Numbered Exercises.
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