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![]() Parametric equations and polar coordinates - 10.1. Predator-prey systems - Review - Problems plus - 10. Separable equations - Applied project : how fast does a tank drain? - Applied project : which is faster, going up or coming down? - 9.4. Direction fields and Euler's method - 9.3. Modeling with differential equations - 9.2. Probability - Review - Problems plus - 9. Applications to economics and biology - 8.5. Applications to physics and engineering - Discovery project : complementary coffee cups - 8.4. Area of a surface of revolution - Discovery project : rotating on a slant - 8.3. Arc length - Discovery project : arc length contest - 8.2. Further applications of integration - 8.1. Improper integrals - Review - Problems plus - 8. Integration using tables and computer algebra systems - Discovery project : patterns in integrals - 7.7. Integration of rational functions by partial fractions - 7.5. Average value of a function - Applied projects : calculus and baseball - Applied projects : where to sit at the movies - Review - Problems plus - 7. Areas between curves - Applied project : the gini index - 6.2. The substitution rule - Review - Problems plus - 6. Indefinite integrals and the net change theorem - Writing project : Newton, Leibniz, and the invention of calculus - 5.5. The fundamental theorem of calculus - 5.4. The definite integral - Discovery project : area functions - 5.3. Antiderivatives - Review - Problems plus - 5. Optimization problems - Applied project : the shape of a can - Applied project : Planes and birds: Minimizing energy - 4.8. Graphing with calculus and calculators - 4.7. Indeterminate forms and L'Hospital's rule - Writing project : the origins of L'Hospital's rule - 4.5. How derivatives affect the shape of a graph - 4.4. Maximum and minimum values - Applied project : the calculus of rainbows - 4.2. Hyperbolic functions - Review - Problems plus - 4. Linear approximations and differentials - Laboratory project : Taylor polynomials - 3.11. Rates of change in the natural and social sciences - 3.8. Derivatives of logarithmic functions - 3.7. The chain rule - Applied project : where should a pilot start descent? - 3.5. Derivatives of trigonometric functions - 3.4. Derivatives of polynomials and exponential functions - Applied project : building a better roller coaster - 3.2. The derivative as a function - Review - Problems plus - 3. ![]() Derivatives and rates of change - Writing project : early methods for finding tangents - 2.8. Limits at infinity horizontal asymptotes - 2.7. Calculating limits using the limit laws - 2.4. Inverse functions and logarithms - Review - Principles of problem solving - 2. Graphing calculators and computers - 1.5. Mathematical models : a catalog of essential functions - 1.3. Preface - To the student - Diagnostic tests - A preview of calculus - 1.
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