Calculus: An Integrated Approach to Functions and Their Rates of Change

A major complaint of professors teaching calculus is that students don't have the appropriate background to work through the calculus course successfully. This text is targeted directly at this underprepared audience. This is a single-variable (2-semester) calculus text that incorporates a conceptual re-introduction to key precalculus ideas throughout the exposition as appropriate. This is the ideal resource for those schools dealing with poorly prepared students or for schools introducing a slower paced, integrated precalculus/calculus course.

PART I Functions: An IntroductionCh1. Functions Are Lurking EverywhereCh2. Characterizing Functions and Introducing Rates of ChangeCh3. Functions Working TogetherPART II Rates of Change: An Introduction to the DerivativeCh4. Linearity and Local LinearityCh5. The Derivative FunctionCh6. The Quadratics: A Profile of a Prominent Family of FunctionsCh7. The Theoretical Backbone: Limits and ContinuityCh8. Fruits of Our Labor: Derivatives and Local Linearity RevisitedPART III Exponential, Polynomial, and Rational Functions--with ApplicationsCh9. Exponential FunctionsCh10. OptimizationCh11. A Portrait of Polynomials and Rational FunctionsPART IV Inverse Functions: A Case Study of Exponential and Logarithmic FunctionsCh12. Inverse Functions: Can What Is Done Be Undone?Ch13. Logarithmic FunctionsCh14. Differentiating Logarithmic and Exponential FunctionsCh15. Take It to the LimitPART V Adding Sophistication to Your DifferentiationCh16. Taking the Derivative of Composite FunctionsCh17. Implicit Differentiation and its ApplicationsPART VI An Excursion into Geometric SeriesCh18. Geometric Sums, Geometric SeriesPART VII Trigonometric FunctionsCh19. Trigonometry: Introducing Periodic FunctionsCh20. Trigonometry--Circles and TrianglesCh21. Differentiation of Trigonometric FunctionsPART VIII Integration: An IntroductionCh22. Net Change in Amount and Area: Introducing the Definite IntegralCh23. The Area Function and Its CharacteristicsCh24. The Fundamental Theorem of CalculusPART IX Applications and Computation of the IntegralCh25. Finding Antiderivatives--An Introduction to Indefinite IntegrationCh26. Numerical Methods of Approximating Definite IntegralsCh27. Applying the Definite Integral: Slice and ConquerCh28. More Applications of IntegrationCh29. Computing VolumesPART X SeriesCh30. SeriesCh31. Differential Equations