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Full Description
For students who have completed an introductory calculus course in high school, this textbook provides a thorough grounding in many subsequent single variable calculus topics. Beginning with a review of some high school calculus content, it proceeds to more advanced material including integration techniques, applications of the definite integral, separable and linear differential equations, hyperbolic functions, parametric equations and polar coordinates, L'Hopital's rule and improper integrals, continuous probability models, and infinite series. Each chapter concludes with several 'Explorations', extended discovery investigations to supplement that chapter's material and enhance the learning experience. The text is ideal as the basis of a course for prospective majors in the STEM disciplines (science, technology, engineering, and mathematics). A one-term course based on this text provides students with a solid foundation in single variable calculus and prepares them for the next course in college-level mathematics, be it multivariable calculus, linear algebra, discrete mathematics or statistics.
Contents
Preface; 0. Preparation for college calculus; 1. Volume integrals and integration by parts; 2. Arc length, trigonometric substitution, and surface area; 3. Differential equations; 4. The logistic model, partial fractions, and least squares; 5. Physical applications of integration; 6. The hyperbolic functions; 7. Numerical integration; 8. Parametric equations and polar coordinates; 9. Improper integrals, L'Hopital's rule, and probability; 10. Infinite series (part I); 11. Infinite series (part II); Appendix A. Topic outline for AP calculus AB; Appendix B. Useful formulas from geometry and trigonometry; Appendix C. Supplemental topics in single variable calculus; Appendix D. Supplemental explorations; Appendix E. Answers to odd-numbered exercises; Index.
