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Full Description
College Calculus: A One-Term Course for Students with Previous Calculus Experience is a textbook for students who have successfully experienced an introductory calculus course in high school. College Calculus begins with a brief review of some of the content of the high school calculus course, and proceeds to give students a thorough grounding in the remaining topics in single variable calculus, 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.
The text is ideal as the basis of a course focused on the needs of 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, a course in discrete mathematics, statistics, etc.
Contents
Preface
Chapter 0. Preparation for College Calculus
Chapter 1. Volume Integrals and Integration by Parts
Chapter 2. Arc Length, Trigonometric Substitution, and Surface Area
Chapter 3. Differential Equations
Chapter 4. Logistic Model, Partial Fractions, Least Squares
Chapter 5. Physical Applications of Integration
Chapter 6. The Hyperbolic Functions
Chapter 7. Numerical Integration
Chapter 8. Parametric Equations and Polar Coordinates
Chapter 9. Improper Integrals, L'Hôpital's Rule, and Probability
Chapter 10. Infinite Series (Part I)
Chapter 11. Infinite Series (Part II)
Appendices A-E
Index
