Textbook of Calculus

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Calculus is a required, three-semester course for all hard science majors such as mathematics, engineering, physics, statistics, computer science, and chemistry. One or more semesters of calculus are required for a number of other majors. The course can take many forms, but the the most common is Single Variable Calculus. This is usually a two-semester course that does not cover multivariable material. Calculus of a Single Variable covers all the material usually taught in this two-semester course. Once again, this course is largely for math, science, and engineering majors. For the instructors, this book aims to provide a comprehensive teaching instrument that employs proven pedagogical techniques, freeing instructors to make the most efficient use of classroom time. Key Feature Exercises: New exercises are based on analyses of actual student data, the exercise sets have been overhauled to improve student understanding. Many exercises were added, some were revised, and some were removed. The result is exercise sets that effectively address student learning needs 3-D Rotatable Graphs: Rotatable Graphs allow you to view three-dimensional graphs as they rotate. These graphs can be viewed from different angles to enhance both visual and theoretical understanding of complex calculus concepts. Each graph was created using the optimal combination of color, transparency, view, perspective, light sources, and shadows to show the perspective of surfaces and solids Table of Contents 1. Limits and Their Properties 2. Differentiation 3. Applications of Differentiation 4. Integration 5. Applications of Integration 6. Logarithmic,Exponential, and Other Transcendental Functions 7. differential Equations 8. Integration Techniques, L'Ho^pital'sRule, and Improper Integrals 9. Infinite Series 10. Conics, Parametric Equations, and Polar Coordinates 11. Vectors and the Geometry of Space 12. Vector-Valued Functions 13. Functions of Several Variables 14. Multiple Integration