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*Precision and Clarity: Emphasis on mathematical exposition-an accurate and understandable treatment of the topics. The mathematical statements are careful and precise. The basic concepts and important points are not obscured by excess verbiage. * Accessibility: Completely accessible to the beginning calculus student without sacrificing mathematical rigor. * Balance of Theory and Applications: Problems drawn from the sciences and engineering are used to motivate calculus concepts and these concepts, in return, are applied to a variety of disciplines in the examples and exercises.
Chapter 1. Precalculus Review.
Chapter 2. Limits and Continuity.
Chapter 3. Differentiation.
Chapter 4. The Mean-Value Theorem and Applications.
Chapter 5. Integration.
Chapter 6. Applications of the Integral.
Chapter 7. The Transcendental Functions.
Chapter 8. Techniques of Integration.
Chapter 9. The Conic Sections; Polar Coordinates; Parametric Equations.
Chapter 10. Sequences; Indeterminate Forms; Improper Integrals.
Chapter 11. Infinite Series.
Chapter 12. Vectors.
Chapter 13. Vector Calculus.
Chapter 14. Functions of Several Variables.
Chapter 15. Gradients; Extreme Values; Differentials.
Chapter 16. Double and Triple Integrals.
Chapter 17. Line Integrals and Surface Integrals.
Chapter 18. Elementary Differential Equations.
Appendix A.
Appendix B. Some Additional Topics.
Answers to Odd-Numbered Exercises.
Index.
Tables of Integrals.
*Precision and Clarity: Emphasis on mathematical exposition-an accurate and understandable treatment of the topics. The mathematical statements are careful and precise. The basic concepts and important points are not obscured by excess verbiage. * Accessibility: Completely accessible to the beginning calculus student without sacrificing mathematical rigor. * Balance of Theory and Applications: Problems drawn from the sciences and engineering are used to motivate calculus concepts and these concepts, in return, are applied to a variety of disciplines in the examples and exercises.
Table of Contents
Chapter 1. Precalculus Review.
Chapter 2. Limits and Continuity.
Chapter 3. Differentiation.
Chapter 4. The Mean-Value Theorem and Applications.
Chapter 5. Integration.
Chapter 6. Applications of the Integral.
Chapter 7. The Transcendental Functions.
Chapter 8. Techniques of Integration.
Chapter 9. The Conic Sections; Polar Coordinates; Parametric Equations.
Chapter 10. Sequences; Indeterminate Forms; Improper Integrals.
Chapter 11. Infinite Series.
Chapter 12. Vectors.
Chapter 13. Vector Calculus.
Chapter 14. Functions of Several Variables.
Chapter 15. Gradients; Extreme Values; Differentials.
Chapter 16. Double and Triple Integrals.
Chapter 17. Line Integrals and Surface Integrals.
Chapter 18. Elementary Differential Equations.
Appendix A.
Appendix B. Some Additional Topics.
Answers to Odd-Numbered Exercises.
Index.
Tables of Integrals.