Working Analysis

Klappentext The text is for a two semester course in advanced calculus. It develops the basic ideas of calculus rigorously but with an eye to showing how mathematics connects with other areas of science and engineering. In particular! effective numerical computation is developed as an important aspect of mathematical analysis. Maintains a rigorous presentation of the main ideas of advanced calculus! interspersed with applications that show how to analyze real problems Includes a wide range of examples and exercises drawn from mechanics! biology! chemical engineering and economics Describes links to numerical analysis and provides opportunities for computation; some MATLABcodes are available on the author's webpage Enhanced by an informal and lively writing style Zusammenfassung Suitable for a two semester course in advanced calculus! this work develops the basic ideas of calculus with an eye to showing how mathematics connects with other areas of science and engineering. It includes a range of examples and exercises drawn from mechanics! biology! chemical engineering and economics. Inhaltsverzeichnis Preface Part I: 1. Foundations 2. Sequences of Real Numbers 3. Continuity 4. The Derivative 5. Higher Derivatives and Polynomial Approximation 6. Solving Equations in One Dimension 7. Integration 8. Series Appendix I Part II: 9. Convergence and Continuity in Rn 10. The Derivative in Rn 11. Solving Systems of Equations 12. Quadratic Approximation and Optimization 13. Constrained Optimization 14. Integration in Rn 15. Applications of Integration to Differential Equations Appendix II Solutions to Selected Exercises References Index

Zusammenfassung
Suitable for a two semester course in advanced calculus, this work develops the basic ideas of calculus with an eye to showing how mathematics connects with other areas of science and engineering. It includes a range of examples and exercises drawn from mechanics, biology, chemical engineering and economics.

Inhalt
Preface Part I: 1. Foundations 2. Sequences of Real Numbers 3. Continuity 4. The Derivative 5. Higher Derivatives and Polynomial Approximation 6. Solving Equations in One Dimension 7. Integration 8. Series Appendix I Part II: 9. Convergence and Continuity in Rn 10. The Derivative in Rn 11. Solving Systems of Equations 12. Quadratic Approximation and Optimization 13. Constrained Optimization 14. Integration in Rn 15. Applications of Integration to Differential Equations Appendix II Solutions to Selected Exercises References Index