Description
Elsevier Working Analysis by Jeffery Cooper
Working Analysis 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. PrefacePart I: 1. Foundations2. Sequences of Real Numbers3. Continuity4. The Derivative5. Higher Derivatives and Polynomial Approximation6. Solving Equations in One Dimension7. Integration8. SeriesAppendix IPart II: 9. Convergence and Continuity in Rn10. The Derivative in Rn11. Solving Systems of Equations12. Quadratic Approximation and Optimization13. Constrained Optimization14. Integration in Rn15. Applications of Integration to Differential EquationsAppendix IISolutions to Selected ExercisesReferencesIndex