Written in an appealing and informal style, this text is a self-contained second course on mathematical methods in linear algebra and multivariate calculus. The prerequisites are elementary courses in linear algebra and calculus, but the author has maintained a balance between a rigorous theoretical and a "cookbook" approach, so that the material will be accessible to students who have not studied mathematics in depth. Indeed, as much of the material is normally available only in technical textbooks, this book will have wide appeal to students whose interests are in application rather than…mehr
Written in an appealing and informal style, this text is a self-contained second course on mathematical methods in linear algebra and multivariate calculus. The prerequisites are elementary courses in linear algebra and calculus, but the author has maintained a balance between a rigorous theoretical and a "cookbook" approach, so that the material will be accessible to students who have not studied mathematics in depth. Indeed, as much of the material is normally available only in technical textbooks, this book will have wide appeal to students whose interests are in application rather than theory. The book is amply supplied with examples and exercises: complete solutions to a large proportion of these are provided.
Adam Ostaszewski is a lawyer by profession who lives in Poland. He is an author of novels and short stories. He is also a fan of historical, science fiction and political fiction literature. "Reflection" is his publishing debut.
Inhaltsangabe
Preface Part I. Linear Algebra: 1. Vector spaces (revision) 2. Geometry in R 3. Matrices 4. Projections 5. Spectral theory 6. The upper triangular form 7. The tri-diagonal form 8. Inverses 9. Convexity 10. The separating hyperplane theorem 11. Linear inequalities 12. Linear programming and game theory 13. The simplex method 14. Partial derivatives (revision) 15. Convex functions 16. Non-linear programming Part II. Advanced Calculus: 1. The integration process 2. Manipulation of integrals 3. Multiple integrals 4. Differential and difference equations (revision) 5. Laplace transforms 6. Series solutions of differential equations 7. Calculus of variations Part III. Solutions to Selected Exercises Index.
Preface Part I. Linear Algebra: 1. Vector spaces (revision) 2. Geometry in R 3. Matrices 4. Projections 5. Spectral theory 6. The upper triangular form 7. The tri-diagonal form 8. Inverses 9. Convexity 10. The separating hyperplane theorem 11. Linear inequalities 12. Linear programming and game theory 13. The simplex method 14. Partial derivatives (revision) 15. Convex functions 16. Non-linear programming Part II. Advanced Calculus: 1. The integration process 2. Manipulation of integrals 3. Multiple integrals 4. Differential and difference equations (revision) 5. Laplace transforms 6. Series solutions of differential equations 7. Calculus of variations Part III. Solutions to Selected Exercises Index.
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