Advanced mathematical methods

Adam Ostaszewski

Written in an appealing and informal style, this text is a self-contained second course on mathematical methods dealing with topics in linear algebra and multivariate calculus that can be applied to statistics, operations research, computer science, econometrics and mathematical economics. 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, giving concrete and geometric explanations, 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 interest is in application rather than theory. The book is amply supplied with examples and exercises: complete solutions to a large proportion of these are provided.

「Nielsen BookData」より

Written in an appealing and informal style, this text is a self-contained second course on mathematical methods dealing with topics in linear algebra and multivariate calculus that can be applied to statistics, operations research, computer science, econometrics and mathematical economics. 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, giving concrete and geometric explanations, 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 interest is in application rather than theory. The book is amply supplied with examples and exercises: complete solutions to a large proportion of these are provided.

「Nielsen BookData」より

[目次]

  • 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.

「Nielsen BookData」より

[目次]

  • 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.

「Nielsen BookData」より

この本の情報

書名 Advanced mathematical methods
著作者等 Ostaszewski, Adam
シリーズ名 LSE mathematical series
出版元 Cambridge University Press
刊行年月 1990
ページ数 xiii, 545 p.
大きさ 23 cm
ISBN 0521289645
0521247888
NCID BA11377591
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言語 英語
出版国 イギリス
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