Advanced Engineering Mathematics, 10th Edition

ISBN: 9780470458365

Advanced Engineering Mathematics, 10th Edition provides you with a comprehensive and up-to-date resource for learning engineering mathematics. Known for its comprehensive coverage, high level of accuracy and outstanding exercises, Kreyszig’s coverage of the content ensures that you will have all of the tools that you need to succeed in your course. This textbook will also serve as an excellent resource in future years for students studying engineering, physics, mathematics or computer science.



  • Simplicity of Examples: The text utilises well-written simple examples which are designed to be more instructive and more easily understood.
  • Uses Modern Standard Notation: To help you with other courses, modern books, and mathematical and engineering journals.
  • Independence of Chapters: To provide flexibility in tailoring courses to specific needs.
  • Self-Contained Presentation: With the exception of a few clearly marked sections where a proof would exceed the level of the book, and a reference is given instead.
Ernin Kreyszig was a Professor of Mathematics at Carleton University in Ottawa, Canada. Throughout his career he taught at a variety of institutions, including Stanford University, Ohio State University, and the University of Dusseldorf. He published 176 papers in refereed journals throughout his research career, and this achievement was recognised in 1991 when he was awarded the title of Distinguished Research Professor.
PART A Ordinary Differential Equations (ODEs)
1. First-Order ODEs
2. Second-Order Linear ODEs
3. Higher Order Linear ODEs
4. Systems of ODEs. Phase Plane. Qualitative Methods
5. Series Solutions of ODEs. Special Functions
6. Laplace Transforms

PART B Linear Algebra. Vector Calculus
7. Linear Algebra: Matrices, Vectors, Determinants. Linear Systems
8. Linear Algebra: Matrix Eigenvalue Problems
9. Vector Differential Calculus. Grad, Div, Curl
10. Vector Integral Calculus. Integral Theorems

PART C Fourier Analysis. Partial Differential Equations (PDEs)
11. Fourier Analysis
12. Partial Differential Equations (PDEs)

PART D Complex Analysis
13. Complex Numbers and Functions. Complex Differentiation
14. Complex Integration
15. Power Series, Taylor Series
16. Laurent Series. Residue Integration
17. Conformal Mapping

PART E Numeric Analysis
18. Software
19. Numerics in General
20. Numeric Linear Algebra
21. Numerics for ODEs and PDEs

PART F Optimization, Graphs
22. Unconstrained Optimization. Linear Programming
23. Graphs: Combinatorial Optimization
24. Data Analysis: Probability Theory
25. Mathematical Statistics

APPENDIX 1 References
APPENDIX 2 Answers to Odd-Numbered Problems
APPENDIX 3 Auxiliary Material
APPENDIX 4 Additional Proofs

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