Thoroughly updated and streamlined to reflect new developments in the field, the ninth edition of this bestselling text features modern engineering applications and the uses of technology. Kreyszig introduces engineers and computer scientists to advanced math topics as they relate to practical problems. The material is arranged into seven independent parts: ODE; Linear Algebra, Vector Calculus; Fourier Analysis and Partial Differential Equations; Complex Analysis; Numerical methods; Optimization, graphs; and Probability and Statistics.
Table of Contents
Introduction, General Commands. PART A. ORDINARY DIFFERENTAIL EQUATIONS (ODEs). Chapter 1. First-Order ODEs. Chapter 2 and 3. Linear ODEs of Second and Higher Order. Chapter 4. Systems of ODEs. Phase Plane, Qualitative Methods. Chapter 5. Series Solution of ODEs. Chapter 6. Laplace Transform Method for Solving ODEs. PART B. LINEAR ALGEBRA, VECTOR CALCULUS. Chapter 7. Matrices, Vectors, Determinants. Linear Systems of Equations. Chapter 8. Matrix Eigenvalue Problems. Chapter 9. Vector Differential Calculus Grad, Div, Curl. Chapter 10. Vector Integral Calculus. Integral Theorems. PART C. FOURIER ANALYSIS AND PARTIAL DIFFERENTIAL EQUATIONS (PDEs). Chapter 11. Fourier Series, Integrals, and Transforms. Chapter 12. Partial Differential Equations (PDEs). PART D. COMPLEX ANALYSIS. CHAPTER 13. AND 17. Complex Numbers and Functions. Conformal Mapping. Chapter 14. Complex Integration. Chapter 15. Power Series, Taylor Series. Chapter 16. Laurent Series. Residue Integration. Chapter 17. See before. Chapter 18. Complex Analysis in Potential Theory. PART E. NUMERIC ANALYSIS. Chapter 19. Numerics in General. Chapter 20. Numeric Linear Algebra. Chapter 21. Numerics for ODEs and PDEs. PART F. OPTIMIZATION GRAPHS. Chapter 22. Unconstrained Optimization, Linear Programming. Chapter 23. No examples, no problems. PART G. PROBABILITY AND STATISTICS. Chapter 24. Data Analysis. Probability Theory. Chapter 25. Mathematical Statistics. Appendix 1. References. Appendix 2. Answers to Odd-Numbered Problems. Index.