Advanced engineering mathematics / Peter V. O'Neil

Includes index.

Part 1. Ordinary Differential Equations -- Chapter 1. First-Order Differential Equations -- Chapter 2. Linear Second-Order Equations -- Chapter 3. The Laplace Transform -- Chapter 4. Series Solutions -- Chapter 5. Approximation of Solutions -- Part 2. Vectors, Linear Algebra and Systems of Linear Differential Equations -- Chapter 6. Vectors and Vector Spaces -- Chapter 7. Matrices and Linear Systems -- Chapter 8. Determinants -- Chapter 9. Eigenvalues, Diagonalization and Special Metrices -- Chapter 10. Systems of Linear Differential Equations -- Part 3. Vector Analysis -- Chapter 11. Vector Differential Calculus -- Chapter 12. Vector Integral Calculus -- Part 4. Fourier Analysis, Special Functions, and Eigenfunction Expansions -- Chapter 13. Fourier Series -- Chapter 14. The Fourier Integral and Transforms -- Chapter 15. Special Functions and Eigenfunction Expansions -- Part 5. Partial Differential Equations -- Chapter 16. The Wave Equation -- Chapter 17. The Heat Equation -- Chapter 18. The Potential Equation -- Part 6. Complex Function -- Chapter 19. Complex Numbers and Functions -- Chapter 20. Complex Integration -- Chapter 21. Series Representations of Functions -- Chapter 22. Singularities and the Residue Theorem -- Chapter 23. Conformal Mappings and Applications -- Part 7. Probability and Statistics -- Chapter 24. Probability -- Chapter 25. Statistics.

Through previous editions, Peter O'Neil has made rigorous engineering mathematics topics accessible to thousands of students by emphasizing visuals, numerous examples, and interesting mathematical models. Now, "Advanced Engineering Mathematics" features revised examples and problems as well as newly added content that has been fine-tuned throughout to improve the clear flow of ideas. The computer plays a more prominent role than ever in generating computer graphics used to display concepts and problem sets. In this new edition, computational assistance in the form of a self contained Maple Primer has been included to encourage students to make use of such computational tools. The content has been reorganized into six parts and covers a wide spectrum of topics including Ordinary Differential Equations, Vectors and Linear Algebra, Systems of Differential Equations and Qualitative Methods, Vector Analysis, Fourier Analysis, Orthogonal Expansions, and Wavelets, and much more.