Foundations of Mathematical Modeling and Analysis in Engineering offers a comprehensive
presentation of the mathematical principles underpinning modern engineering and the quantitative sciences, and develops mathematical modeling as a foundational intellectual discipline. Designed for graduate and advanced undergraduate students, and accessible to seasoned professionals, it provides the means to develop and employ mathematical representations of physical processes and systems.
1. Chapter 1: Introduction - p. 1 2. Chapter 2: Mathematical representations of physical phenomena - p. 9 3. Chapter 3: Solving linear algebraic equations - p. 61 4. Chapter 4: Vector spaces and their representations - p. 71 5. Chapter 5: Linear transformations and representations - p. 91 6. Chapter 6: Inner product spaces - p. 117 7. Chapter 7: Operators and matrix representations - p. 155 8. Chapter 8: Ordinary differential equations - p. 177 9. Chapter 9: Function representation and transforms - p. 199 10. Chapter 10: Partial differential equations - p. 219 11. Chapter 11: System and parameter identification - p. 271 12. Appendix A: A word on proofs - p. 337 13. Appendix B: Vector calculus and operations - p. 339 14. Appendix C: Simulate measurement errors - p. 357 15. Appendix D: Additional operations with square matrices - p. 361 16. Appendix E: Addendum to Chapter 7 - p. 367 17. Appendix F: Higher-order linear ODEs - p. 375 18. Appendix G: QR factorization - p. 381 19. Appendix H: Sequences and convergence - p. 385 20. Appendix I: Euler's equidimensional equation - p. 387 21. Appendix J: Sturm–Liouville equations - p. 389 22. Appendix K: Bessel's equation - p. 393 23. Appendix L: Best linear unbiased predictions and estimates - p. 397 24. Bibliography - p. 401 25. Index - p. 405
Foundations of Mathematical Modeling and Analysis in Engineering offers a comprehensive
presentation of the mathematical principles underpinning modern engineering and the quantitative sciences, and develops mathematical modeling as a foundational intellectual discipline. Designed for graduate and advanced undergraduate students, and accessible to seasoned professionals, it provides the means to develop and employ mathematical representations of physical processes and systems.
1. Chapter 1: Introduction - p. 1 2. Chapter 2: Mathematical representations of physical phenomena - p. 9 3. Chapter 3: Solving linear algebraic equations - p. 61 4. Chapter 4: Vector spaces and their representations - p. 71 5. Chapter 5: Linear transformations and representations - p. 91 6. Chapter 6: Inner product spaces - p. 117 7. Chapter 7: Operators and matrix representations - p. 155 8. Chapter 8: Ordinary differential equations - p. 177 9. Chapter 9: Function representation and transforms - p. 199 10. Chapter 10: Partial differential equations - p. 219 11. Chapter 11: System and parameter identification - p. 271 12. Appendix A: A word on proofs - p. 337 13. Appendix B: Vector calculus and operations - p. 339 14. Appendix C: Simulate measurement errors - p. 357 15. Appendix D: Additional operations with square matrices - p. 361 16. Appendix E: Addendum to Chapter 7 - p. 367 17. Appendix F: Higher-order linear ODEs - p. 375 18. Appendix G: QR factorization - p. 381 19. Appendix H: Sequences and convergence - p. 385 20. Appendix I: Euler's equidimensional equation - p. 387 21. Appendix J: Sturm–Liouville equations - p. 389 22. Appendix K: Bessel's equation - p. 393 23. Appendix L: Best linear unbiased predictions and estimates - p. 397 24. Bibliography - p. 401 25. Index - p. 405
