Advanced Engineering Mathematics 2E PIE
Develops a deep understanding of essential principles as well as hands-on/how-to knowledge of actual practices.
Serves as an excellent reference tool for both students and practitioners with coverage reaching well beyond Ordinary Differential Equations.
Reflects the authors vast engineering background, making mathematical principles and applications more relevant to future engineers. Physical applications integrated throughout the text include...
- Harmonic oscillator systems.
- Discussion of beats.
- Application of rank to stoichiometry and dimensional analysis.
Designs pedagogy with the needs of both instructors and students in mind, combining technical rigor with clarity and accessibility.
Features a wealth of diverse exercise and problem sets to both challenge and reinforce students understanding.
Provides unique Closure features at the end of each section and chapter reviews at the end of each chapter to review and summarize main points.
Includes useful and unique topics often ignored by other texts, including...
- Dimensional analysis to minimize parameters and guide plots and experiments.
- Introduction to singular integrals.
- Application of the mathematical concept of nonlinearity to nerve impulse and visual perception.
- An "omega method" for the derivation of the various space derivatives of base vectors in non-Cartesian coordinate systems.
Table of Contents
I. ORDINARY DIFFERENTIAL EQUATIONS
1. Introduction to Differential Equations
2. Equations of First Order
3. Linear Differential Equations of Second Order and Higher
4. Power Series Solutions
5. Laplace Transform
6. Quantitative Methods: Numerical Solution of Differential Equations
7. Qualitative Methods: Phase Plane and Nonlinear Differential Equations
II. LINEAR ALGEBRA
8. Systems of Linear Algebraic Equations
9. Gauss Elimination
10. Vector Space
11. Matrices and Linear Equations
12. The Eigenvalue Problem
13. Extension to Complex Case (Optional)
III. SCALAR AND VECTOR FIELD THEORY
14. Differential Calculus of Functions of Several Variables
15. Vectors in 3-Space
16. Curves, Surfaces, and Volumes
17. Scalar and Vector Field Theory
IV. FOURIER SERIES AND PARTIAL DIFFERENTIAL EQUATIONS
18. Fourier Series, Fourier Integral, Fourier Transform
19. Diffusion Equation
20. Wave Equation
21. Laplace Equation
V. COMPLEX VARIABLE THEORY
22. Functions of a Complex Variable
23. Conformal Mapping
24. The Complex Integral Calculus
25. Taylor Series, Laurent Series, and the Residue Theorem
Appendix A: Review of Partial Fraction Expansions
Appendix B: Existence and Uniqueness of Solutions of Systems of Linear Algebraic Equations
Appendix C: Table of Laplace Transforms
Appendix D: Table of Fourier Transforms
Appendix E: Table of Fourier Cosine and Sine Transforms
Appendix F: Table of Conformal Maps