Appropriate for one- or two-semester Advanced Mathematics courses in departments of Mathematics and . This clear, pedagogically rich develops a strong understanding of the principles and practices that today’s need to know. Equally as effective as either a textbook or reference manual, it approaches concepts from an engineering perspective, making physical applications more vivid and substantial.

Its comprehensive instructional framework supports a conversational, down-to-earth narrative style, offering easy accessibility and frequent opportunities for application and reinforcement.

I. ORDINARY DIFFERENTIAL EQUATIONS.
1. 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 .
8. Systems of Linear Algebraic Equations; Gauss Elimination.
9. Vector Space.
10. Matrices and Linear Equations.
11. The Eigenvalue Problem.
12. Extension to Complex Case (Optional).

III. SCALAR and VECTOR FIELD THEORY.
13. Differential Calculus of Functions of Several .
14. Vectors in 3-Space.
15.Curves, Surfaces, and Volumes.
16. Scalar and Vector Field Theory.

IV. FOURIER SERIES AND PARTIAL DIFFERENTIAL EQUATIONS.
17. Fourier Series, Fourier Integral, Fourier Transform.
18. Diffusion Equation.
19. Wave Equation.
20. Laplace Equation.

V. COMPLEX VARIABLE THEORY.
21. Functions of a Complex Variable.
22. Conformal Mapping.
23. The Complex Integral Calculus.
24. 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.

Title: Advanced Engineering Mathematics
Author: Michael D. Greenberg
Edition: 2nd Edition
ISBN: 0133214311 | 9780133214314
Type: eBook | Solution Manual
Language: English