Advanced engineering mathematics
Langue : Anglais
Auteur : LOPEZ
This innovative text was written for the one or two-semester, sophomore/junior level advanced maths course for engineers. It was built from the ground up using a Computer Algebra System, offering the student opportunities to visualize and experience the maths at every turn. The text has been designed to accommodate a variety of teaching styles, and varying levels on technology integration. It has a logical arrangement with many short self-contained sections, and many real-world applications of interest to engineering students. Chapter Introductions and Chapter Summaries help to make the material more accessible, and Chapter Review Exercises provides constant checks along the way.
- Preface.
UNIT I. ORDINARY DIFFERENTIAL EQUATIONS - PART 1.
1. First-Order Differential Equations.
2. Models.
3. Methods.
4. Numeric Solutions.
5. Second-Order.
6. The Laplace Transform.
UNIT II. INFINITE SERIES.
7. Sequences and Series of Numbers.
8. Sequences and Series of Functions.
9. Power Series.
10. Fourier Series.
11. Asymptotic Series.
UNIT III. ORDINARY DIFFERENTIAL EQUATIONS - PART 2.
12. Systems of First-Order ODEs.
13. Numerical Techniques for Second-Order ODEs.
14. Series Solutions.
15. Boundary Value Problems.
16. The Eigenvalue Problem.
UNIT IV. VECTOR CALCULUS.
17. Space Curves.
18. The Gradient Vector.
19. Line Integrals in the Plane.
20. Additional Vector Differential Operators.
21. Integration.
22. Non-Cartesian Coordinates.
23. Miscellaneous Results.
UNIT V. BOUNDARY VALUE PROBLEMS FOR PDEs.
24. Wave Equation.
25. Heat Equation.
26. Laplace's Equation on a Rectangle.
27. Nonhomogeneous Boundary Value Problems.
28. Two-Dimensional Problems.
29. Separation of Variables in Non-Cartesian Coordinates.
30. Transform Techniques.
UNIT VI. MATRIX ALGEBRA.
31. Vectors as Arrows.
32. Change of Coordinates.
33. Matrix Computations.
34. Matrix Factorizations.
UNIT VII. COMPLEX VARIABLES.
35. Fundamentals.
36. Applications.
UNIT VIII. NUMERICAL METHODS
37. Equations on One Variable - Preliminaries.
38. Equations on One Variable - methods.
39. Systems of Equations.
40. Interpolation.
41. Approximation of Continuous Functions.
42. Numeric Differentation.
43. Numeric Intergration.
44. Approximation of Discrete Data.
45. Numerical Calculation of Eigenvalues.
UNIT IX. CALCULUS OF VARIATIONS.
46. Basic Formalisms.
47. Constrained Optimization.
48. Variational Mechanics.
- A CD-ROM is included in the back of every book, which contains Maple worksheets. The Maple worksheets are fully integrated with the books content, and provide a great resource for students when working on exercise sections. The CD-ROM allows the instructor and the student to take full advantage of what the text has to offer.
- Logical arrangement with many short self-contained sections.
- Exercises are divided into two sections: those designed to be computed by hand (A exercises), and those to be computed with a Computer Algebra System program (B exercises).
- Examples throughout which illustrate to students how concepts are conceived.
- Multi-stage exercises appear in every section, which include exercises that demand interpretation and analysis.
- Unit and Chapter
Date de parution : 03-2001
Ouvrage de 1300 p.
Thème d’Advanced engineering mathematics :
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