Grant B Gustafson, Calvin H Wilcox

Analytical and Computational Methods of Advanced Engineering Mathematics

• Gebundenes Buch

Produktbeschreibung

(NOTES)This text focuses on the topics which are an essential part of the engineering mathematics course:ordinary differential equations, vector calculus, linear algebra and partial differential equations. Advantages over competing texts: 1. The text has a large number of examples and problems - a typical section having 25 quality problems directly related to the text. 2. The authors use a practical engineering approach based upon solving equations. All ideas and definitions are introduced from this basic viewpoint, which allows engineers in their second year to understand concepts that would otherwise be impossibly abstract. Partial differential equations are introduced in an engineering and science context based upon modelling of physical problems. A strength of the manuscript is the vast number of applications to real-world problems, each treated completely and in sufficient depth to be self-contained. 3. Numerical analysis is introduced in the manuscript at a completely elementary calculus level. In fact, numerics are advertised as just an extension of the calculus and used generally as enrichment, to help communicate the role of mathematics in engineering applications. 4.The authors have used and updated the book as a course text over a 10 year period. 5. Modern outline, as contrasted to the outdated outline by Kreysig and Wylie. 6. This is now a one year course. The text is shorter and more readable than the current reference type manuals published all at around 1300-1500 pages.

---

This book focuses on the topics which provide the foundation for practicing engineering mathematics: ordinary differential equations, vector calculus, linear algebra and partial differential equations. Destined to become the definitive work in the field, the book uses a practical engineering approach based upon solving equations and incorporates computational techniques throughout.

Produktdetails

• Verlag: Springer Nature Singapore / Springer US
• 1998 edition
• Seitenzahl: 733
• Erscheinungstermin: 25. September 1998
• Englisch
• Abmessung: 261mm x 186mm x 48mm
• Gewicht: 1511g
• ISBN-13: 9780387982656
• ISBN-10: 0387982655
• Artikelnr.: 07716491

Inhaltsangabe

1 Numerical Analysis.
1.1 The Nature of Numerical Analysis.
1.2 Polynomial Interpolation.
1.3 Numerical Integration and Differentiation.
1.4 Solution of Equations.
1.5 Inverse Functions.
1.6 Implicit Functions.
1.7 Numerical Summation of Infinite Series.
2 Ordinary Differential Equations of First Order.
2.1 The Nature of Differential Equations.
2.2 Separable Equations.
2.3 Linear First
Order Equations.
2.4 Exact Equations.
2.5 Applications to Some Second
Order Equations.
2.6 The Initial Value Problem.
2.7 Numerical Methods for the Initial Value Problem.
3 Ordinary Differential Equations of Higher Order.
3.1 Examples from Engineering and Physics.
3.2 Linear Second
Order Equations
Structure of Solutions.
3.3 Linear Second
Order Equations with Constant Coefficients.
3.4 Linear Second
Order Equations with Analytic Coefficients.
3.5 Numerical Methods for Second
Order Equations.
3.6 Linear Equations of Order n > 2.
4 The Laplace Transform.
4.1 The Nature of the Laplace Transform.
4.2 The Laplace Transforms of Some Elementary Functions.
4.3 Operational Rules for the Laplace Transform.
4.4 Applications to Differential Equations.
4.5 Applications to Systems of Differential Equations.
5 Linear Algebra.
5.1 Systems of Linear Equations.
5.2 The Gauss Elimination Method.
5.3 Vector Spaces.
5.4 Matrices and Matrix Algebra.
5.5 The Fundamental Theorem of Linear Algebra.
5.6 Determinants and Cramer's Rule.
5.7 Eigenvalues and Eigenvectors.
6 Vector Analysis.
6.1 Vector Algebra.
6.2 Vector Calculus of Curves in Space.
6.3 Vector Calculus of Surfaces in Space.
6.4 Calculus of Scalar and Vector Fields.
6.5 Integral Theorems of Vector Calculus.
6.6 X
Ray Diffraction and Crystal Structure.
7 Partial Differential Equations of MathematicalPhysics.
7.1 Vibrating Strings: D'Alembert's Wave Equation.
7.2 Heat Diffusion in Rods: Fourier's Heat Equation.
7.3 Heat Diffusion in Plates.
7.4 Steady
State Heat Diffusion in Plates: The Laplace Equation.
7.5 Vibrations of Drums.
7.6 Heat Diffusion in Solids.
7.7 Steady
State Heat Diffusion in Solids.
8 Fourier Analysis and Sturm
Liouville Theory.
1 Fourier Series.
II Fourier Integrals.
III Sturm
Liouville Theory.
9 Boundary Value Problems of Mathematical Physics.
9.1 Heat Diffusion in One Dimension.
9.2 Vibration of Strings and Traveling Waves.
9.3 Steady
State Diffusion of Heat in Plates.
9.4 Transient Diffusion of Heat in Plates.
9.5 Vibrations of Drums.
9.6 Steady
State Diffusion of Heat in Solids.
9.7 The Laplace Transform Method.
Appendix: Answers and Hints to Selected Exercises.
References.

Rezensionen

G.B. Gustafson and C. H. Wilcox Analytical and Computational Methods of Advanced Engineering Mathematics "This is a modern version of the textbook on applied mathematics for undergraduate engineering students. It provides a quick survey to ordinary differential equations, linear algebra, the Laplace transform, vector analysis, Fourier series and other eigenfunction expansions, and Fourier transforms, with applications to the wave equation and heat equation . . . has an excellent set of exercises, and the appendix provides answers."-ZENTRALBLATT MATH