Advanced Engineering Mathematics

Beginning with linear algebra and later expanding into calculus of variations, Advanced Engineering Mathematics provides accessible and comprehensive mathematical preparation for advanced undergraduate and beginning graduate students taking engineering courses. This book offers a review of standard mathematics coursework while effectively integrating science and engineering throughout the text. It explores the use of engineering applications, carefully explains links to engineering practice, and introduces the mathematical tools required for understanding and utilizing software packages.

• Provides comprehensive coverage of mathematics used by engineering students
• Combines stimulating examples with formal exposition and provides context for the mathematics presented
• Contains a wide variety of applications and homework problems
• Includes over 300 figures, more than 40 tables, and over 1500 equations
• Introduces useful Mathematica™ and MATLAB® procedures
• Presents faculty and student ancillaries, including an online student solutions manual, full solutions manual for instructors, and full-color figure sides for classroom presentations

Advanced Engineering Mathematics

covers ordinary and partial differential equations, matrix/linear algebra, Fourier series and transforms, and numerical methods. Examples include the singular value decomposition for matrices, least squares solutions, difference equations, the z-transform, Rayleigh methods for matrices and boundary value problems, the Galerkin method, numerical stability, splines, numerical linear algebra, curvilinear coordinates, calculus of variations, Liapunov functions, controllability, and conformal mapping.

This text also serves as a good reference book for students seeking additional information. It incorporates Short Takes sections, describing more advanced topics to readers, and Learn More about It sections with direct references for readers wanting more in-depth information.

Table of Contents

Chapter 1 Linear Algebraic Equations, Matrices, And Eigenvalues
Chapter 2 Matrix Theory
Chapter 3 Scalar Odes I: Homogeneous Problems
Chapter 4 Scalar Odes Ii: Nonhomogeneous Problems
Chapter 5 Linear Systems Of Odes
Chapter 6 Geometry, Calculus, And Other Tools
Chapter 7 Integral Theorems, Multiple Integrals, And Applications
Chapter 8 Numerical Methods I
Chapter 9 Fourier Series
Chapter 10 Partial Differential Equations Models
Chapter 11 Separation Of Variables For Pdes
Chapter 12 Numerical Methods Ii
Chapter 13 Optimization
Chapter 14 Calculus Of Variations
Chapter 15 Functions Of A Complex Variable
Chapter 16 Conformal Mapping
Chapter 17 Integral Transform Methods
Chapter 18 Nonlinear Ordinary Differential Equations
Appendix A: Partial Fractions
Appendix B: Laplace Transforms Definitions and Derivations
Appendix C: Series Solutions of ODEs