This book is intended to provide students with an efficient introduction and accessibility to ordinary and partial differential equations, linear algebra, vector analysis, Fourier analysis, and special functions and eigenfunction expansions, for their use as tools of inquiry and analysis in modeling and problem solving. It should also serve as preparation for further reading where this suits individual needs and interests. Although much of this material appears in Advanced Engineering Mathematics, 6th edition, ELEMENTS OF ADVANCED ENGINEERING MATHEMATICS has been completely rewritten to provide a natural flow of the material in this shorter format. Many types of computations, such as construction of direction fields, or the manipulation Bessel functions and Legendre polynomials in writing eigenfunction expansions, require the use of software packages. A short MAPLE primer is included as Appendix B. This is designed to enable the student to quickly master the use of MAPLE for such computations. Other software packages can also be used.

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PART 1: ORDINARY DIFFERENTIAL EQUATIONS 1. First-Order Differential Equations 2. Linear Second-Order Equations 3. The Laplace Transform 4. Series Solutions PART 2: VECTORS, LINEAR ALGEBRA, AND SYSTEMS OF LINEAR DIFFERENTIAL EQUATIONS 5. Algebra and Geometry of Vectors 6. Matrices and Systems of Linear Equations 7. Determinants 8. Eigenvalues and Diagonalization 9. Systems of Linear Differential Equations PART 3: VECTOR ANALYSIS 10. Vector Differential Calculus 11. Vector Integral Calculus PART 4: FOURIER ANALYSIS AND EIGENFUNCTION EXPANSIONS 12. Fourier Series 13. The Fourier Integral and Transforms 14. Eigenfunction Expansions PART 5: PARTIAL DIFFERENTIAL EQUATIONS 15. The Wave Equation 16. The Heat Equation 17. The Potential Equation APPENDIX A. GUIDE TO NOTATION APPENDIX B. A MAPLE PRIMER

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Elements of Advanced Engineering Mathematics

O'Neil, Peter V.

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