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Advanced Engineering Mathematics (10E) by Erwin Kreyszig

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Advanced Engineering Mathematics (10E) written by Erwin Kreyszig , Professor of Mathematics Ohio State University Columbus, Ohio. In collaboration with
Herbert Kreyszig , New York, New York
Edward J. Normintion, Associate Professor of Mathematics, Carleton University, Ottawa, Ontario.
This book provides a comprehensive, thorough, and up-to-date treatment of engineering mathematics. It is intended to introduce students of engineering, physics, mathematics, computer science, and related fields to those areas of applied mathematics that are most relevant for solving practical problems. A course in elementary calculus is the sole prerequisite. (However, a concise refresher of basic calculus for the student is included on the inside cover and in Appendix 3.)
The parts of the book are kept independent. In addition, individual chapters are kept as independent as possible. (If so needed, any prerequisites—to the level of individual sections of prior chapters—are clearly stated at the opening of each chapter.) We give the instructor maximum flexibility in selecting the material and tailoring it to his or her need. The book has helped to pave the way for the present development of engineering mathematics. This new edition will prepare the student for the current tasks and the future by a modern approach to the areas listed above. We provide the material and learning tools for the students to get a good foundation of engineering mathematics that will help them in their careers and in further studies.

Title: Advanced Engineering Mathematics
Edition: 10th
Author(s): Erwin Kreyszig, Herbert Kreyszig, Edward J. Norminton
Publisher: Wiley
Year: 2011
Pages: 1283
Type: PDF
Language: English
ISBN: 9780470458365,0470458364
Country: Canada
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About Author :- Erwin O. Kreyszig (1922–2008) was a German Canadian applied mathematician and the Professor of Mathematics at Carleton University in Ottawa, Ontario, Canada. He was a pioneer in the field of applied mathematics: non-wave replicating linear systems. He was also a distinguished author, having written the textbook Advanced Engineering Mathematics, the leading textbook for civil, mechanical, electrical, and chemical engineering undergraduate engineering mathematics.
Kreyszig received his Ph.D. degree in 1949 at the University of Darmstadt under the supervision of Alwin Walther.

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Advanced Engineering Mathematics (10E) written by Erwin Kreyszig cover the following topics.

  • Ordinary Differential Equations (ODEs)
    First-Order ODEs, Second-Order Linear ODEs, Higher Order Linear ODEs, Systems of ODEs. Phase Plane. Qualitative Methods, For Reference: Basics of Matrices and Vectors, Systems of ODEs as Models in Engineering Applications, Basic Theory of Systems of ODEs. Wronskian, Constant-Coefficient Systems. Phase Plane Method, Criteria for Critical Points. Stability, Qualitative Methods for Nonlinear Systems, Nonhomogeneous Linear Systems of ODEs, Series Solutions of ODEs. Special Functions, Power Series Method, Legendre’s Equation. Legendre Polynomials Pn(x), Extended Power Series Method: Frobenius Method, Bessel’s Equation. Bessel Functions J(x), Bessel Functions of the Y(x). General Solution, Laplace Transforms, Laplace Transform. Linearity. First Shifting Theorem (s-Shifting), Transforms of Derivatives and Integrals. ODEs, Unit Step Function (Heaviside Function) Second Shifting Theorem (t-Shifting), Short Impulses. Dirac’s Delta Function. Partial Fractions, Convolution. Integral Equations, Differentiation and Integration of Transforms, ODEs with Variable Coefficients, Systems of ODEs, Laplace Transform: General Formulas, Table of Laplace Transforms

  • Linear Algebra
    Linear Algebra, Linear Algebra: Matrix Eigenvalue Problems, Vector Differential Calculus. Grad, Div, Curl, Vector Integral Calculus. Integral Theorems

  • Fourier Analysis. Partial Differential Equations (PDEs)
    Fourier Analysis, Partial Differential Equations (PDEs)

  • Complex Analysis
    Complex Numbers and Functions, Complex Differentiation, Review Questions and Problems, Complex Integration, Power Series, Taylor Series, Laurent Series. Residue Integration, Conformal Mapping, Complex Analysis and Potential Theory

  • Numeric Analysis
    Numerics in General, Numeric Linear Algebra, Numerics for ODEs and PDEs

  • Optimization, Graphs
    Unconstrained Optimization. Linear Programming, Graphs. Combinatorial Optimization

  • Probability, Statistics
    Data Analysis. Probability Theory, Mathematical Statistics

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