Advanced Applied Mathematics

by Ram Bilas Misra

Overview

The book deals with advanced topics of applied mathematics taught in universities and technical institutions. The subject matter is presented in 15 chapters. The first chapter offers the pre-requisites starting from numbers extending up to complex numbers. Vivid topics on group theory, vector algebra and vector calculus are included. The second chapter offers a comprehensive course on 'ordinary differential equations (ODE)' needed in the subsequent discussion. Möbius transformations, Laplace transform, inverse Laplace transform, their applications to solve ODEs, Fourier series, Bessel's and wave equations are dealt in detail while multi-valued functions, diffusion equation, rotation group and non-relativistic scattering are briefly covered. The book is suitable for one year/two semester course for graduate students with 3 hours weekly credits. The presentation is made as lucid as possible based on the author's long teaching experience of the subject for over 5 decades at different universities worldwide.

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Product Details

ISBN-13:	9781925823110
Publisher:	Central West Publishing
Publication date:	10/31/2018
Series:	Mathematics
Pages:	270
Product dimensions:	6.00(w) x 9.00(h) x 0.57(d)

About the Author

Prof. Dr. Ram Bilas Misra, former vice-Chancellor of Avadh University, Faizabad (Ayodhya), India, has a long experience of teaching the subject since 1962 at different universities worldwide. He has published 64 original research papers on Diff. Geom. of Finslerian Manifolds and Mathematical Physics in the leading research journals. As a regular reviewer, he has published reviews of over 100 research papers in "Mathl. Reviews" and "Zentralblatt für Mathematik". He has been frequently quoted both at home and abroad; notably, in the research monographs: "Foundations of Finsler Geometry" and "Special Finsler Spaces" by Prof. Makoto Matsumoto of Kyoto Univ., Japan and "Finsler Geometry, Relativity and Gauge Theories" by Prof. G.S. Asanov of Moscow State Univ. He has been a frequent visitor to the universities at Turin, Padua and ICTP, Trieste (all in Italy) and a visiting professor to the universities at Sopron (Hungary), Wroclaw (Poland) and Mahatma Gandhi Kashi Vidyapith, Varanasi (India).

Table of Contents

1. Pre-requisites (1-38)

2. Ordinary Differential Equations (39-104)

3. Bilinear (or Mobius) Transformations (105-110)

4. Multi-valued Functions (111-114)

5. Integral Representation of Functions (115-118)

6. Laplace Transforms of Functions (119-144)

7. Inverse Laplace Transform (145-166)

8. Applications of Laplace Transforms to Differential Equations (167-184)

9. Fourier Transforms of Functions (185-212)

10. Green's Function for Laplacian Operator (213-216)

11. Diffusion Equation (217-220)

12. Green's Function for the Helmholtz Operator (221-222)

13. Partial Differentiation & Wave Equation (223-234)

14. The Rotation Group (235-242)

15. Non-relativistic Scattering of Matter (243-246)