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Course Information

Course Title

Introduction to Mathematical Physics 1

Course Description

 This course covers the following topics: Principles of Integral Evaluation, Different system of coordinates, Multi dimensional differential operators and its application in Physics, Complex number, Differential equations and Fourier Series.

Text Book

References

Mathematical methods in the physical science,

 2nd Edition Mary Boas

Course Objectives

 Present new types of integrals

Introduce different system of coordinates

Using multi dimensional differential operators in different system of coordinates

Present the complex numbers

Solving first order and second order differential equations

Present Fourier series

Useful Resources

Mathematical Methods in the Physical Sciences. By Arfken, 2nd Ed.

Course Content

Week

Topics

Chapter in Text

1

Review to Principles Scalars and vectors,

Chapter 1

2-4

rotation of axes, scalar product, vector product, division by a vector, triple product, gradient, differentiation of vectors, vector integration, divergence, Gauss’s divergence theorem, Gauss’s law, the curl, Stokes’s theorem, successive application of gradient, Greens theorem, potential theory.

Chapter 1

5-9

Curvilinear Coordinate:

Cartesian, spherical, and cylindrical coordinates, transformation from spherical to Cartesian, from Cartesian to spherical, from cylindrical to Cartesian, from Cartesian to cylindrical, separation of variables in Cartesian, spherical, and Cylindrical system of coordinates.

Chapter 2

10

Chapter (3) Complex Numbers

Introduction, graphical representation of complex number, complex conjugate, Addition, subtraction, multiplication and division of complex numbers, De Moivre’s formula, powers and roots of a complex number, function of complex variable, examples and applications

Chapter 3

11-13

Chapter (6) Ordinary Differential Equations

Introduction, separable equations, linear equations, exact equations, homogenous differential equations, Bernoulli equation, homogenous second order linear differential equations with constant coefficients, Inhomogeneous second order linear differential equations with constant coefficients.

Chapter 6

14-15

Chapter (7) Fourier Series

Introduction, useful integrals, calculations of Fourier coefficients, general form of Fourier series, complex form of Fourier series, periodic functions with interval 2l, Fourier expansion of even and odd functions, completeness relation (Parseval’s theorem), some properties and uses of Fourier series

Chapter 7