MTH-483 Mathematical Methods of Physics

80 Pages·2013·0.62 MB·English

MTH-483
Mathematical Methods of Physics
MSc Mathematics
COMSATSInstituteofInformationTechnology
Islamabad,Pakistan
Instructor
DR SALEEM AHMED
Assistant Professor
COMSATS Institute of Information Technology, Islamabad
Since December 2011
Education
PhD - State University of New York, USA
MPhil - Quaid-i-Azam University, Islamabad
MSc - Quaid-i-Azam University, Islamabad
Motivation
The course introduces variety of mathematical methods essential for
technical proficiency in advanced courses of mathematics, theoretical
physics and engineering. The class will focus on developing both an
understanding of basic techniques and skill in their application. The
objective of this course is to provide an introductory overview of linear
integral and Partial differential equations and the integral transforms as
they apply in engineering and physics problems. Basic physical laws are
reviewed and applied to the derivation and interpretation of initial- and
boundary-value problems.
To introduce the methods that permits the determination of maximal
and minimal values of functionals
To show students how to formulate physical problems in terms of
partial differential equations
To provide students with a basic knowledge of Fourier series and
separation of variables and integral transforms.
Objectives
This course has the following four objectives:
To provide students with basic knowledge of integral equations
To show students how to formulate physical problems in terms of
partial differential equations
To provide students with a basic knowledge of Fourier series and
separation of variables and integral transforms.
Objectives
This course has the following four objectives:
To provide students with basic knowledge of integral equations
To introduce the methods that permits the determination of maximal
and minimal values of functionals
To provide students with a basic knowledge of Fourier series and
separation of variables and integral transforms.
Objectives
This course has the following four objectives:
To provide students with basic knowledge of integral equations
To introduce the methods that permits the determination of maximal
and minimal values of functionals
To show students how to formulate physical problems in terms of
partial differential equations
Objectives
This course has the following four objectives:
To provide students with basic knowledge of integral equations
To introduce the methods that permits the determination of maximal
and minimal values of functionals
To show students how to formulate physical problems in terms of
partial differential equations
To provide students with a basic knowledge of Fourier series and
separation of variables and integral transforms.
Objectives
This course has the following four objectives:
To provide students with basic knowledge of integral equations
To introduce the methods that permits the determination of maximal
and minimal values of functionals
To show students how to formulate physical problems in terms of
partial differential equations
To provide students with a basic knowledge of Fourier series and
separation of variables and integral transforms.
Integral equations of Volterra and Fredholm types
Introduction to calculus of variation of one variable: Euler Lagrange
equation
Solution of differential equations by Green functions
Boundary value problems
Solution of partial differential equations by separation of variables
Fourier series
Laplace and Fourier integral transformations and their applications to
solve ODEs and PDEs
Orthogonal functions and solution of Strum-Lioville system of
equations
Series solution methods of ODEs
Bessel functions, Legendre, Hermite polynomials etc.
Course Contents
Linear operators
Introduction to calculus of variation of one variable: Euler Lagrange
equation
Solution of differential equations by Green functions
Boundary value problems
Solution of partial differential equations by separation of variables
Fourier series
Laplace and Fourier integral transformations and their applications to
solve ODEs and PDEs
Orthogonal functions and solution of Strum-Lioville system of
equations
Series solution methods of ODEs
Bessel functions, Legendre, Hermite polynomials etc.
Course Contents
Linear operators
Integral equations of Volterra and Fredholm types