Course No Course Title L T P U
PHY123T Mathematical Physics-II 3 1 0 4
1. Course Objective:
Mathematics is the language in which Physics is expressed. So, it is essential to have a firm
grasp of Mathematics for a deeper understanding of Physical theories. This course, along with
Mathematical Physics-I, is designed to equip the students with some of the basic
mathematical tools. The main objectives of the course are to equip the students with the tools
of Matrix analysis to give the students a working knowledge Fourier series, to train the
students to solve ordinary differential equations, to make the students familiar with power
series method and Frobenius method for solving ordinary differential equations, to train the
students to solve partial differential equations using separation of variables, to make the
students familiar with some of the important special functions that are frequently encountered
in physics
2. Course outcome:
After the completion of the course, the students will have learnt some of the basic
mathematical tools to analyse physical problems.
✓ The students will have become familiar with Matrices; their eigenvalues and eigenvectors
✓ The students will learn about the properties of trace and determinant
✓ The students will be able to diagonalize symmetric matrix, a very useful procedure frequently
applied to analyse physical problems.
✓ The students will be familiar with Fourier series, a technique often applied by physicists to
simplify problems.
✓ The students will learn how to solve ordinary differential equations which comes up
frequently in physical problems such as Lagrange’s and Hamilton’s equation and many more
✓ The students will learn how to solve partial differential equations such as Laplace’s equation,
Heat equation, wave equation
✓ The students will be familiar with some of the special functions which often comes up as a
solution of differential equations.
✓ The students will be familiar with some of the special integrals which also comes up
frequently in physics
3. Text Book T1: Mathematical Methods in the Physical Sciences, Mary L. Boas
T2: Advanced Engineering Mathematics, Erwin Kreyszig
T3: Mathematical Methods for Physicists,
George B. Arfken Hans J. Weber
Reference Books:
R1: Mathematics for Physicists, Philippe Dennery, Andre Krzywicki
4. Lecture-wise plan:
Lecture Learning Objective Topics to be covered Chap./Sec.
Nos. (Text Book)
1-2 Introduction to Matrices Concept of the vector spaces . T1(3/1)
Introduction to Matrices as linear
transformation , matrix
operations
3-4 Rank of a matrix Concept of linear independence and T1(3/8)
the rank of a matrix
5 Matrix determinant and trace Definition of the determinant and trace T1(3/3),
of a matrix, properties of the
determinant and trace
6-9 Eigenvalues and Eiegenvectors Determination of eigenvalues and T1(10/4)
eigenvectors of a matrix, Cayley-
Hamilton's theorem
10 Tutorial-1 Tutorial session on eigenvalues and
eigenvectors
11 Orthogonal transformation Concept of inner product and T1(3/9),
orthogonality and orthogonal matrices. T1(10/3)
12-13 Some special matrices Symmetric and anti-symmetric T1(3/9)
matrices, Hermitian matrices, Unitary
matrices, showing that the
eigenvectors of a symmetric matrix
with different eigenvalues are
orthogonal to each other.
14 Tutorial-2 Tutorial on orthogonality and
symmetric matrices
15-18 Diagonalization Diagonalization of symmetric matrices T1(10/3)
by orthogonal transformations
19 Tutorial-3 Tutorial on determinant, trace and
diagonalization
20-23 Fourier Series Expansion of periodic functions in T1(7/1),
terms of sines and cosines, Fourier sine T1(7/5)
series of odd functions and cosine
series for even functions, Parseval's
theorem
24 Tutorial-4 Tutorial on Fourier Series
25 Parseval's theorem Derivation of Parseval's theorem T1(7/11)
26-28 Taylor Series Taylor series of a function around a T3(5/6)
point, convergence of Taylor series
29-31 Ordinary differential equations Solution of first order and second T1(8/5),
order ordinary differential equations T1(8/6)
with zero and nonzero right hand side;
concept of particular integral and
complementary functions
32-33 Tutorial-5 and 6; Forced and Solving the differential equation for
damped oscillation damped and forced oscillation.
34-36 Special functions; Legendre Frobenius method for solving T1(12/1)-
Polynomial differential equations and special T1(12/7)
functions; Legendre's differential
equation and Legendre polynomial,
Rodrigue's formula, orthogonality,
Generating function
37 Tutorial-7 Tutorial on Legendre's polynomial
38-39 Bessel function Bessel differential equation and bessel T1(12/12)-
functions, Recursion relations,
orthogonality of Bessel's functions. T1(12/19)
40-42 Hermite's polynomial Hermite's differential equation and T1(12/22)
Hermite's polynomial, generating
function for Hermite's polynomial
43 Tutorial-8 Tutorial on Bessel and Hermite's
Polynomial
44-54 Partial differential equation Solution of partial differential T1(13/2),
equations by separation of variables; T1(13/3),
solution of the wave equation, T1(13/4)
diffusion equation and Laplace's
equation
55 Tutorial-9 Tutorial on Partial differential
equations
56-59 Some special integrals Gamma and Beta functions-their T1(11/3),
properties and integral representations, T1(11/6),
relation between Gamma and Beta T1(11/7)
functions,
60 Tutorial-10 Tutorial and Beta and Gamma
functions
5. Evaluation Scheme:
Component Duration Weightage(%) Remarks
Internal I 25 Assignments/Quiz/Viva
Midterm 2 hours 20
Internal II 25 Assignments/Quiz/Viva
Comprehensive 3 hours 30
1. Chamber Consultation Hour: Course Instructor will announce in the class.
(During the Chamber Consultation Hours, the students can consult in Faculty’s
chamber without prior appointment.)
2. Attendance Policy: A Student must normally maintain a minimum of 75%
attendance in the course without which he/she shall be disqualified from appearing in
the respective examination.
3. Make-up Policy: A student, who misses any component of evaluation for genuine
reasons, must immediately approach the instructor with a request for make-up
examination stating reasons. The decision of the instructor in all matters of make-
up shall be final.
Date: C/I
