# Mathematical Methods in Physics 1

By Prof. Auditya Sharma   |   IISER Bhopal
Learners enrolled: 233
This would be the first of a two-part series on Mathematical Methods in Physics. The aim here is to provide a solid mathematical foundation for the budding Physicist eager to climb the ladder of self-learning. This course is designed to cater to an undergraduate student who excitedly embarks on a study of Physics, but is obstructed by the mathematics which appears so forbidding. The approach we will follow is one of showing many examples, and weaving the theory around examples. When possible, we will show how Mathematica can be used to offer extra insight.

INTENDED AUDIENCE
None
PREREQUISITES : We try to make this self-contained. However, some familiarity with the basic mathematical tools used in say, the first courses on Mechanics, Electromagnetism, would help.
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Summary
 Course Status : Upcoming Course Type : Core Duration : 8 weeks Start Date : 21 Feb 2022 End Date : 15 Apr 2022 Exam Date : 23 Apr 2022 IST Category : Mathematics Credit Points : 3 Level : Undergraduate

### Course layout

Week 1:Linear Algebra 1 : vectors, linear vector spaces, inner product, C-S inequality, linear independence, row-reduction
Week 2:Linear Algebra 2 : Matrices, determinants, span, basis, orthonormal basis, subspaces, linear operators.
Week 3: Linear Algebra 3: Direct sum, eigenvalues and eigenvectors, unitary, Hermitian, normal operators, transformations, defective matrices, diagonalization.
Week 4: Fourier Series and Transforms: periodic functions, series expansion, Fourier coefficients, Completeness relation, Fourier transforms.
Week 5: Ordinary Differential Equations 1: Introduction, Separable variables, orthogonal trajectories, linear first-order ODEs, Wronksian, exact ODEs, auxiliary equation.
Week 6: Ordinary Differential Equations 2: Inhomogeneous second order ODEs, method of undetermined coefficients, vibrations in mechanical systems, forced vibrations, resonance, linear superposition.
Week 7: Ordinary Differential Equations 3: Laplace transforms, Solving ODEs using Laplace transforms, Dirac Delta function.
Week 8: Ordinary Differential Equations 4: Green's function method, power series method, Frobenius method.

### Books and references

We aim to make the lectures self-contained. Standard undergraduate texts for Mathematical Methods in Physics like Mathematical Methods in the Physical Sciences (Mary Boas), Mathematical Physics (Joglekar), Mathematical Methods for Physicists (Arfken, Weber, Harries) could be useful aids.

### Prof. Auditya Sharma

IISER Bhopal
Auditya Sharma: Got a B.Tech in Engineering Physics from IIT Madras in 2006, followed by a PhD in Physics with specialization in Statistical Physics from the University of California at Santa Cruz in 2011. He followed this with two postdoctoral stints: one at the International Institute of Physics, Natal, Brazil from 2011-2013, and another at Tel Aviv University, Israel from 2014-2015. He has been on the faculty in the Department of Physics at IISER Bhopal since 2015.

### Course certificate

The course is free to enroll and learn from. But if you want a certificate, you have to register and write the proctored exam conducted by us in person at any of the designated exam centres.
The exam is optional for a fee of Rs 1000/- (Rupees one thousand only).
Date and Time of Exams: 23 April 2022  Morning session 9am to 12 noon; Afternoon Session 2pm to 5pm.
Registration url: Announcements will be made when the registration form is open for registrations.
The online registration form has to be filled and the certification exam fee needs to be paid. More details will be made available when the exam registration form is published. If there are any changes, it will be mentioned then.
Please check the form for more details on the cities where the exams will be held, the conditions you agree to when you fill the form etc.

CRITERIA TO GET A CERTIFICATE

Average assignment score = 25% of average of best 6 assignments out of the total 8 assignments given in the course.
Exam score = 75% of the proctored certification exam score out of 100

Final score = Average assignment score + Exam score

YOU WILL BE ELIGIBLE FOR A CERTIFICATE ONLY IF AVERAGE ASSIGNMENT SCORE >=10/25 AND EXAM SCORE >= 30/75. If one of the 2 criteria is not met, you will not get the certificate even if the Final score >= 40/100.

Certificate will have your name, photograph and the score in the final exam with the breakup. It will have the logos of NPTEL and IISER Bhopal .It will be e-verifiable at nptel.ac.in/noc.

Only the e-certificate will be made available. Hard copies will not be dispatched.

Once again, thanks for your interest in our online courses and certification. Happy learning.

- NPTEL team