# Mathematical Methods In Physics -I

By Prof. Samudra Roy   |   IIT Kharagpur
Learners enrolled: 1079
Mathematical Methods in Physics- I is a basic course in physics for M.Sc (and/or B.Sc 3rd year) students which provides an overview of the essential mathematical methods used in different branches of physics. This course is mainly divided into two parts. In the first part we learn different aspects of the linear vector space which is the essential mathematical tool for quantum mechanics and can be applicable for many physical systems outside the domain of quantum mechanics. In the second part we cover complex analysis whose general application is vast. Students in 3rd year B. Sc or 1st year M. Sc are encouraged to take this course. All the assignments and the final examination will be of objective type.

INTENDED AUDIENCE: M.Sc Physics

PREREQUISITES: Basic calculus; Algebra; Basic complex numbers
Summary
 Course Status : Completed Course Type : Core Duration : 12 weeks Category : Physics Credit Points : 3 Level : Undergraduate Start Date : 25 Jul 2022 End Date : 14 Oct 2022 Enrollment Ends : 08 Aug 2022 Exam Date : 29 Oct 2022 IST

Note: This exam date is subjected to change based on seat availability. You can check final exam date on your hall ticket.

### Course layout

Week 1: Concept of Set, Binary composition, Group, Ring, Field, Vector Space, Examples of vector space in Euclidean space (R), Metric Space
Week 2:  Linearly dependent & independent vectors, Dimensions, Basis, Span, Linear Functional, Dual space, Inner Product, Normed Space, Schwarz inequality, Gram-Schmidt orthonormalization, Completeness
Week 3:  Linear Operator, Matrix representation, Transformation of axis, Change of Basis, Unitary transformation, Similarity transformation, Eigen value & Eigen vectors, Matrix decomposition
Week 4:  Elementary Matrices,Rank, Subspace with examples. Diagonalization of matrix, The Cayley-Hamilton theorem, Function, mapping, Function space, Linearly dependent & independent function, Examples, Wronskian, Gram-determinant
Week 5:  Inner product in function space, Orthogonal functions, Delta function, Completeness, Gram-Schmidt orthogonalization in function space, Legendre polynomials
Week 6:  Fourier coefficients, Fourier Transform, Examples, Fourier Series, Parseval’s relation, Convolution theorem, Polynomial Space
Week 7:  Complex numbers, Roots of the complex numbers, Complex variable & Function, Limit and continuity, differentiability of a complex function, Branch Cut and branch point
Week 8:  Cauchy-Riemann equation, Analytic function, Harmonic conjugate function, Examples, Singularities and their classifications
Week 9:  Complex integration, Simply and multiply connected regions, Cauchy-Goursat theorem, Cauchy’s integral formula, Examples
Week 10:  Series & Sequence, Convergence test, Radius of convergence, Taylor’s series, Maclaurin Series, Examples
Week 11:  Laurent Series, Zeros and poles, Essential singularity, Examples, Residue, Classification of residue, Residue calculations for different orders of poles
Week 12:  Cauchy’s residue theorem, Application of residue theorem to calculate the definite integrals, Examples

### Books and references

1. Matrices and Tensors in Physics by A.W Joshic
2. Mathematical Methods for Physicists by G. Arfken
3. Mathematical Methods for Physics by J. Mathews & R.L Walker
4. Mathematics for Physicists by P. Dennery & A. Krzywicki
5. Mathematics for Quantum Mechanics by J.D Jackson
6. Vector space and Matrix in Physics by M.C Jain
7. A first course in Complex Analysis by D.G. Zill & P.D. Shanahan
8. Complex Variable (Schaum’s Series) By M.R Spiegel
9. Complex Variable and Application by R.V Churchill and J.W Brown
10. Mathematical Methods in the Physical Sciences by M.L.Boas

### Prof. Samudra Roy

IIT Kharagpur
I did my PhD from CGCRI (a CSIR Lab) in 2009 and carried out my post-doctoral research from Hokkaido University, Japan and Max Planck Institute, Germany during 2009-2013. In 2013, I joined in the Physics Department, IIT-Kharagpur as an assistant professor and also associated with the Center for Theoretical Studies-IIT Kharagpur. My research field is nonlinear photonics.

### 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:  29 October 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 8 assignments out of the total 12 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 IIT Kharagpur. 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