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

Week

Topics

1.

Concept of Set, Binary
composition, Group, Ring, Field, Vector Space, Examples of
vector space in Euclidean space (ï•’3), Metric Space

Linear Operator, Matrix
representation, Transformation of axis, Change of Basis,
Unitary transformation, Similarity transformation, Eigen
value & Eigen vectors, Matrix decomposition

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

B.Sc,M.Sc,

1. Matrices and Tensors in Physics by A.W Joshi 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 (Schaums 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

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