Course Structure

• There will be approximately 35-45 marks out of 200 marks for CSIR-NET Exam.
• Expected Number of Questions & Marks Weightage for GATE Exam: 5 to 6 Questions and 9-10 marks out of 100 marks.
• Expected Number of Questions & Marks Weightage for JEST Exam: 7 to 8 Questions and 14-15 marks out of 100 marks.

• Dimensional Analysis
• Vector Algebra and Vector Calculus; Curvilinear Coordinate Systems

• Linear Algebra: Matrices, Cayley-Hamilton Theorem, Eigenvalues, Eigenvectors, Basis, Orthogonality, Completeness, Similarity Transformations, Diagonalization

• Linear Differential Equations: First and Second Order; Sturm–Liouville Theory
• Special Functions: Hermite, Bessel, Laguerre, Legendre
• Partial Differential Equations: Laplace, Wave, Heat Equations in 2D and 3D
• Green’s Functions

• Fourier Series, Fourier Transforms, Laplace Transforms

• Complex Analysis: Elements of Complex Analysis, Analytic Functions, Cauchy-Riemann Conditions, Cauchy's Theorem, Singularities, Residue Theorem and Applications, Taylor and Laurent Series

• Random Variables, Binomial, Poisson, Normal Distributions; Central Limit Theorem

• Root Finding, Interpolation, Extrapolation, Integration by trapezoidal and Simpson's Rule, Solution of first-order differential equations using Runge-Kutta Method, and Finite differences methods.

• Tensors: Covariant and Contravariant
• Group Theory Basics: Discrete Groups, SU(2), O(3)

•  Precision, Accuracy, Propagation of Errors, Least Squares Fitting

• Mathematical Physics: H. K. Dass, Dr. Rama Verma (S. Chand Publications)
• Advanced Engineering Mathematics: Erwin Kreyszig (Wiley Publications)