Dimensional analysis. Vector algebra and vector calculus. Linear algebra, matrices, Cayley-Hamilton Theorem. Eigenvalues and eigenvectors. Linear ordinary differential equations of first & second order,Special functions (Hermite, Bessel, Laguerre and Legendre functions). Fourier series, Fourier and Laplace transforms. Elements of complex analysis, analytic functions; Taylor & Laurent series; poles, residues and evaluation of integrals. Elementary probability theory, random variables, binomial, Poisson and normal distributions. Central limit theorem.
Green’s function. Partial differential equations (Laplace, wave and heat equations in two and three dimensions). Elements of computational techniques: root of functions, interpolation, extrapolation, integration by trapezoid and Simpson’s rule, Solution of first order differential equation using Runge Kutta method. Finite difference methods. Tensors. Introductory group theory: SU(2), O(3).
|Beta and Gamma Function||00:33:00|
|Introduction to Double Integrals||00:12:00|
|Change of Order||01:50:00|
|Tangent Plane and Normal||00:18:00|
|Problems on Gradient||00:07:00|
|Divergence and Curl||00:41:00|
|Gauss Divergence Theorem||01:36:00|
|Conservative Vector Field||00:23:00|
|Introduction to Differential Equations||00:25:00|
|Differential Equation of First order and First Degree||02:01:00|
|Differential Equation with Constant Coefficient||01:19:00|
|Homogeneous Linear Differential Equation||00:49:00|
|Differential Equation of Second Order||01:24:00|
|Introduction to Matrices||02:17:00|
|Rank of Matrix||00:54:00|
|Revision of Matrices||02:03:00|
|Linear Equations – Vector Space Approach||01:43:00|
|Introduction to Eigenvalues and Eigenvectors||00:36:00|
|Diagonalisation of Matrices and its Applications||00:59:00|
|Properties of Eigenvalues||00:18:00|
|Cayley Hamilton Equation||00:08:00|
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