Linear Algebra: Matrix Algebra, Systems of linear equations, Eigenvalues, Eigenvectors.
Calculus: Mean value theorems, Theorems of integral calculus, Evaluation of definite and improper
integrals, Partial Derivatives, Maxima and minima, Multiple integrals, Fourier series, Vector identities,
Directional derivatives, Line integral, Surface integral, Volume integral, Stokes’s theorem, Gauss’s
theorem, Green’s theorem.
Differential equations: First order equations (linear and nonlinear), Higher order linear differential
equations with constant coefficients, Method of variation of parameters, Cauchy’s equation, Euler’s
equation, Initial and boundary value problems, Partial Differential Equations, Method of separation of
Complex variables: Analytic functions, Cauchy’s integral theorem, Cauchy’s integral formula, Taylor
series, Laurent series, Residue theorem, Solution integrals.
Probability and Statistics: Sampling theorems, Conditional probability, Mean, Median, Mode, Standard
Deviation, Random variables, Discrete and Continuous distributions, Poisson distribution, Normal
distribution, Binomial distribution, Correlation analysis, Regression analysis.
Numerical Methods: Solutions of nonlinear algebraic equations, Single and Multi‐step methods for
Transform Theory: Fourier Transform, Laplace Transform, z‐Transform.
|Introduction to Matrices||02:17:00|
|Rank of Matrix||00:54:00|
|Revision of Matrices||02:03:00|
|Linear Equations – Vector Space Approach||FREE||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|
|Lagrange Mean Value Theorem||00:33:00|
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