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SYLLABUS

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
variables.
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
differential equations.
Transform Theory: Fourier Transform, Laplace Transform, z‐Transform.

### Course Curriculum

 LINEAR ALGEBRA Introduction to Matrices 02:17:00 Rank of Matrix 00:54:00 Linear Equations 02:04:00 Determinant 02:14:00 Revision of Matrices 02:03:00 Vector Spaces 01:05:00 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 Symmetric Matrices FREE 01:09:00 Cayley Hamilton Equation 00:08:00 Similar Matrices 00:16:00 CALCULUS Rolle Theorem 00:25:00 Lagrange Mean Value Theorem 00:33:00 Taylors Theorem 00:33:00

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