Linear Algebra : Review: Groups, Fields, & Matrices – Vector Spaces, Subspaces, Linearly dependent / independent of vectors – Basis, Dimension, Rank and Matrix Inverse – Linear Transformation, Isomorphism & Matrix Representation – System of Linear Equations, Eigenvalues and Eigenvectors – Method to find Eigenvalues and Eigenvectors, Diagonalization of Matrices – Jordan Canonical Form, Cayley Hamilton Theorem – Innerproduct Spaces, Cauchy-Schwarz Inequality – Orthogonality, Gram-Schmidt Orthogonalization Process – Spectrum of Special Matrices, Positive / Negative Definite Matrices.
Theory of Complex Variables : Concept of Domain, Limit, Continuity & Differentiability – Analytic Functions, C-R Equations – Harmonic Functions – Line Integral in the complex – Cauchy Integral Theorem – Cauchy Integral Formula – Power & Taylor’s Series of Complex Numbers – Power & Taylor’s Series of Complex Numbers (Contd.) – Taylor’s Laurent Series of f(z) & Singularities – Classification of Singularities , Residue and Residue Theorem.
Transform Calculus : Laplace Transform and its Existence – Properties of Laplace Transform – Evaluation of Laplace and Inverse Laplace Transform – Applications of Laplace Transform to Integral Equations and ODEs – Applications of Laplace Transform to PDEs – Fourier Series – Fourier Integral Representation of a Function – Introduction to Fourier Transform – Applications of Fourier Transform t PDEs.
Probability & Statistics : Laws of Probability – Problems in Probability – Random Variables – Special Discrete Distributions – Special Continuous Distributions – Joint Distributions and Sampling Distributions – Point Estimation – Interval Estimation – Basic Concepts of Testing of Hypothesis – Tests for Normal Populations.
No Reviews found for this course.