Lecture 1 - Set, Group, Field, Ring
Lecture 2 - Vector Space
Lecture 3 - Span, Linear combination of vectors
Lecture 4 - Linearly dependent and independent vector, Basis
Lecture 5 - Dual Space
Lecture 6 - Inner Product
Lecture 7 - Schwarz Inequality
Lecture 8 - Inner product space, Gram-Schmidt Ortho-normalization
Lecture 9 - Projection operator
Lecture 10 - Transformation of Basis
Lecture 11 - Transformation of Basis (Continued...)
Lecture 12 - Unitary transformation, Similarity Transformation
Lecture 13 - Eigen Value, Eigen Vectors
Lecture 14 - Normal Matrix
Lecture 15 - Diagonalization of a Matrix
Lecture 16 - Hermitian Matrix
Lecture 17 - Rank of a Matrix
Lecture 18 - Cayley - Hamilton Theorem, Function space
Lecture 19 - Metric Space, Linearly dependent - independent functions
Lecture 20 - Linearly dependent –independent functions (Continued...), Inner Product of functions
Lecture 21 - Orthogonal functions
Lecture 22 - Delta Function, Completeness
Lecture 23 - Fourier
Lecture 24 - Fourier Series (Continued...)
Lecture 25 - Parseval Theorem, Fourier Transform
Lecture 26 - Parseval Relation, Convolution Theorem
Lecture 27 - Polynomial space, Legendre Polynomial
Lecture 28 - Monomial Basis, Factorial Basis, Legendre Basis
Lecture 29 - Complex Numbers
Lecture 30 - Geometrical interpretation of complex numbers
Lecture 31 - de Moivre’s Theorem
Lecture 32 - Roots of a complex number
Lecture 33 - Set of complex no, Stereographic projection
Lecture 34 - Complex Function, Concept of Limit
Lecture 35 - Derivative of Complex Function, Cauchy-Riemann Equation
Lecture 36 - Analytic Function
Lecture 37 - Harmonic Conjugate
Lecture 38 - Polar form of Cauchy-Riemann Equation
Lecture 39 - Multi-valued function and Branches
Lecture 40 - Complex Line Integration, Contour, Regions
Lecture 41 - Complex Line Integration (Continued...)
Lecture 42 - Cauchy-Goursat Theorem
Lecture 43 - Application of Cauchy-Goursat Theorem
Lecture 44 - Cauchy’s Integral Formula
Lecture 45 - Cauchy’s Integral Formula (Continued...)
Lecture 46 - Series and Sequence
Lecture 47 - Series and Sequence (Continued...)
Lecture 48 - Circle and radius of convergence
Lecture 49 - Taylor Series
Lecture 50 - Classification of singularity
Lecture 51 - Laurent Series, Singularity
Lecture 52 - Laurent series expansion
Lecture 53 - Laurent series expansion (Continued...), Concept of Residue
Lecture 54 - Classification of Residue
Lecture 55 - Calculation of Residue for quotient from
Lecture 56 - Cauchy’s Residue Theorem
Lecture 57 - Cauchy’s Residue Theorem (Continued...)
Lecture 58 - Real Integration using Cauchy’s Residue Theorem
Lecture 59 - Real Integration using Cauchy’s Residue Theorem (Continued...)
Lecture 60 - Real Integration using Cauchy’s Residue Theorem (Continued...)
