Lecture Notes

   Linear Algebra (Instructor : Abhijit Pal)

   Linear Algebra Lecture Note Files 

• Lecture 1 : Matrices, System of Linear Equations, Gauss Elimination Method

• Lecture 2 : Echelon Form, Elementary Matrices & Row Reduction

• Lecture 3 : Invertible Matrices

• Lecture 4 : Determinant and its properties

• Lecture 5 : Determinant, Computation of Inverse & Cramer's Rule

• Lecture 6 : Vector Space & Subspaces

• Lecture 7 : Linear Span of vectors, Linearly Independent & Basis Vectors

• Lecture 8 : Dimension of Vector Space

• Lecture 9 : Intersection, sum of Subspaces & Quotient Space

• Lecture 10 : Linear Transformation & Rank-Nullity Theorem

• Lecture 11 : Isomorphism Theorem & Rank of a Matrix

• Lecture 12 : Solvability of System of Linear Equations using Rank

• Lecture 13 : Inner Product Space & Cauchy-Schwarz Inequality

• Lecture 14 : Orthogonal Basis, Gram Schmidt Orthogonalization & Orthogonal projection

• Lecture 15 : Direct Sum of Subspaces, Fundamental Subspaces, Lease Square Solutions

• Lecture 16 : Eigen Vectors, Eigen Values & Diagonalization of Matrices

• Lecture 17 : Diagonalization of Matrices, Examples and applications

• Lecture 18 : Orthogonal Matrix and Diagonalization of real symmetric matrices

• Lecture 19 : Existence of Basis : Zorn's Lemma

    ODE (Instructor : S.Ghorai)

     ODE Lecture Note Files 

• Lecture 1 : Introduction, Concept of Solutions, Applications

• Lecture 2 : Geometrical Interpretation

• Lecture 3 : Solution of First Order Equations

• Lecture 4 : Linear Equations, Bernoulli Equations, Orthogonal trajectories, Oblique trajectories

• Lecture 5 : Picard’s existence and uniquness theorem, Picard’s iteration

• Lecture 6 : Numerical methods: Euler’s method, improved Euler’s method

• Lecture 7 : Second order linear ODE, fundamental solutions, reduction of order

• Lecture 8 : Homogeneous linear ODE with constant coefficients

• Lecture 9 : Non-homogeneous linear ODE, method of undetermined coefficients

• Lecture 10 : Non-homegeneous linear ODE, method of variation of parameters

• Lecture 11 : Euler-Cauchy Equation

• Lecture 12 : Power Series Solutions: Ordinary points

• Lecture 13 : Legendre Equation, Legendre Polynomial

• Lecture 14 : Frobenius series: Regular singular points

• Lecture 15 : Bessel’s equation, Bessel’s function

• Lecture 16 : Strum comparison theorem, Orthogonality of Bessel functions

• Lecture 17 : Laplace Transform, inverse Laplace Transform, Existence and Properties of Laplace Transform

• Lecture 18 : Unit step function, Laplace Transform of Derivatives and Integration, Derivative and Integration of Laplace Transforms

• Lecture 19 : Laplace Transform of Periodic Functions, Convolution, Applications

    The End !