Introduction of vector space;Metric, Norm, Inner Product space;Examples
Onto, into, one to one function, completeness of space
Vectors: Linear combination of vectors, dependent/independent vectors; Orthogonal and orthonormal vectors; Gram-Schmidt orthogonalization; Examples
Contraction Mapping: Definition; Applications in Chemical Engineering; Examples
Matrix, determinants and properties
Eigenvalue Problem:Various theorems; Solution of a set of algebraic equations; Solution of a set of ordinary differential equations; Solution of a set of non-homogeneous first order ordinary differential equations (IVPs)
Applications of eigenvalue problems: Stability analysis; Bifurcation theory; Examples
Partial Differential equations:Classification of equations; Boundary conditions;Principle of Linear superposition
Special ODEs and Adjoint operators:Properties of adjoint operator; Theorem for eigenvalues and eigenfunctions;
Solution of linear, homogeneous PDEs by separation of variables: Cartesian coordinate system & different classes of PDEs; Cylindrical coordinate system ; Spherical Coordinate system
Solution of non-homogeneous PDEs by Green’s theorem
Solution of PDEs by Similarity solution method
Solution of PDEs by Integral method
Solution of PDEs by Laplace transformation
Solution of PDEs by Fourier transformation

Other Resources

Course Curriculum

Introduction to vector space Details 56:36
Introduction to vector space (Contd.) Details 54:49
Onto, into, one to one function Details 57:2
Vectors Details 52:27
Vectors (Contd.) Details 54:3
Contraction Mapping Details 57:48
Contraction Mapping (Contd.) Details 57:54
Matrix, Determinant Details 55:10
Eigenvalue Problem in Discrete Domain Details 55:9
Eigenvalue Problem in Discrete Domain (Contd.) Details 53:40
Mod-06 Lec 11 Eigenvalue Problem in Discrete Domain (Contd.) Details 56:39
Eigenvalue Problem in Discrete Domain (Contd.) Details 55:43
Stability Analysis Details 52:28
Stability Analysis (Contd.) Details 57:1
Stability Analysis (Contd.) Details 57:34
More Examples Details 55:8
Partial Differential Equations Details 55:45
Partial Differential Equations(Contd.) Details 55:33
Eigenvalue Problem in Continuous Domain Details 53:54
Mod-09 Lec 20 Special ODEs Details 52:17
Adjoint Operator Details 58:21
Theorems of Eigenvalues and Eigenfunction Details 57:7
Solution PDE : Separation of Variables Method Details 55:45
Solution of Parabolic PDE : Separation of variables method Details 53:7
Solution of Parabolic PDE : Separation of Variables Method (Contd.) Details 57:37
Solution of Higher Dimensional PDEs Details 54:12
Solution of Higher Dimensional PDEs (Contd.) Details 55:52
Four Dimensional Parabolic PDE Details 52:39
Solution of Elliptic and Hyperbolic PDE Details 54:5
Solution of Elliptic and Hyperbolic PDE (Contd.) Details 56:5
PDE in Cylindrical and Spherical Coordinate Details 52:43
Solution of non-homogeneous PDE Details 54:24
Solution of non-homogeneous Parabolic PDE Details 56:40
Solution of non-homogeneous Elliptic PDE Details 56:37
Solution of non-homogeneous Elliptic PDE (Contd.) Details 54:59
Similarity Solution Details 52:38
Similarity Solution (Contd.) Details 57:1
Integral Method Details 53:41
Laplace Transform Details 55:40
Fourier Transform Details 55:42

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