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Advanced Mathematical Techniques in Chemical Engineering

Advanced Mathematical Techniques in Chemical Engineering. Instructor: Prof. S. De, Department Of Chemical Engineering, IIT Kharagpur. This course deals with advanced mathematical methods in chemical engineering. Topics covered in this course include Introduction to vector space; Vectors; Contraction mapping; Matrix, Determinants and Properties; Eigenvalue and applications of eigenvalue problems; Partial differential equations; Special ordinary differential equations; Solution of linear, homogeneous PDEs by separation of variables; Solution of nonhomogeneous PDEs by Green's function; 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. (from nptel.ac.in)

Lecture 19 - Eigenvalue Problem in Continuous Domain


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Introduction to Vector Space
Lecture 01 - Introduction to Vector Space
Lecture 02 - Introduction to Vector Space (cont.)
Onto, Into, One to One function, Completeness Space
Lecture 03 - Onto, Into, One to One Function
Vectors
Lecture 04 - Vectors
Lecture 05 - Vectors (cont.)
Contraction Mapping
Lecture 06 - Contraction Mapping
Lecture 07 - Contraction Mapping (cont.)
Matrix, Determinants and Properties
Lecture 08 - Matrix, Determinant
Eigenvalue Problem
Lecture 09 - Eigenvalue Problem in Discrete Domain
Lecture 10 - Eigenvalue Problem in Discrete Domain (cont.)
Lecture 11 - Eigenvalue Problem in Discrete Domain (cont.)
Lecture 12 - Eigenvalue Problem in Discrete Domain (cont.)
Applications of Eigenvalue Problems
Lecture 13 - Stability Analysis
Lecture 14 - Stability Analysis (cont.)
Lecture 15 - Stability Analysis (cont.)
Lecture 16 - More Examples
Partial Differential Equations
Lecture 17 - Partial Differential Equations
Lecture 18 - Partial Differential Equations (cont.)
Lecture 19 - Eigenvalue Problem in Continuous Domain
Special Ordinary Differential Equations and Adjoint Operators
Lecture 20 - Special Ordinary Differential Equations
Lecture 21 - Adjoint Operators
Lecture 22 - Theorems of Eigenvalues and Eigenfunctions
Solution of Linear, Homogeneous PDEs by Separation of Variables
Lecture 23 - Solution of PDE: Separation of Variables Method
Lecture 24 - Solution of Parabolic PDE: Separation of Variables Method
Lecture 25 - Solution of Parabolic PDE: Separation of Variables Method (cont.)
Lecture 26 - Solution of Higher Dimensional PDEs
Lecture 27 - Solution of Higher Dimensional PDEs (cont.)
Lecture 28 - Four Dimensional Parabolic PDE
Lecture 29 - Solution of Elliptic and Hyperbolic PDE
Lecture 30 - Solution of Elliptic and Hyperbolic PDE (cont.)
Lecture 31 - PDE in Cylindrical and Spherical Coordinates
Solution of Nonhomogeneous PDEs by Green's Function
Lecture 32 - Solution of Nonhomogeneous PDE
Lecture 33 - Solution of Nonhomogeneous PDE (cont.)
Lecture 34 - Solution of Nonhomogeneous Parabolic PDE
Lecture 35 - Solution of Nonhomogeneous Elliptic PDE
Lecture 36 - Solution of Nonhomogeneous Elliptic PDE (cont.)
Solution of PDEs by Similarity Solution Method
Lecture 37 - Similarity Solution
Lecture 38 - Similarity Solution (cont.)
Solution of PDEs by Integral Method
Lecture 39 - Integral Method
Solution of PDEs by Laplace Transformation
Lecture 40 - Laplace Transform
Solution of PDEs by Fourier Transformation
Lecture 41 - Fourier Transform