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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 40 - Laplace Transform

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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