Advanced Mathematical Techniques in Chemical Engineering


Lecture 1 - Introduction to vector space


Lecture 2 - Introduction to vector space (Continued...)


Lecture 3 - Onto, into, one to one function


Lecture 4 - Vectors


Lecture 5 - Vectors (Continued...)


Lecture 6 - Contraction Mapping


Lecture 7 - Contraction Mapping (Continued...)


Lecture 8 - Matrix, Determinant


Lecture 9 - Eigenvalue Problem in Discrete Domain


Lecture 10 - Eigenvalue Problem in Discrete Domain (Continued...)


Lecture 11 - Eigenvalue Problem in Discrete Domain (Continued...)


Lecture 12 - Eigenvalue Problem in Discrete Domain (Continued...)


Lecture 13 - Stability Analysis


Lecture 14 - Stability Analysis (Continued...)


Lecture 15 - Stability Analysis (Continued...)


Lecture 16 - More Examples


Lecture 17 - Partial Differential Equations


Lecture 18 - Partial Differential Equations (Continued...)


Lecture 19 - Eigenvalue Problem in Continuous Domain


Lecture 20 - Special ODEs


Lecture 21 - Adjoint Operator


Lecture 22 - Theorems of Eigenvalues and Eigenfunction


Lecture 23 - Solution 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 (Continued...)


Lecture 26 - Solution of Higher Dimensional PDEs


Lecture 27 - Solution of Higher Dimensional PDEs (Continued...)


Lecture 28 - Four Dimensional Parabolic PDE


Lecture 29 - Solution of Elliptic and Hyperbolic PDE


Lecture 30 - Solution of Elliptic and Hyperbolic PDE (Continued...)


Lecture 31 - PDE in Cylindrical and Spherical Coordinate


Lecture 32 - Solution of non-homogeneous PDE


Lecture 33 - Solution of non-homogeneous PDE (Continued...)


Lecture 34 - Solution of non-homogeneous Parabolic PDE


Lecture 35 - Solution of non-homogeneous Elliptic PDE


Lecture 36 - Solution of non-homogeneous Elliptic PDE (Continued...)


Lecture 37 - Similarity Solution


Lecture 38 - Similarity Solution (Continued...)


Lecture 39 - Integral Method


Lecture 40 - Laplace Transform


Lecture 41 - Fourier Transform