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## Advanced Mathematical Techniques in Chemical Engineering

Course Home
Syllabus/Outline
Lectures
• ### Course Description

The course covers lesoons on Advanced Mathematical Techniques such as Introduction of Vector Space, Matrix, Determinants and properties. There are 41 Lectures.

### About Prof S. De

Date Taught
Fall 2013

Level
1. Introduction of vector space;Metric, Norm, Inner Product space;Examples
2. Onto, into, one to one function, completeness of space
3. Vectors: Linear combination of vectors, dependent/independent vectors; Orthogonal and orthonormal vectors; Gram-Schmidt orthogonalization; Examples
4. Contraction Mapping: Definition; Applications in Chemical Engineering; Examples
5. Matrix, determinants and properties
6. 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)
7. Applications of eigenvalue problems: Stability analysis; Bifurcation theory; Examples
8. Partial Differential equations:Classification of equations; Boundary conditions;Principle of Linear superposition
9. Special ODEs and Adjoint operators:Properties of adjoint operator; Theorem for eigenvalues and eigenfunctions;
10. Solution of linear, homogeneous PDEs by separation of variables: Cartesian coordinate system & different classes of PDEs; Cylindrical coordinate system ; Spherical Coordinate system
11. Solution of non-homogeneous PDEs by Green's theorem
12. Solution of PDEs by Similarity solution method
13. Solution of PDEs by Integral method
14. Solution of PDEs by Laplace transformation
15. Solution of PDEs by Fourier transformation

 S.No Topics Lectures 1 Introduction of vector space Metric, Norm, Inner Product space Examples 7 2 Onto, into, one to one function, completeness of space 1 3 Vectors Linear combination of vectors, dependent/independent vectors Orthogonal and orthonormal vectorsGram-Schmidt orthogonalization Examples 3 4 Contraction Mapping Definition Applications in Chemical EngineeringGram-Schmidt orthogonalization Examples 3 5 Matrix, determinants and properties 2 6 Eigenvalue Problem Various theorems Solution of a set of algebraic equationsSolution of a set of ordinary differential equations Solution of a set of non-homogeneous first order ordinary differential equations (IVPs) 4 7 Applications of eigenvalue problems Stability analysis Bifurcation theory Examples 3 8 Partial Differential equations Classification of equations Boundary conditions Principle of Linear superposition 2 9 Special ODEs and Adjoint operators Properties of adjoint operator Theorem for eigenvalues and eigenfunctions 3 10 Solution of linear, homogeneous PDEs by separation of variables Cartesian coordinate system & different classes of PDEs Cylindrical coordinate system Spherical Coordinate system 8 11 Solution of non-homogeneous PDEs by Green's theorem 5 12 Solution of PDEs by Similarity solution method 2 13 Solution of PDEs by Integral method 1 14 Solution of PDEs by Laplace transformation 2 15 Solution of PDEs by Fourier transformation
• Lectures
Advanced Mathematical Techniques in Chemical Engineering - Lecture 1 - Prof S. DeView
Advanced Mathematical Techniques in Chemical Engineering - Lecture 2 - Prof S. DeView
Advanced Mathematical Techniques in Chemical Engineering - Lecture 3 - Prof S. DeView
Advanced Mathematical Techniques in Chemical Engineering - Lecture 4 - Prof S. DeView
Advanced Mathematical Techniques in Chemical Engineering - Lecture 5 - Prof S. DeView
Advanced Mathematical Techniques in Chemical Engineering - Lecture 6 - Prof S. DeView
Advanced Mathematical Techniques in Chemical Engineering - Lecture 7 - Prof S. DeView
Advanced Mathematical Techniques in Chemical Engineering - Lecture 8 - Prof S. DeView
Advanced Mathematical Techniques in Chemical Engineering - Lecture 9 - Prof S. DeView
Advanced Mathematical Techniques in Chemical Engineering - Lecture 10 - Prof S. DeView
Advanced Mathematical Techniques in Chemical Engineering - Lecture 11 - Prof S. DeView
Advanced Mathematical Techniques in Chemical Engineering - Lecture 12 - Prof S. DeView
Advanced Mathematical Techniques in Chemical Engineering - Lecture 13 - Prof S. DeView
Advanced Mathematical Techniques in Chemical Engineering - Lecture 14 - Prof S. DeView
Advanced Mathematical Techniques in Chemical Engineering - Lecture 15 - Prof S. DeView
Advanced Mathematical Techniques in Chemical Engineering - Lecture 16 - Prof S. DeView
Advanced Mathematical Techniques in Chemical Engineering - Lecture 17 - Prof S. DeView
Advanced Mathematical Techniques in Chemical Engineering - Lecture 18 - Prof S. DeView
Advanced Mathematical Techniques in Chemical Engineering - Lecture 19 - Prof S. DeView
Advanced Mathematical Techniques in Chemical Engineering - Lecture 20 - Prof S. DeView
Advanced Mathematical Techniques in Chemical Engineering - Lecture 21 - Prof S. DeView
Advanced Mathematical Techniques in Chemical Engineering - Lecture 22 - Prof S. DeView
Advanced Mathematical Techniques in Chemical Engineering - Lecture 23 - Prof S. DeView
Advanced Mathematical Techniques in Chemical Engineering - Lecture 24 - Prof S. DeView
Advanced Mathematical Techniques in Chemical Engineering - Lecture 25 - Prof S. DeView
Advanced Mathematical Techniques in Chemical Engineering - Lecture 26 - Prof S. DeView
Advanced Mathematical Techniques in Chemical Engineering - Lecture 27 - Prof S. DeView
Advanced Mathematical Techniques in Chemical Engineering - Lecture 28 - Prof S. DeView
Advanced Mathematical Techniques in Chemical Engineering - Lecture 29 - Prof S. DeView
Advanced Mathematical Techniques in Chemical Engineering - Lecture 30 - Prof S. DeView
Advanced Mathematical Techniques in Chemical Engineering - Lecture 31 - Prof S. DeView
Advanced Mathematical Techniques in Chemical Engineering - Lecture 32 - Prof S. DeView
Advanced Mathematical Techniques in Chemical Engineering - Lecture 33 - Prof S. DeView
Advanced Mathematical Techniques in Chemical Engineering - Lecture 34 - Prof S. DeView
Advanced Mathematical Techniques in Chemical Engineering - Lecture 35 - Prof S. DeView
Advanced Mathematical Techniques in Chemical Engineering - Lecture 36 - Prof S. DeView
Advanced Mathematical Techniques in Chemical Engineering - Lecture 37 - Prof S. DeView
Advanced Mathematical Techniques in Chemical Engineering - Lecture 38 - Prof S. DeView
Advanced Mathematical Techniques in Chemical Engineering - Lecture 39 - Prof S. DeView
Advanced Mathematical Techniques in Chemical Engineering - Lecture 40 - Prof S. DeView
Advanced Mathematical Techniques in Chemical Engineering - Lecture 41 - Prof S. DeView
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