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Advanced Mathematical Techniques in Chemical Engineering

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  • 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

    Note: Contents for this page are Licensed from http://nptel.iitm.ac.in/ under the Creative Commons Attribution Share-Alike license.

    School
    Indian Institute of Technology, Kharagpur

    Date Taught
    Fall 2013

    Level
    Undergraduate (First Year)
    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 vectors
    • Gram-Schmidt orthogonalization
    • Examples

    3

    4

    Contraction Mapping
    • Definition
    • Applications in Chemical Engineering
    • Gram-Schmidt orthogonalization
    • Examples

    3

    5

    Matrix, determinants and properties

    2

    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)

    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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