IIT Kharagpur Course , Prof. S. De

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IIT Kharagpur Course , Prof. S. De

Introduction of vector space;Metric, Norm, Inner Product space;Examples

Onto, into, one to one function, completeness of space

Vectors: Linear combination of vectors, dependent/independent vectors; Orthogonal and orthonormal vectors; Gram-Schmidt orthogonalization; Examples

Contraction Mapping: Definition; Applications in Chemical Engineering; Examples

Matrix, determinants and properties

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)

Applications of eigenvalue problems: Stability analysis; Bifurcation theory; Examples

Partial Differential equations:Classification of equations; Boundary conditions;Principle of Linear superposition

Special ODEs and Adjoint operators:Properties of adjoint operator; Theorem for eigenvalues and eigenfunctions;

Solution of linear, homogeneous PDEs by separation of variables: Cartesian coordinate system & different classes of PDEs; Cylindrical coordinate system ; Spherical Coordinate system

Solution of non-homogeneous PDEs by Green's theorem

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

Onto, into, one to one function, completeness of space

Vectors: Linear combination of vectors, dependent/independent vectors; Orthogonal and orthonormal vectors; Gram-Schmidt orthogonalization; Examples

Contraction Mapping: Definition; Applications in Chemical Engineering; Examples

Matrix, determinants and properties

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)

Applications of eigenvalue problems: Stability analysis; Bifurcation theory; Examples

Partial Differential equations:Classification of equations; Boundary conditions;Principle of Linear superposition

Special ODEs and Adjoint operators:Properties of adjoint operator; Theorem for eigenvalues and eigenfunctions;

Solution of linear, homogeneous PDEs by separation of variables: Cartesian coordinate system & different classes of PDEs; Cylindrical coordinate system ; Spherical Coordinate system

Solution of non-homogeneous PDEs by Green's theorem

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

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Advanced Mathematical Techniques in Chemical Engineering by Prof. S. De, Department of Chemical Engineering, IIT Kharagpur. For more details on NPTEL visit httpnptel.iitm.ac.in

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- 1.Introduction to vector space
- 2.Introduction to vector space (Contd.)
- 3.Onto, into, one to one function
- 4.Vectors
- 5.Vectors (Contd.)
- 6.Contraction Mapping
- 7.Contraction Mapping (Contd.)
- 8.Matrix, Determinant
- 9.Eigenvalue Problem in Discrete Domain
- 10.Eigenvalue Problem in Discrete Domain (Contd.)
- 11.Mod-06 Lec 11 Eigenvalue Problem in Discrete Domain (Contd.)
- 12.Eigenvalue Problem in Discrete Domain (Contd.)
- 13.Stability Analysis
- 14.Stability Analysis (Contd.)
- 15.Stability Analysis (Contd.)
- 16.More Examples
- 17.Partial Differential Equations
- 18.Partial Differential Equations(Contd.)
- 19.Eigenvalue Problem in Continuous Domain
- 20.Mod-09 Lec 20 Special ODEs
- 21.Adjoint Operator
- 22.Theorems of Eigenvalues and Eigenfunction
- 23.Solution PDE Separation of Variables Method
- 24.Solution of Parabolic PDE Separation of variables method
- 25.Solution of Parabolic PDE Separation of Variables Method (Contd.)
- 26.Solution of Higher Dimensional PDEs
- 27.Solution of Higher Dimensional PDEs (Contd.)
- 28.Four Dimensional Parabolic PDE
- 29.Solution of Elliptic and Hyperbolic PDE
- 30.Solution of Elliptic and Hyperbolic PDE (Contd.)
- 31.PDE in Cylindrical and Spherical Coordinate
- 32.Solution of non-homogeneous PDE
- 33.Solution of non-homogeneous Parabolic PDE
- 34.Solution of non-homogeneous Elliptic PDE
- 35.Solution of non-homogeneous Elliptic PDE (Contd.)
- 36.Similarity Solution
- 37.Similarity Solution (Contd.)
- 38.Integral Method
- 39.Laplace Transform
- 40.Fourier Transform

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