### 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

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- 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

**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. De View Advanced Mathematical Techniques in Chemical Engineering - Lecture 2 - Prof S. De View Advanced Mathematical Techniques in Chemical Engineering - Lecture 3 - Prof S. De View Advanced Mathematical Techniques in Chemical Engineering - Lecture 4 - Prof S. De View Advanced Mathematical Techniques in Chemical Engineering - Lecture 5 - Prof S. De View Advanced Mathematical Techniques in Chemical Engineering - Lecture 6 - Prof S. De View Advanced Mathematical Techniques in Chemical Engineering - Lecture 7 - Prof S. De View Advanced Mathematical Techniques in Chemical Engineering - Lecture 8 - Prof S. De View Advanced Mathematical Techniques in Chemical Engineering - Lecture 9 - Prof S. De View Advanced Mathematical Techniques in Chemical Engineering - Lecture 10 - Prof S. De View Advanced Mathematical Techniques in Chemical Engineering - Lecture 11 - Prof S. De View Advanced Mathematical Techniques in Chemical Engineering - Lecture 12 - Prof S. De View Advanced Mathematical Techniques in Chemical Engineering - Lecture 13 - Prof S. De View Advanced Mathematical Techniques in Chemical Engineering - Lecture 14 - Prof S. De View Advanced Mathematical Techniques in Chemical Engineering - Lecture 15 - Prof S. De View Advanced Mathematical Techniques in Chemical Engineering - Lecture 16 - Prof S. De View Advanced Mathematical Techniques in Chemical Engineering - Lecture 17 - Prof S. De View Advanced Mathematical Techniques in Chemical Engineering - Lecture 18 - Prof S. De View Advanced Mathematical Techniques in Chemical Engineering - Lecture 19 - Prof S. De View Advanced Mathematical Techniques in Chemical Engineering - Lecture 20 - Prof S. De View Advanced Mathematical Techniques in Chemical Engineering - Lecture 21 - Prof S. De View Advanced Mathematical Techniques in Chemical Engineering - Lecture 22 - Prof S. De View Advanced Mathematical Techniques in Chemical Engineering - Lecture 23 - Prof S. De View Advanced Mathematical Techniques in Chemical Engineering - Lecture 24 - Prof S. De View Advanced Mathematical Techniques in Chemical Engineering - Lecture 25 - Prof S. De View Advanced Mathematical Techniques in Chemical Engineering - Lecture 26 - Prof S. De View Advanced Mathematical Techniques in Chemical Engineering - Lecture 27 - Prof S. De View Advanced Mathematical Techniques in Chemical Engineering - Lecture 28 - Prof S. De View Advanced Mathematical Techniques in Chemical Engineering - Lecture 29 - Prof S. De View Advanced Mathematical Techniques in Chemical Engineering - Lecture 30 - Prof S. De View Advanced Mathematical Techniques in Chemical Engineering - Lecture 31 - Prof S. De View Advanced Mathematical Techniques in Chemical Engineering - Lecture 32 - Prof S. De View Advanced Mathematical Techniques in Chemical Engineering - Lecture 33 - Prof S. De View Advanced Mathematical Techniques in Chemical Engineering - Lecture 34 - Prof S. De View Advanced Mathematical Techniques in Chemical Engineering - Lecture 35 - Prof S. De View Advanced Mathematical Techniques in Chemical Engineering - Lecture 36 - Prof S. De View Advanced Mathematical Techniques in Chemical Engineering - Lecture 37 - Prof S. De View Advanced Mathematical Techniques in Chemical Engineering - Lecture 38 - Prof S. De View Advanced Mathematical Techniques in Chemical Engineering - Lecture 39 - Prof S. De View Advanced Mathematical Techniques in Chemical Engineering - Lecture 40 - Prof S. De View Advanced Mathematical Techniques in Chemical Engineering - Lecture 41 - Prof S. De View