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

2

Chemical Process Calculation

Reaction Engineering

Mathematical Methods in Chemical Engineering by S. Pushpavanam, Prentice Hall of India.

Applied Mathematics and Modeling for Chemical Engineers by R. G. Rice & D. D. Do, Wiley.

Mathematical Method in Chemical Engineering by A. Varma & M. Morbidelli, Oxford University Press.

Applied Mathematical Methods for Chemical Engineers by N. W. Loney, CRC Press.

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