# Advanced Mathematical Techniques in Chemical Engineering

Indian Institute of Technology Kharagpur

Course Outline:

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
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