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Chemical Engineering  Advanced Mathematical Techniques in Chemical Engineering
Title: Advanced Mathematical Techniques in Chemical Engineering
Department: Chemical Engineering
Author: Prof. S. De
University: IIT Kharagpur
Type: WebLink

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

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