###### Chemical Engineering  Advanced Mathematical Techniques in Chemical Engineering
 List Lectures   [ 1 ]  2  3  4  5
 # Lecture Name 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.)

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