# Optimal PWM using harmonic elimination method

Mathematical Methods in Chemical Engineering

Paper Code: CHE 701

Module I
Mathematical statement of Chemical Engineering problems: Introduction; Representation of the problems: Solvent extraction in two stages, Solvent extraction in N stages, Simple water still with preheated feed, unsteady state operations; Dependent and Independent variables and parameters; boundary conditions.
Matrix: Introduction; Matrix algebra; Determinant of square matrix and matrix products; Transpose, Adjoint & Inverse of a matrix; Rank & degeneracy of a matrix; Sub matrix; Solution of linear algebraic equations; Matrix series; Differentiation & Integration of matrix; Lamda matrix; Characteristics equation; Sylvester’s theorem; Solution of systems of linear
differential equations by matrix.

Module II
Ordinary Differential Equations: Introduction; Order & Degree; First order differential equations: Characteristics, General method of solution, related problems; Second order differential equations: Linear & simultaneous differential equations, related problems.
Solution by series: Introduction; Infinite series; Power series; Method of Frobenius and Related problems: Temperature distribution in a transverse fin of triangular cross section, Tubular gas preheater; Bessel’s Equation, Problem of heat loss through pipe flanges, properties of Bessel function.

Module III:
Partial differentiation & Partial Differential Equations: Introduction; Interpretation of partial derivatives, Formulation of partial differential equations; Boundary conditions; Particular solutions of partial differential equations; Orthogonal functions; Method of separation of variables; Laplace transform method.

Module IV:
Finite Differences: Introduction; The Difference Operator (∆); other difference operators; Interpolation & Extrapolation; Finite Difference Equations: Linear Finite Difference Equations & Nonlinear Finite Difference Equations; Differential- Difference Equations; Related Chemical Engineering Problems.

Text Book/ References:

1.  Mathematical Methods in Chemical Engineering: V. G. Jenson & G.V. Jeffreys: Academic Press.
2. Mathematical Methods in Chemical Engineering: S. Pushpavanam: Prentice Hall of India

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