# CH5520 – Mathematical Methods for Chemical Engineers

### CH5520 – Mathematical Methods for Chemical Engineers

#### Objectives:

The objective of this course is to introduce the student to analytical methods of solving linear algebraic, ordinary differential and partial differential equations. The course will also cover numerical methods to solve algebraic and differential equations.

#### Course Contents:

• Review of Matrix Algebra; Solvability conditions for systems of linear algebraic equations. Vector Algebra; Linear independence, Norm and Inner Product; Linear Operators, Adjoint of an operator, Self-adjoint operators. Transformations under change of basis, eigen values and eigen vectors. Applications to solution of systems of linear algebraic equations and systems of first order ordinary differential equations (ODEs). Stability analysis; Examples from reaction engineering, process control etc.
• Second order linear ODEs, Sturm Liouville Operators, Spectral expansion, Special functions. Inverse of second order operators and Green’s function.
• Second order linear partial differential equations (PDEs): Classification, canonical forms. Solution methods for hyperbolic, elliptic and parabolic equations: Eigenfunctionexpansion, separation of variables, transform methods. Applications from heat and mass transfer, reaction engineering.
• Numerical solution of linear and nonlinear algebraic equations, Gauss elimination methods, LU decomposition, Newton-Raphson method; Finite difference method for solving ODEs and PDEs. Chemical engineering applications from separation processes, reaction engineering, fluid mechanics etc..

#### References:

1. Schneider,H., Barker, G.P.Matrices and Linear Algebra, Dover, NY (1972).
2. Ray, A. K., Gupta, S. K. Mathematical Methods in Chemical and Environmental Engineering, International Thomson Learning,Singapore (2004).
3. Pushpavanam, S. Mathematical Methods in Chemical Engineering, Prentice-Hall of India, New Delhi (2004).
4. Ramkrishna, D., Amundson, N. R.; Linear Operator Methods in Chemical Engineering; Prentice-Hall: Englewood Cliffs, New Jersey, 1985.
5. Chapra, S. C., Canale, R. P. Numerical Methods for Engineers, Tata McGraw-Hill, New Delhi (2006).
6. Hoffman, J. D. Numerical Methods for Engineers and Scientists, Taylor and Francis, Boca Raton (2001).