Courses Taught

CHE 321: Chemical Reaction Engineering (Spring 2019)

CHE 445: Mathematical Methods in Chemical Engineering (Fall 2016, 2017, 2018)

This is one the most comprehensive courses on applied mathematics focused on the formulation and analytical solutions of the chemical engineering problems. In this course, students will learn analytical techniques to solve linear and non-linear equations, ordinary differential equations, partial differential equations, Integral equations, Integrodifferential equations and stochastic differential equations. Following topics are covered in this course-


  1. Linear Algebra - Determinants, Matrix theory, Dimensional Analysis, Eigenvalues and Eigenvectors, Solution of Linear Systems, Analysis of First-Order Reactions, and Distillation Columns

  2. Optimization - Linear Programming, Simplex Method, KKT Conditions, Quadratic Programming, Steepest Descent, Conjugate Gradient, Newton's Method, Geometric Programming, Least Square Method, Sequential Quadratic Programming

  3. Differential Equations - Method of Series, Method of Frobenius, Bessel's Equation, Hypergeometric Differential Equation, Strum-Liouville Theory, Finite Fourier Transform, Method of Superimposition, Integrating Factors, Method of Variation of Parameters, Green's Function, Infinite Fourier Transform

  4. Complex Analysis - Cauchy-Riemann Conditions, Cauchy's Theorem, Residues, Jordan's Lemma, Laplace Transform, Inversion Integral

  5. Theory of First-Order Linear PDEs - Method of Characteristics

  6. Theory of Non-Linear PDEs

  7. Non-Linear Dynamics - Stability Analysis, Phase Portraits, Lyapunov Stability, Bifurcation

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