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ME01030011
Code: ME01030011
Credits: 4
Semester 1
CE
Mathematical and Statistical Methods in Chemical Engineering
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Follow on Instagram for UpdatesMathematical and Statistical Methods in Chemical Engineering Syllabus — Unit-wise Content
The official GTU curriculum for Mathematical and Statistical Methods in Chemical Engineering (subject code ME01030011) as prescribed for CE · Semester 1 divides the course into 6 units, covering 73 listed topics. The unit-wise breakdown below is read from the GTU syllabus document for this subject code, so you can check what the course actually covers before deciding which papers to attempt.
Download the official syllabus PDF (ME01030011)Unit 1 Equation Forms in Process Modeling
- Introduction and motivation
- linear and nonlinear algebraic equation
- optimization based formulations
- Ordinary Differential Equations Program Name: M.E. in Chemical Engineering Level: Post Graduate Degree Branch: Chemical Engineering Course / Subject Code: ME01030011 Course / Subject Name: Mathematical and Statistical Methods in Chemical Engineering (ODE) - Initial Value Problems (IVPs) and Differential Algebraic Equations (DAEs)
- ODE - Initial Value Problems (IVPs) and Partial Differential Equations (PDEs)
- abstract model forms
- fundamentals of vector spaces
- generalized concepts of vector space
- linear dependence
- concept of basis
- norms defined on general vector spaces
- norms defined on different vector spaces
- Cauchy sequence and convergence
- Cauchy-Schwartz inequality and orthogonal sets
- Gram-Schmidt process and generation of orthogonal basis
- orthogonal basis matrix norms
- classification of problems in numerical analysis
- polynomial approximations
- Taylor series approximation
- Necessary and sufficient conditions for unconstrained multivariate optimization
- transformations and unified view of problems through the concept of transformations
Unit 2 Interpolation & Curve Fitting
- Least square approximations
- Formulation and derivation of weighted linear least square estimation
- Geormtraic interpretation of least squares Projections and least square solution
- Function approximations and normal equation in any inner product space
- Model Parameter Estimation using linear least squares method
- Generic equation forms in transformed problems
- Linear and Polynomial Regression
- Introduction to polynomial interpolation
- Polynomial and function interpolations
- Lagrange Interpolating Polynomials
- Spline Interpolation
- Cubic Spline
Unit 3 Linear Algebraic Equations
- System of linear algebraic equations
- conditions for existence of solution - geometric interpretations (row picture and column picture)
- review of concepts of rank and fundamental theorem of linear algebra
- Classification of solution approaches as direct and iterative
- review of Gaussian elimination
- Introduction to methods for solving sparse linear systems: Thomas algorithm for tri-diagonal and block tri- diagonal matrices
- triangular and block-triangular systems
- solution by matrix decomposition
- Iterative methods: Derivation of Jacobi
- Gauss-Siedel and successive over-relaxation methods
- Convergence of iterative solution schemes: analysis of asymptotic behavior of linear difference equations using Eigen values
- convergence of iterative solution schemes
- Optimization based solution of linear algebraic equations
- matrix conditioning
- examples of well conditioned and ill-conditioned linear systems
Unit 4 Nonlinear Algebraic Equations
- 5 Program Name: M.E. in Chemical Engineering Level: Post Graduate Degree Branch: Chemical Engineering Course / Subject Code: ME01030011 Course / Subject Name: Mathematical and Statistical Methods in Chemical Engineering Method of successive substitutions
- derivative free iterative solution approaches
- Secant method
- Regulafalsi method and Wegsteine iterations
- Modified Newton’s method and Qausi-Newton method with Broyden’s update
- Optimization based formulations and Leverberg-Marquardt method
- contraction mapping principle and introduction to convergence analysis
Unit 5 Ordinary Differential Equations - Initial Value Problems (ODE- IVPs)
- Analytical Solutions of Linear ODE-IVPs
- basic concepts in Numerical solutions of ODE-IVP: step size and marching
- concept of implicit and explicit methods
- Taylor series based and Runge-Kutta methods
- Multi-step (predictor-corrector) approaches
- Stability of ODEIVP solvers
- choice of step size and stability envelopes
- stiffness and variable step size implementation
- Introduction to solution methods for differential algebraic equations (DAEs)
Unit 6 Ordinary Differential Equations – Boundary Value Problems (ODE-BVPs)
- Method of least squares for solving ODE-BVP
- Gelarkin’s method and generic equation forms arising in problem discretization
- Errors in Discretization
- Discretization using approximation theory
- finite difference method for solving ODE-BVPs with examples
- finite difference method for solving PDEs with examples
- Orthogonal Collocations method for solving ODE-BVPs with examples
- Orthogonal Collocations method for solving PDEs with examples
- Single shooting method for solving ODE-BVPs
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