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10.34

Numerical Methods Applied to Chemical Engineering

4-0-8 units · Graduate

Numerical methods for solving problems arising in heat and mass transfer, fluid mechanics, chemical reaction engineering, and molecular simulation. Topics: numerical linear algebra, solution of nonlinear algebraic equations and ordinary differential equations, solution of partial differential equations (e.g., Navier-Stokes), numerical methods in molecular simulation (dynamics, geometry optimization). All methods are presented within the context of chemical engineering problems. Familiarity with structured programming is assumed.

Fall 2015

Topics

  • Linear algebra 1
  • Linear algebra 2
  • Linear algebra 3
  • Linear algebra 4
  • Linear algebra 5
  • Linear algebra 6
  • Systems of nonlinear equations 1
  • Systems of nonlinear equations 2
  • Summary and review on linear algebra and systems of nonlinear equations
  • Optimization 1
  • Optimization 2
  • Optimization 3
  • Optimization 4
  • ODE-IVP and numerical integration 1
  • ODE-IVP and numerical integration 2
  • Differential-algebraic equations 1
  • Differential-algebraic equations 2
  • Differential-algebraic equations 3
  • Boundary value problems 1
  • Boundary value problems 2
  • Boundary value problems 3
  • Partial differential equations 1
  • Partial differential equations 2
  • Partial differential equations 3
  • Summary and review on IVP, differential-algebraic equations, and boundary value
  • Probability theory 1
  • Probability theory 2
  • Models vs. data 1
  • Models vs. data 2
  • Models vs. data 3
  • Operator splitting
  • Monte Carlo methods 1
  • Monte Carlo methods 2
  • Stochastic chemical kinetics 1
  • Stochastic chemical kinetics 2

Readings

Fall 2005

Topics

  • Introduction
  • MATLAB® Programming (cont.)
  • Linear Systems
  • Sparse and Banded Matrices, Solving Linear BVPs with Finite Differences
  • Ax=b as Linear Transformation
  • Newton’s Method for Solving Sets of Nonlinear Algebraic Equations
  • Quasi-Newton and Reduced-step Algorithms
  • Orthogonal Matrices
  • Schur Decomposition
  • Numerical Calculation of Matrix Eigenvalues, Eigenvectors
  • Interpolation and Numerical Integration
  • ODE Initial Value Problems
  • Numerical Issues (Stiffness) and MATLAB® ODE Solvers
  • DAE Systems and Applications
  • Nonlinear Optimization
  • Treating Constraints and Optimization Routines in MATLAB®
  • Optimization Examples
  • Nonlinear Reaction/Diffusion PDE-BVPs
  • Treating Convection Terms in PDEs
  • Finite Volume and Finite Element Methods
  • Introduction to Probability Theory
  • Random Variables, Binomial, Gaussian, and Poisson Distributions
  • Random Walks
  • Brownian Dynamics and Stochastic Calculus
  • Theory of Diffusion
  • Monte Carlo Simulation
  • Monte Carlo Simulation (cont.)
  • Introduction to Statistics and Parameter Estimation
  • Linear Least Squares Regression
  • Choosing Priors
  • Non-linear Regression
  • Bayesian Monte Carlo Methods for Single-response Regression
  • Applications of Bayesian MCMC
  • Multi-response Parameter Estimation
  • Regression from Composite Single and Multi Response Data Sets
  • Model Criticism and Validation

Readings

  • Beers, Kenneth. Numerical Methods for Chemical Engineering: Applications in MATLAB®. New York, NY: Cambridge University Press, November 2006. ISBN: 9780521859714.
    Required
  • Allen, Erik C., and Kenneth J. Beers. “Ab Initio Study of the Binding Strength of POSS-cation Complexes.” Polymer 46 (2005): 569–573.
    Listed reading
  • Wylie, C. Ray, and Louis C. Barrett. Advanced Engineering Mathematics . New York, NY: McGraw-Hill, 1982. ISBN: 9780070721883.
    Listed reading
  • Hassani, Sadri. Mathematical Physics: A Modern Introduction to Its Foundations . New York, NY: Springer, 1999. ISBN: 9780387985794.
    Listed reading
  • Naylor, Arch W., and George R. Sell. Linear Operator Theory in Engineering and Science . New York, NY: Springer-Verlag, 1994. ISBN: 9780387907482.
    Listed reading
  • Stackgold, Ivar. Green’s Functions and Boundary Value Problems . New York, NY: Wiley, 1979. ISBN: 9780471819677.
    Listed reading
  • Arnold, V. I. Mathematical Methods of Classical Mechanics . New York, NY: Springer, 1997. ISBN: 9780387968902.
    Listed reading
  • Seydel, R. Practical Bifurcation and Stability Analysis: From Equilibrium to Chaos . New York, NY: Springer-Verlag, 1994. ISBN: 9780387943169.
    Listed reading
  • Stoer, J., and Bulirsch. Introduction to Numerical Analysis . New York, NY: Springer-Verlag, 1996. ISBN: 9780387978789.
    Listed reading
  • Strang, Gilbert. Introduction to Applied Mathematics . Wellesley, MA: Wellesley-Cambridge Press, 1986. ISBN: 9780961408800.
    Listed reading
  • ———. Inroduction to Linear Algebra . 2nd ed. Wellesley, MA: Wellesley-Cambridge Press, 1993. ISBN: 9780961408855.
    Listed reading
  • Press, W. H., W. T. Vetterline, S. A. Teukolsky, and B. P. Flannery. Numerical Recipes in C . New York, NY: Cambridge University Press, 1992. ISBN: 9780521431088.
    Listed reading
  • ———. Numerical Recipes in Fortran . New York, NY: Cambridge University Press, 1996. ISBN: 052143064.
    Listed reading
  • ———. Numerical Recipes in Fortran 90: The Art of Parallel Scientific Computing . New York, NY: Cambridge University Press, 1996. ISBN: 9780521574396.
    Listed reading
  • Schiesser, William E. Computational Mathematics in Engineering and Applied Science . Boca Raton, FL: CRC Press, 1993. ISBN: 9780849373732.
    Listed reading
  • Rozanov, Y. A. Probability Theory: A Concise Course . New York, NY: Dover, 1977. ISBN: 9780486635446.
    Listed reading
  • McPherson, Glen. Applying and Interpreting Statistics: A Comprehensive Guide . New York, NY: Springer, 2001. ISBN: 9780387951102.
    Listed reading
  • Keeping, E. S. Introduction to Statistical Inference . New York, NY: Dover, 1995. ISBN: 9780486685021.
    Listed reading
  • Sen, Ashish, and Muni Srivastava. Regression Analysis: Theory, Methods, and Applications . New York, NY, Springer, 1997. ISBN: 9780387972114.
    Listed reading
  • Bernardo, Jose M., and Adrian F. M. Smith. Bayesian Theory . New York, NY: Wiley, 1994. ISBN: 9780471924166.
    Listed reading
  • Zachmanoglou, E. C., and D. W. Thoe. Introduction to Partial Differential Equations with Applications . New York, NY: Dover, 1987. ISBN: 9780486652511.
    Listed reading
  • Bathe, K. J. Finite Element Procedures . Upper Saddle River, NJ: Prentice Hall, 1995. ISBN: 9780133014587.
    Listed reading
  • Akin, J. E. Finite Elements for Analysis and Design . London, UK: Academic Press, 1994. ISBN: 9780120476541.
    Listed reading
  • Ferziger, J. H., and M. Peric. Computational Methods for Fluid Dynamics . New York, NY: Springer, 1997. ISBN: 9783540594345.
    Listed reading
  • Wendt, J. F., ed. Computational Fluid Dynamics . New York, NY: Springer, 1996. ISBN: 9783540594710.
    Listed reading
  • Peyret, R., ed. Handbook of Computational Fluid Mechanics . London, UK: Academic Press, 1996. ISBN: 9780125530101.
    Listed reading
  • Part-Enander, Eva, and Anders Sjoberg. The MATLAB® 5 Handbook . Reading, MA: Addison-Wesley, 2000. ISBN: 9780201398458.
    Listed reading
  • Ellis, T. M. R., I. R. Philips, and T. M. Lahey. Fortran 90 Programming . Reading, MA: Addison-Wesley, 1994. ISBN: 9780201544466.
    Listed reading
  • Barton, J. J., and L. R. Nackman. Scientific and Engineering C++ . Reading, MA: Addison Wesley, 1994. ISBN: 9780201533934.
    Listed reading
  • McConnell, Steve. Code Complete: A Practical Handbook of Software Construction . Redmond, WA: Microsoft Press, 1993. ISBN: 9780201533934.
    Listed reading
  • Frenkel, Daan, and Berend Smit. Understanding Molecular Simulation: From Algorithms to Applications . San Diego, CA: Academic Press, 1996. ISBN: 9780122673702.
    Listed reading
  • Kloeden, P. E., and E. Platen. Numerical Solution of Stochastic Differential Equations . New York, NY: Springer, 1992. ISBN: 9783540540625.
    Listed reading

Prerequisites & course information

Prereq: Permission of instructor G (Fall) 4-0-8 units

Sources