10.34. Numerical Methods Applied to Chemical Engineering

Fall 2002 Class Schedule

 

Class meets MWF 9-10, 66-110

 

Office Hours

Instructor

K. J. Beers                               TR 1-2, 66-558,  kbeers@mit.edu

TA’s

Irina Elkin                                 W 10-11, 66-265, ielkin@mit.edu

Keith Dalbey                            M 10-11, 66-265, keithd@mit.edu

 

Reading assignments are to be completed before the noted date and are taken from

(GB) – G. J. Borse. Numerical Methods with MATLABâ, PWS Publishing, Boston, 1997

[KB] – K. J. Beers, 10.34 class handouts

 

Course Grading Policy

HW – 25%            Exam I – 25%              Exam II – 25%  Final Exam – 25%

Homework assignments (10 points each)

HW

Date Assigned

Date Due

Subject

1

F 9/6

F 9/13

linear algebraic equation sets

2

F 9/13

W 9/25

nonlinear algebraic systems

3

F 9/20

F 9/27

matrix eigenvalue problems

4

F 9/27

W 10/9

function-space methods for BVP’s

5

W 10/9

F 10/18

function-space methods for BVP’s

6

F 10/18

F 10/25

Fourier analysis

7

F 10/25

F 11/1

Finite-difference method

8

F 11/1

F 11/8

Finite-element method

9

F 11/8

M 11/18

Initial value problems

10

M 11/18

M 11/25

Probability theory

11

F 11/22

M 12/2

Linear least squares

12

W 11/27

F 12/6

Parameter estimation

 

Exams (100 points each)

Exam

Date

Subject

I

F 10/4 in class

 Linear and Nonlinear algebraic systems, eigenvalue analysis

II

F 11/15 in class

 Boundary and initial value problems

Final

TBA, 12/16-12/20

 Probability and statistics

 

 

Lectures

 

#

 

Date

Readings / Assignments

 

Subject

1

W 9/4

(GB: 1, app. A)

 

 Introduction.  Sets of linear algebraic equations, matrix/vector operations

2

F 9/6

(GB: 2)

[KB: 1.1-1.2]

{HW 1 out}

 Gaussian elimination, Gauss-Jordan elimination, partial-pivoting and round-off error

3

M 9/9

[KB: 1.3.1-1.3.4]

 Interpreting Ax=b as a linear transformation, basis sets and vector spaces, Gram-Schmidt orthogonalization

4

W 9/11

[KB: 1.3.4-1.3.6]

 Existence/uniqueness of solutions to Ax=b, determinants

5

F 9/13

[KB: 1.4]

{HW 1 due, 2 out}

 LU and Cholesky decomposition, matrix inversion

6

M 9/16

(GB: 4, 5)

[KB: 2.1]

 Solving a single nonlinear algebraic equation, Newton’s method in 1-D, Taylor series

7

W 9/18

(GB: 8, 9)

[KB: 2.2]

 Solving sets of nonlinear algebraic equations with Newton’s method, convergence properties, estimating the Jacobian, reduced-step algorithms

8

F 9/20

(GB: 3)

[KB: 3.1.1-3.1.2]

{HW 3 out}

 orthogonal matrices, matrix eigenvalues/eigenvectors, Gershorgin’s theorem

9
W 9/25

[KB: 3.1.3]

{HW 2 due}
normal matrices, completeness of eigenvector bases

10

F 9/27

[KB: 3.1.4-3.1.5]

{HW 3 due, 4 out}

 Jordan normal forms, Schurr decomposition, numerical calculation of eigenvalues

11

M 9/30

[KB: 4.1]

 function-space discretization, use of basis-function expansions, conversion of boundary value problems to algebraic equation sets

12

W 10/2

[KB: 4.2.1]

 basic definitions from functional analysis, eigenfunctions of self-adjoint boundary value problems

13

F 10/4

EXAM
Exam I – Linear and Nonlinear algebraic systems, eigenvalue analysis

14

M 10/7

[KB: 4.2.2-4.2.3]

 analytical solutions of boundary value problems using separation of variables

15

W 10/9

[KB: 4.2.4]

{HW 4 due, 5 out}

 Bessel functions, boundary value problems in cylindrical coordinates, Frobenius method

16

F 10/11

[KB: 4.2.5]

 spherical harmonics, BVP’s in spherical coordinates

17

W 10/16

(GB: 7, 16)

[KB: 4.4]

 numerical evaluation of integrals, interpolation

18

F 10/18

(GB: 17)

[KB: 4.5.1]

{HW 5 due, 6 out}

 Fourier series and transforms in 1-D

19

M 10/21

[KB: 4.5.2]

 Fourier convolution and correlation operations

20

W 10/23

[KB: 4.5.3]

 2-D and 3-D Fourier transforms, scattering theory

21

F 10/25

(GB: 20)

[KB: 5.1]

{HW 6 due, 7 out}

 real-space discretization, method of finite differences, conversion of boundary value problems to sets of linear and nonlinear algebraic equations

22

M 10/28

[KB: 5.2]

 Iterative methods for solving large sets of algebraic equations

23

W 10/30

(GB: 22)

[KB: 5.3]

 Examples – numerical solution of boundary value problems with finite difference method

24

F 11/1

[KB: 5.4.1]

{HW 7 due, 8 out}

 Finite element method in 1-D

25

M 11/4

[KB: 5.4.2-5.4.3]

 2-D and 3-D finite element method in solid mechanics and transport phenomena

26

W 11/6

(GB: 19)

[KB: 6.1-6.2]

 Solution of initial value problems of sets of first

order differential equations, considerations of stability and accuracy (order)

27

F 11/8

[KB: 6.3-6.4]

{HW 8 due, 9 out}

 Numerical time integration of ODE-IVP’s, methods for treating stiffness, systems of many equations

28

W 11/13

[KB: 6.5]

 Examples – numerical solution of boundary and initial value problems in chemical engineering

29
F 11/15
EXAM
Exam II. Boundary and initial value problems

30

M 11/18

(GB: 13)

[KB: 7.1-7.2]

{HW 9 due, 10 out}

 Introduction to probability theory, conditional and joint probabilities, statistical independence

31

W 11/20

[KB: 7.3]

 Random variables, binomial and Gaussian distributions, Poisson distribution, central limit theorem

32

F 11/22

[KB: 7.4]

{HW 11 out}

 random walks, Markov processes, transition probabilities

33

M 11/25

(GB: 14)

[KB: 8.1-8.3]

{HW 10 due}

 Least squares linear regression of parameters

34

W 11/27

[KB: 8.4-8.5]

{HW 12 out}

 Analysis of residuals and  the Gauss-Markov conditions, confidence intervals of model parameters and model predictions

35

M 12/2

[KB: 8.6]

{HW 11 due}

 Examples of linear least squares

36

W 12/4

[KB: 8.7-8.8]

 Examples of linear least squares

37

F 12/6

(GB: 10, 15)

[KB: 9.1-9.2]

{HW 12 due}

 Nonlinear least squares, Newton-type and Marquardt methods

38

M 12/9

[KB: 9.3-9.4]

 Examples of parameter estimation

39

W 12/11

 

 Examples of parameter estimation