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ECH5842 CHEMICAL ENGINEERING ANALYSIS Fall '98


COURSE OUTLINE AND OBJECTIVES



INSTRUCTOR: Dr. R. Chella (158 CEB)

CLASS TIME: TR 1:15-2:30pm (B115)

OFFICE HOURS: TR 8:30am - 10:00am

PREREQUISITES MAP 3305, ECH 4403 and ECH 4504 (or equivalents).



COURSE DESCRIPTION

This course will focus on developing the tools for the mathematical formulation of conservation laws and the solution of the resulting partial differential equations. In the first part of the course, the vector and tensor algebra and calculus necessary for the derivation of the generalized balances for conserved quantities are covered, followed by techniques for the scaling and simplification of the model equations, as well as dimensional analysis. In the second part of the course both analytical (eigenfunction expansions, similarity transforms, etc.) and asymptotic (regular and singular perturbation techniques) methods of solution will be discussed for the resulting model equations.



TEXT

Arfken, G.B., Mathematical Method for Physicists, 4th Edn., Academic Press, 1995.



REFERENCES

1.
Greenberg, M.D., Foundations of Applied Mathematics, Prentice-Hall, 1978.
2.
Lin, C.C. and L.A. Segel, Mathematics Applied to Deterministic Problems in the Natural Sciences, SIAM, 1974.

3.
Jeffreys, H., and B.S. Jeffreys, Methods of Mathematical Physics, 3rd Edn., Cambridge University Press, 1956.

4.
Papers from the literature and class handouts.




GRADING The course grade will be based on assigned homework problems, two mid-term exams, quizzes, and a final exam, weighted as follows. 




Two Mid-term Exams 		40%
		Final Exam 		30%
		Quizzes 		10%
		Homework 		20%
Exams will be ``closed-book'', but students may bring in with them one page of notes for the mid-term exams and upto five pages of notes for the final exam. There will be about ten homework assigments during the course of the semester. Homework assignments are due at the beginning of the class session one week after they are assigned. All homeworks are to be done individually.

ECH5842 COURSE OUTLINE Fall'98
1.
Vector Analysis - basic vector operations; coordinate transformations; differentiation of scalar and vector fields; line, surface, and volume integrals; integral theorems: divergence, Stokes', and Reynolds' transport; potential Theory; Dirac delta functions and representations

2.
Vector Analysis in Curved Coordinates Orthogonal Coordinates; differential vector operations; cylindrical and spherical coordinate systems; tensor analysis

3.
Matrix Analysis Determinants and basic marix operations; orthogonal and Hermitian matrices; matrix diagonalization; normal matrices

4.
Scaling and Simplification - non-dimensionalization; scaling and characteristic quantities; ordering; consistency checking; dimensional Analysis - Buckingham-Pi theorem; geometric & dynamic similarity

5.
Partial Differential Equations - classification and characterization; linearity and superposition; separation of variables; singular points and series solutions; Green's functions; similarity transforms

6.
Sturm-Liouville Theory - Self-adjoint operators; Hermitian operators; completeness of eigenfunctions; eigenfunction expansions

7.
Fourier Series - representation of periodic functions; properties and applications; operations on Fourier series; discrete Fourier transform

8.
Asymptotic Techniques - asymptotic series; regular perturbations; singular perturbations - matched asymptotic expansion and method of multiple scales

ECH5842 COURSE SCHEDULE Fall'98
1.
8/25 Introduction
2.
8/27 Vector Algebra and Differentiation (1.1-1.9)
3.
9/01 Integral Theorems (1.10-1.12)
4.
9/03 Potential Theory (1.13-1.14)
5.
9/08 Delta Functions (1.15-1.16)
6.
9/10 Vector Analysis in Curved Coordinates (2.1-2.2)
7.
9/15 Special Coordinate Systems (2.3-2.5)
8.
9/17 Tensor Analysis (2.6-2.9)
9.
9/22 Matrix Algebra (3.1-3.2)
10.
9/24 Orthogonal and Hermitian Matrices (3.3-3.4)
11.
9/29 Matrix Diagonalization (3.5-3.6)
12.
10/01 ... Exam 1
13.
10/06 Simplification and Scaling, Dimensional Analysis (Notes)
14.
10/08 Geometric and Dynamic Similarity (Notes)
15.
10/13 Classification and Characterization of PDEs (8.1-8.3)
16.
10/15 Singular Points and Series Solutions (8.4-8.5)
17.
10/20 Wronskian Integral (8.6)
18.
10/22 Self-Adjoint and Hermitian Operators (9.1-9.2)
19.
10/27 Eigenfunctions & Gram-Schmidt Orthogonalization (9.3-9.4)
20.
10/29 Green's Function -- Eigenfunction Expansions (9.5)
21.
11/03 Fourier Series -- Definition and Completeness (14.1-14.2)
22.
11/05 Fourier Series -- Applications & Properties (14.3-14.4)
23.
11/10 Discrete Fourier Transform (14.5-14.6)
24.
11/12 Perturbation Techniques -- Regular perturbations
25.
11/17 Perturbation Techniques -- Regular perturbations
26.
11/19 Perturbation Techniques -- Singular Perturbations
27.
11/24 Perturbation Techniques -- Singular Perturbations
28.
12/01 ... Exam 2
29.
12/03 Similarity Transforms
30.
12/10 (3:00-5:00p) FINAL EXAM

ECH 5842 CHEMICAL ENGINEERING ANALYSIS Fall'98
BACKGROUND MATERIAL


REFERENCES

1.
Any undergraduate Calculus and Analytic Geometry text: e.g. Thomas, G.B. and R.L. Finney, Calculus and Analytic Geometry, 5th ed., Addison-Wesley, 1979.
2.
Amundson, N.R., Mathematical Methods in Chemical Engineering -- Matrices and their Applications, Prentice-Hall, 1966.

3.
Boyce, W. and R. Diprima, Elementary Differential Equations and Boundary Value Problems, 2nd ed., Wiley, 1969.

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Ravindran Chella
8/25/1998