..Methods of Engineering Analysis


Lectures: M/W/F (and if needed T or Th) 12:30-1:20 BNS115
Problem sessions/Recitations: Th 12:30-1:20 BNS115
Instructors: Prof. François Baneyx, BNS307, 685-7659
TAs: Tyler House, BNS236 and Beau Richardson, BNS256
Office Hours: Tyler House: Wednesdays 3:00-4:00PM and Thursdays 1:30-2:30PM in BNS236. Beau Richardson: Tuesdays 2:00-3:00PM and Thursdays: 3:00-4:00PM. Prof. Baneyx: Fridays 2:00-3:00PM in BNS307. Other times by appointment
Grading: Midterm 30%; Final 50%; Homeworks 20%
Textbook: Hildebrand, FB: Advanced Calculus for Applications, 2nd Ed, Prentice Hall, Englewood Cliffs (1976)
Objectives: By the end of the course, students should be able to: (i) carry out vector and tensor calculations including surface and volume integrations; (ii) solve ordinary differential equations with constant and non-constant coefficients using classical approaches, Laplace transformations, and power series approaches; (iii) solve partial differential equations by separation and combination of variables; and (iv) apply the above techniques to engineering problems.


Tentative Topic
Week 1: 9/24-9/28

Lectures: MTuWF

Recitation: Th

Introduction to vectors and tensors

Vector algebra, dot and cross products, semi Einstein notations

Gradient, divergence, curl and Laplacian operations

Week 2: 10/1-10/5

Lecture: MW

Recitation: Th

Vector integration

Surface and volume integrals

Week 3: 10/8-10/12

Lectures: MWF

Recitation: Th

Gauss's, Green's and Stokes' theorems

Coordinate Transformations

Review of ODEs

Week 4: 10/15-10/19

Lectures: MWF

Recitation: Th

Solution techniques

Variation of parameters

Reduction to well-known forms

Week 5: 10/22-10/26

Lectures: MWF

Recitation: Th

Midterm exam: Mo 10/22; 12:30-1:20

Introduction to Laplace transformations

Elementary transformations

Week 6: 10/29-11/2

Lectures: MWF

Recitation: Th

Shifting theorem and convolution

Special functions defined by integrals

Applications of Laplace transformations

Week 7: 11/5-11/9

Lectures: MWF

Recitation: Th

ODE with non-constant coefficients: power series approaches

Introduction to special functions defined by series

Bessel's equation and Bessel functions

Week 8: 11/12-11/16

Lecture: F

Recitation: Th

Properties of Bessel functions
Week 9: 11/19-11/23

Lecture: MW

Recitation: None

Applications of Bessel functions in heat and mass transfer

Legendre polynomials

Week 10: 11/26-11/30

Lecture: MWF

Recitation: Th

Applications of Legendre polynomials

Fourier analysis

Sturm-Liouville theory

Week 11: 12/3-12/7

Lecture: MWF

Recitation: Th


PDE solution techniques

Application to heat and mass transfer problems

Week 12: 12/10-12/14 Final exam: Th 12/13; 8:30-10:20
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Contact: François Baneyx, University of Washington, Department of Chemical Engineering, Box 351750, Seattle, WA Tel: 206-685-7659 Fax: 206-685-3451 E-mail:

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