ME 140B: Theoretical Analysis in Mechanical Engineering

 

·       Professor

·       Teaching Assistant

·       Syllabus

·       Goals for the Class

·       Textbook

·       Grading Policy

·       Homework

 

Professor

Name: Frederic Gibou
Office: Engineering II Bldg. room 2334
Phone: 893-7152
e-mail: fgibou@engineering.ucsb.edu

Lectures: TR 3:30 - 4:45. Room: BUCH 1934

Office Hours: TR after class or by appointment

Teaching Assistants

Name: Yentin Ng
Officeroom 2311
e-mail: yenting@cs.ucsb.edu

Office Hours: TBA

Syllabus

 

Goal for the Class

The goal for the class is for the students to learn and master the following:

·       Derivation of Conservation Laws (Advection – Diffusion – Laplace – Burgers).

·       Classification of PDEs and their properties.

·       Difference between linear .vs. nonlinear, homogeneous .vs. nonhomogeneous.

·       Method of Separation of Variables - Fourier Series.

·       Method of Characteristics.

·       Numerical Methods for Hyperbolic, Parabolic, and Elliptic PDEs.

·       Stability and Consistency Analysis.

·       If time permits, Nonlinear Phenomena (shock waves and rarefaction waves).

Textbook

The textbook for the course is Applied Partial Differential Equations with Fourier Series and Boundary Value Problem, by R. Haberman. Prentice Hall; 4th edition, ISBN-10: 0-13-065243-1

Grading Policy

Your grade will be based on homework (30%), one midterm (30%) on Tuesday April 29 in class from 3:30-4:45 and a final (40%) on Thursday June 12 from 4-7pm in class.

Homework

Homework 1: 2.2.2, 2.3.3 b, 2.4.1 b. In addition answer the questions given in class. Make sure you can do all the problems worked out in class.

Homework 2: Questions from class:

1- Compute the drag of a flow past a circular cylinder.

2- Comment on the oddness of this result (compare with your physical intuition for real fluid flows).

3- Plot the contour of the streamlines when the circulation is given by c1/(Ua)=0, c1/(Ua)=1, c1/(Ua)=2 and c1/(Ua)=3.

Solution code: Flow_Past_Cylinder.m

Homework 3: Click here.

Homework 4: Click here. Solution code: Advection.m, which needs the function Update_Unew_With_Upwind.m

Homework 5: Click here.