Memorial University of Newfoundland

Faculty of Engineering and Applied Science

Engineering: 5434	Applied Mathematical Analysis
	Instructor: Dr. Seshu M.R. Adluri
Student Consultation Time (office hours): 11:00-12:50 Monday		Office: EN 3044 Tel: x3800
Course Outline: Course pre-requisite: Eng.4422. Also, a good working knowledge of spreadsheets such as EXCEL is required. If the students need a quick review in the use of spreadsheets, the class representative can schedule a tutorial or two for this purpose. The students may need to brush up on their MATLAB knowledge as well. Ordinary Differential Equations Quick Review Euler, Heun, Runge-Kutta, etc., for single first order differential equations Systems of first order equations and Higher order differential equations Numerical solution for initial value problems Boundary Value Problems –shooting or secant methods, etc. Stiff Equations -First order and higher order, implicit methods of solution, etc. Introduction to Finite Difference Methods, dynamic response of systems, marching solutions Eigen value Problems Eigen Value Problems -formation and numerical techniques Eigen Value Problems -numerical techniques for Eigen problems -variations of Power method, bounding theorems, Faddeeve-Leverrier method. Fourier Analysis Introduction Theorems, Series, even & odd functions, etc. Fourier series expansions and applications Numerical Fourier Analysis -Harmonics, confidence of fit, data analysis, etc. Partial Differential Equations Introduction - Numerical solution Elliptic Partial Differential Equations: Introduction, Laplace and Poisson equations, steady state heat equation, finite difference solution, Introduction to problems like Torsion of prismatic bars, etc. Parabolic Partial Differential Equations: Thermal conduction, diffusion, and other applications. Solution techniques for systems of equations, explicit and implicit methods, etc. Hyperbolic Partial Differential Equations: Wave equation, marching solutions, etc. All the above and related topics may be extended with applications depending upon the interest.

Assessment Procedure:

Class Assignments	10% (includes computer work -use of Spread Sheets like EXCEL, and/or programming, including MATLAB. Unless otherwise specified, assignments are due one week from the date of giving. Marks may be reduced for late submission. If a TA is not available for the course for any reason, the assignment marks will be equally reassigned towards the midterm and final exams.)
Midterm Test	30% (March 2)
Final Examination	60%

Text Book: The course material does not have a prescribed textbook. However, the book prescribed for ENG 4422 (if you have it) can be used as supplementary reading material. For Reading: Chapra, S.C., & Canale, R.P.. "Numerical Methods for Engineers," McGraw-Hill. Akai, T.J.,. "Applied Numerical Methods for Engineers," John Wiley & Sons, Inc. Gerald, C.F., and P.O. Wheatly,. "Applied Numerical Analysis," Sixth Ed., Addison-Wesley Publishing Co. O’Neil, P.,. "Advanced Engineering Mathematics," Third Ed., Wadsworth Publishing Co. Epperson, J.F.,. "An Introduction to Numerical Methods and Analysis," John Wiley & Sons.

NOTE:

Please note that prewritten solutions may or may not be available for the assignments. However, the tutorials are specifically marked for discussing the relevant solutions. At that time, if the students ask for it, the problems can be discussed and may be partially or fully solved in class. If the students do not raise their need for discussion of the problems, the time will be spent on solving other example problems, etc. The same policy holds for midterm exams and quizzes, if any. Several handouts, example solutions using EXCEL are posted at the course website: www.engr.mun.ca/~adluri/courses/num_meth. The students are expected to make use of the various files and ask for help if needed. The Faculty of Engineering does not encourage students skipping lectures. Even if lectures are skipped by a few or all the students in the class, the lectures could go on and the corresponding course material may not be repeated at a later time. This is especially true in the case of D-Day activities of the students. This policy is included here as per the instructions of the Dean of Engineering.

Assignment 2

Formula sheet

Handouts and extra material for the students to help in their understanding:

Intro’

Quick Review Example for user defined functions in EXCEL -DOC file Example for user defined functions in EXCEL - EXCEL file Solution to cubic equations Gauss elimination procedure Solving simultaneous equations in EXCEL

Ordinary Differential Equations -First Order

Handout for various procedures Example for Euler, Modified Euler and Runge-Kutta Methods Comparison of relative errors

Systems of ODE -Initial Value Problems

Application: Predator-Prey model Conversion of higher order ODE to a system of First order ODE Application: Cantilever Beam

Systems of ODE -Boundary Value Problems

Notes on Boundary value problems Example of Shooting using Euler Method Example of Shooting with various methods (Macros) Another Example of Shooting with various methods (using Macros) Example of simply supported beam

Stiff Equations

First order stiff equation example System of stiff equations - example

Eigen Values	Review of Eigen Values and Introduction to Power method Example for Power method Faddeeve-Leverrier Method Example for Faddeeve-Leverrier
	Example for Faddeeve-Leverrier- principal stresses Example for Power method-principal stresses Buckling of Tapered column-Faddeeve-Leverrier

Fourier Analysis

Fourier analysis for Discrete data Practice problems for Fourier Analysis

Partial Differential equations are slightly cumbersome to be solved using spreadsheets. Interested students may use MATLAB or other tools for this purpose.

Legal stuff:

The MUN Faculty Association asked us to include the following in Legalese. J So there! J The lectures and displays (and all material) delivered or provided in this course, including any visual or audio recording thereof, are subject to copyright owned by the instructor for the course (Dr. Seshu Adluri). Other copyrights may also be applicable. It is prohibited to record or copy by any means, in any format, openly or surreptitiously, in whole or in part, in the absence of express written permission from the instructor, Dr. Seshu Adluri any of the lectures, materials provided or published in any form during or from the above course.