ENGINEERING 5434: Applied
Mathematical Analysis
Instructor Dr. Seshu Adluri Teaching
Assistants TBA
Email adluri@mun.ca Email
Phone 8643800 Phone
Office Location EN3044 Office
Location
Office Hours Monday
10:0011:50 a.m. Office Hours
Website www.engr.mun.ca/~adluri/5434
CALENDAR ENTRY:
Examines numerical and analytical solutions of applied
mathematical problems in Civil Engineering, problems with higher order ordinary
differential equations, stiff equations, systems of ODE, RungeKutta
methods, boundary value problems, applications of eigen value problems (numerical solutions), Fourier
analysis, elliptic, parabolic and hyperbolic partial differential equations and
their numerical solutions with engineering applications.
COURSE DESCRIPTION:
The course gives an insight into engineering problems
requiring solutions that are more involved than those the students have learned
thus far. They include several types of
first or higher order ordinary and partial differential equations and data
analysis using Fourier methods. In most
practical cases, the problems are complicated and not easily amenable to
classical closed form solutions.
Therefore the main emphasis of the course is on numerical
solutions. Several issues arise in
numerical methods such as matrices, stiff equations, eigen problems, numerical stability. These are addressed using engineering
examples from mechanics, structures, heat transfer, diffusion, fluids, etc.
PREREQUISITES: ENGI 4425
COREQUISITES: A good working
knowledge of spreadsheets such as EXCEL and math software such as MATLAB is
required.
SCHEDULE: LECTURE: MWF 2:002:50 pm Room:
EN1054
TUTORIAL: Friday 4:004:50 Room: EN1054
CREDIT VALUE: 3 credits
RESOURCES: www.engr.mun.ca/~adluri/5434
Text
book: No textbook assigned. However, the book prescribed for ENG 4425 is
used as supplementary reading material for part of the course.
REFERENCES: As
discussed in class from time to time.
Consult the following:
Chapra, S.C., & Canale, R.P.. "Numerical Methods for Engineers," McGrawHill.
Akai, T.J.,. "Applied Numerical Methods for Engineers," John Wiley & Sons, Inc.
Gerald, C.F., and P.O. Wheatly,. "Applied Numerical Analysis," Sixth Ed., AddisonWesley 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.
MAJOR TOPICS:
Any of the above may be extended with related topics and applications
depending upon time and interest.
LEARNING OUTCOMES:
Upon successful completion of this course, the student
will be able to:
1. Understand
the theoretical and practical applications of numerical methods.
2. Find
numerical solutions for Initial Value Problems.
3. Compare and
recommend different methods for numerical solution of Ordinary Differential
Equations.
4. Use
numerical methods to solve Boundary Value Problems.
5. Use
implicit methods of solution to numerically solve Stiff Equation Problems.
6. Use Finite
Difference Methods for solving Differential Equations.
7. Understand
the application of Eigen Values and their use in engineering.
8. Use
numerical techniques to provide solutions to Eigen Value Problems.
9. Use Fourier
analysis to represent and analyze functions and physical data.
10. Identify
and numerically solve Elliptic, Parabolic and Hyperbolic Partial Differential
Equations with applications in heat transfer, diffusion, torsion of prismatic
bars, string vibrations, etc. .
ASSESSMENT:
Approximate Due Dates
Assignments 15%
Assignments are
due one week from announcement unless otherwise agreed upon. Assignments include computer work.
Midterm 25% Feb 7
Final exam 60%
Exam policy: The formula sheet is as per the announcement in the class. All or a subset of the preannounced formula sheet will be provided in the exam. No extra text or notes are permitted in the exam. Electronic storage/retrieval devices are not permitted in the exam. Please see the appropriate guidelines from the University regarding such matters.
Comprehensive examples will be discussed primarily
during tutorials. During tutorials, the students may be required to solve the
problems in class to gain practice.
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. The students are expected to make use of the various files and ask for help if needed.
The students are expected to solve the assignment problems by themselves in order to reinforce the class instruction. Please refer to copying policy of the University if there is any doubt. Help with the assignment problems can be sought during contact hours and/or tutorial time.
ACADEMIC INTEGRITY AND PROFESSIONAL CONDUCT:
Students are
expected to conduct themselves in all aspects of the course at the highest
level of academic integrity. Any student found to commit academic misconduct
will be dealt with according to the Faculty and University practices. More
information is available at www.engr.mun.ca/undergrad/academicintegrity.
Students are
encouraged to consult the Faculty of Engineering and Applied Science Student
Code of Conduct at http://www.engr.mun.ca/policies/codeofconduct.php and Memorial University’s Code of Student Conduct at http://www.mun.ca/student/home/conduct.php.
INCLUSION AND EQUITY:
Students who require physical or academic
accommodations are encouraged to speak privately to the instructor so that
appropriate arrangements can be made to ensure your full participation in the
course. All conversations will remain
confidential.
The university experience is enriched by the diversity
of viewpoints, values, and backgrounds that each class participant
possesses. In order for this course to
encourage as much insightful and comprehensive discussion among class
participants as possible, there is an expectation that dialogue will be
collegial and respectful across disciplinary, cultural, and personal
boundaries.
STUDENT ASSISTANCE: Student Affairs and Services offers help and
support in a variety of areas, both academic and personal. More information can be found at www.mun.ca/student.
Assignments:
Marks going
into final exam
If
there are any discrepancies, please talk to Dr. Adluri immediately after the
final exam (before leaving the exam hall).
Please
note that changes at a later date are not possible.
Sample Midterm Sol:
Midterm Q1, Midterm Q21, Q22
Sample final Exam
Solution: P2, P1, P3a, P3b, P4, P5
Another
Sample exam,

Handouts
and extra material for the students to help in their understanding:
Intro’ 
Example for user defined
functions in EXCEL DOC file 
Ordinary Differential Equations First Order 
Handout for various procedures

Systems of ODE Initial Value Problems 
Application: PredatorPrey model Conversion of higher order
ODE to a system of First order ODE 
Stiff Equations 
Eigen Values 


Example for FaddeeveLeverrier principal stresses 
Fourier Analysis 

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