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Important Requirements

All students are required to
  • Be able to perform simple programming tasks using any platform (preferably Octave)
  • Homework, Projects, and all other assignments will be submitted in electronic format
  • No homework assignments need to be submitted, they are just for personal practice and solutions will be provided.

Assessment Tools

T1: Examinations/Tests
T3: Group Projects
T6: Student Survey

Course Objectives

The course will develop numerical methods aided by technology to solve algebraic, transcendental, and differential equations, and to calculate derivatives and integrals. The course will also develop an understanding of the elements of error analysis for numerical methods and certain proofs. The course will further develop problem solving skills.

Course Intended Learning Outcomes

By the end of this course, the student will be able to:
ILO#
Description
Assessment
Tool
Program
ILO
1
solve an algebraic or transcendental equation using an appropriate numerical method
T1,T6
1,5
2
prove results for numerical root finding methods
T1,T6
1
3
approximate a function using an appropriate numerical method
T1,T6
1,5
4
calculate a definite integral using an appropriate numerical method
T1,T6
1,5
5
solve a differential equation using an appropriate numerical method
T1,T6
1,5
6
evaluate a derivative at a value using an appropriate numerical method
T1,T6
1,
7
find optimal values that satisfy linear and nonlinear optimization problems
T1,T6
1,5
8
code a numerical method in a modern computer language
T3
5,11
9
Coordinate working in a multifunctional team
T3
4,10
10
Prepare and present technical reports
T3
7,11

References

  • Numerical Methods for Engineers, Raymond P. Canale and Steven C. Chapra, 6th ed, 2010, McGraw Hill, ISBN 978–0–07–340106–5

Topics and Schedule

Week #
Topic
Time Line
ILO's
1
9/2/2017
Introduction

Errors

1
2
16/2/2017
Roots of Nonlinear Equations – Bracketing methods

1, 2
3
23/2/2017
Roots of Nonlinear Equations – Open methods

1, 2
4
2/3/2017
Interpolation – Polynomial, Newton, Lagrange

3
5
9/3/2017
Interpolation – Multidimensional
Midterm #1
3
6
16/3/2017
Regression – Least squares method applied for linear and nonlinear regression

3
7
23/3/2017
Numerical Integration – Trapezoidal, Simpson, Interpolation

4
8
30/3/2017
Numerical Differentiation
Initial Value Problems – Euler, Runge-Kuta

5, 6
9
6/4/2017
Initial Value Problems – System of equations and higher order derivatives
First presentation of project
5
10
13/4/2017
Boundary Value Problems – Finite Difference
Midterm #2
5
11
20/4/2017
Spring Break


12
27/4/2017
Boundary Value Problems – Weighted Residual methods
Second Presentation of project
5
13
4/5/2017
Optimization – The objective function

7
14
11/5/2017
Optimization – Golden section and Newton Methods

7
15
18/5/2017
Linear Programming – Graphical and Simplex methods
Final presentation of projectCourse Project due
7

Assessment

30% Final (Have to score at least 50% in final to pass)
20% Midterms (2 midterms, all counted)
10% Pop quizzes (3 to 8 randomly distributed – all counted)
40% Project


Course Project

Topics

  • The topics should include the solution of an initial-boundary value problem (PDE), optimization using genetic algorithms or neural networks, or dynamic finite element analysis of a problem.
  • All topics should include the creation of software for analysis of the collected data based on open source packages or compilers (penalty up to 10% for use of ready-made analysis software, and another 10% for using non open source software or platform)


Teams

The team should include four to eight students who will divide themselves into sub-teams working on different software functions’ development.


Project Evaluation

  • Project management (15%) (3 5-minute presentations by team coordinators)
    • Planning (40%)
    • Follow up (20%)
    • Corrective actions and re-planning (40%)
  • Final Report (40%)
    • Technical report format (Cover, TOC, Introduction and literature survey, mathematical background, results, conclusions, reference, appendices) (25%)
    • Rigor of literature survey (25%)
    • Details of the model derivation and development (25%)
    • Numerical results and verification (25%)
  • Software (25%)
    • Ease of use and operability (30%)
    • Accuracy (40%)
    • Output graphics (40%)
  • Final presentation (20%)
    • Public decimation of knowledge (Website. Wiki, videos, public slides, public reports, design graphics and charts, etc...) (25%)
    • Presentation graphics and appeal (15%)
    • Accuracy of presentation content (15%)
    • Comprehensibility of presentation content (15%)
    • Audience capturing (10%)
    • Audience participation and reply to questions (10%)
    • Timing (10%)





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