Course Name: Numerical Methods

Degree: Bachelor

Code

Year/Semester

Local Credits

ECTS Credits

Course Implementation, Hours/Week

Course

Tutorial

Laboratory

ENG216

2/1 (Fall-Spring)

2.5

4

2

1

-

Department

Mechanical Engineering

Instructors

Lecturer Serap Herdem

Contact Information

skaya@pirireis.edu.tr , 0216 581 00 50 (1628)

Office Hours

Thursday:  13:00-15:00

Web page

http://www.pirireis.edu.tr/pruonline

Course Type

 Compulsory

Course Language

English

Course Prerequisites

MATH113, MATH122

Course Category by Content, %

Basic Sciences

Engineering Science

Engineering Design

Humanities

50

50

-

-

Course Description

Roots of Equations. Systems of Linear Algebraic Equations. Optimization. Curve Fitting. Integration. Ordinary Differential Equations. Partial Differential Equations.

Course Objectives

1. To provide a basis on numerical techniques used in engineering problems,

2. To prepare students for solving engineering problems and mathematical models in computer environment,

3. To introduce numerical techniques selected from a wide range of topics,

4. To give hands-on experience of MATLAB engineering applications,

5. To acquaint students with the right sense of selecting appropriate solution technique for the problem in hand.

Course Learning Outcomes

At the end of this course, students will have a complete understanding of the following fundamental topics in engineering:

1. Defining errors in a computer system and number representation
2. Finding roots of functions, various root finding methods
3. Solving linear systems
4. Optimization
5. Understanding the difference between regression and interpolation
6. Understanding various numerical integration schemes
7. Understanding numerical differentiation and solving ODE’s
8. Finite difference and PDE’s

Instructional Methods and Techniques

Lecture, problem solving

Tutorial Place

Co-term Condition

Textbook

Numerical Methods for Engineers, Chapra, S.C., Canale, R.P., McGraw-Hill

Other References

1. Applied numerical analysis1 Curtis F. Gerald, Patrick O. Wheatey, Pearson Education, Inc.
2. Numerical Analysis, Richard L. Burden and J. Douglas Faires, Brooks/Cole

              Buchanan, J.L. and Turner, P.R.,

3. Numerical Methods and Analysis, McGraw-Hill Gilat, A. and Subramaniam,
4.  V. Numerical Methods for Engineers and Scientists 3rd Edition, Wiley

Homework & Projects

Two sets of problems

Laboratory Work

Computer Use

Program listings and examples will be provided to use with MATLAB etc.

Other Activities

Assessment Criteria

Activities

Quantity

Effects on Grading, %

Attendance

Midterm

1

30

Quiz

Homework

2

20

Term Paper/Project

Laboratory Work

Practices

Tutorial

Seminar

Presentation

Field Study

Final Exam

1

50

TOTAL

100

Effects of Midterm on Grading, %

50

Effects of Final on Grading, %

50

TOTAL

100

ECTS/

WORKLOAD TABLE

Activities

Count

Hours

Total

Workload

Lecture

13

3

39

Midterm

1

12

12

Quiz

Homework

2

12

24

Term Paper/Project

Laboratory Work

Practices

Tutorial

Seminar

Presentation

Field Study

Final Exam

1

15

15

Total Workload

Total Workload/25

90/25

Course ECTS Credits

4

Week

Topics

Course Outcomes

1

 Mathematical Modeling, Engineering Problem Solving,  Programming and Software

I

2

 Approximations, Round-Off Errors,  Truncation Errors and the Taylor Series

I

3

 Bracketing Methods,  Open Methods in root finding

II

4

 Roots of Polynomials

II

5

 Gauss Elimination,  LU Decomposition and Matrix Inversion

III

6

 Special Matrices and Gauss-Seidel

III

7

 One-Dimensional Unconstrained Optimization,  Multidimensional Unconstrained Optimization

IV

8

 Least-Squares Regression,  Interpolation

V

9

 Newton-Cotes Integration Formulas

VI

10

 Numerical Differentiation,  Runge-Kutta Methods

VII

11

 Stiffness and Multistep Methods

VII

12

 Boundary-Value and Eigenvalue Problems

VII

13

 Finite Difference,  Elliptic Equations,  Parabolic Equations

VIII

14

General Overview

-

Program Outcomes

Level of Contribution

1

2

3

a

An ability to apply knowledge of mathematics, science, and engineering

X

b

An  ability to design and conduct experiments, as well as to analyze and interpret data

X

c

An ability to design a system, component or process to meet desired needs

X

d

Ability to function on multi-disciplinary teams

X

e

An ability to identify, formulate, and solve engineering problems

X

f

An understanding of professional and ethical responsibility

X

g

An ability to communicate effectively

h

The broad education necessary to understand the impact of engineering solutions in a global and societal context

X

i

A recognition of the need for, and an ability to engage in life-long learning

X

j

A knowledge of contemporary issues

X

k

An ability to use the techniques, skills and modern engineering tools necessary for engineering practice

X

l

An ability to apply basic knowledge in fluid mechanics, structural mechanics, material properties, and energy/propulsion systems in the context of mechanical engineering design

X

Course

Outcomes

I

II

III

IV

V

VI

VII

VIII

Programme Outcomes

a

X

X

X

X

X

X

X

X

b

X

c

X

X

X

d

X

X

X

e

X

X

X

f

X

X

g

h

X

X

X

X

X

i

X

j

X

X

X

k

X

X

X

X

X

l

X

X

X

X

X

Prepared by

Şengül Ersoy, Ph.D., Lecturer

Date

29.09.2017

Signature