Course Name : Ordinary and Partial Differential Equations

Degree:  Bachelor

Code

Year/Semester

Local Credits

ECTS Credits

Course Implementation, Hours/Week

Course

Tutorial

Laboratory

ENG215

2/1 (Fall-Spring)

4

5

4

-

-

Department

Mechanical Engineering

Instructors

Şengül Ersoy, Ph.D., Lecturer

Contact Information

Piri Reis University, Faculty of Economics and Administrative Sciences

Phone: +90 216 581 00 50

Ext:1737

E-mail: sersoy@pirireis.edu.tr

Office Hours

Monday:  13:00-15:00

Web page

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

Course Type

 Compulsory

Course Language

English

Course Prerequisites

 MATH122

Course Category by Content, %

Basic Sciences

Engineering Science

Engineering Design

Humanities

90

10

Course Description

First Order Differential Equations, Second Order Linear Equations, Higher Order Linear Equations, Series Solutions of  Linear Equations, The Laplace Transform, Systems of First Order Linear Equations, Introduction to Partial Differential Equations

Course Objectives

1. introduce the basic concepts of differential equations

2. present methods to solve differential equations of various types

3. acquire skills to apply the knowledge of differential equations to engineering  problems

Course Learning Outcomes

Upon succesful completion of the course students are expected to

1. classify differential equations by order, linearity, and homogeneity
2. know the menings of an implicit,  explicit, singular,  particular  and general solutions of  a differential equation
3. verify that  a given function is a solution of  a differential equation
4. use appropriate method for solutions of first, second and higher order differential equations
5. solve a nonhomegeneous linear differential equation with constant coefficients by using annihilators or undetermined coefficients ,or variation or parameters
6. solve linear differential equations using power series and Laplace transform methods
7. solve  a  system of first order linear equations by using elimination or Laplace transform methods
8. find Fourier series expansions of periodic functions
9. know what a partial differential equation is and solve initial-boundary value  problems given for the heat, wave and Laplace equations by the method of separation of variables technique
10. apply the knowledge of ordinary and partial differential equations in solving engineering problems

Instructional Methods and Techniques

Lecture, problem solving

Tutorial Place

Co-term Condition

Textbook

Differential Equations with Boundary Value Problems, Dennis G. Zill, Michael R. Cullen,  7th Edition,  Brooks Cole Publishing Company, 2009

Other References

1. Elementary Differential Equations and Boundary Value Problems, 7th Edition, John Wiley and Sons Inc., W. E. Boyce, R. C. DiPrima, 2010.
2. Fundamentals of Differential Equations, 8th Edition,  Addison Wesley, K. Nagle, A. B. Saff, E. D. Snider, 2011

Homework & Projects

At least 5 quizzes and homeworks.

Laboratory Work

Computer Use

Other Activities

Assessment Criteria

Activities

Quantity

Effects on Grading, %

Attendance

Midterm

1

30

Quiz

5

20

Homework

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

4

52

Midterm

1

10

10

Quiz

5

3

15

Homework

3

8

24

Term Paper/Project

Laboratory Work

Practices

Tutorial

Seminar

Presentation

Field Study

Final Exam

1

15

15

Total Workload

115

Total Workload/25

115/25

Course ECTS Credits

5

Week

Topics

Course Outcomes

1

Definitions and Terminology, Initial-Value Problems , Differential Equations as Mathematical Models

I-II-III

2

Separable Variables, Exact Equations, Linear Equations,  Solutions by Substitutions

IV

3

 Linear Equations,  Nonlinear Equations

I-IV

4

Preliminary Theory: Linear Equations, Initial-Value and Boundary-Value Problems, Homogeneous Equations, Nonhomogeneous Equations

III-IV

5

Reduction of Order, Homogeneous Linear Equations with Constant Coefficients, Undetermined Coefficients - Superposition Approach

IV-V

6

Undetermined Coefficients-Annihilator Approach,Variation of Parameters

V

7

Cauchy-Euler Equation,  Review of Power Series; Power Series Solutions

Midterm

VI

8

Solutions About Ordinary Points , Solutions About Singular Points

VI

9

Definition of the Laplace Transform, Inverse Transform,Translation Theorems and Derivatives of a Transform

VI

10

Transforms of Derivatives, Integrals, and Periodic Functions, Applications, Dirac Delta Function

VI

11

Preliminary Theory, Homogeneous Linear Systems with Constant Coefficients, Distinct Real Eigenvalues, Repeated Eigenvalues, Complex Eigenvalues,Variation of Parameters, Matrix Exponential

VII

12

Orhogonal Functions,  Fourier Series, Fourier Sine and Cosine Series

VIII

13

Separable Partial Differential Equations, Classical Equations and  Boundary-Value Problems, Heat Equation

IX-X

14

Wave Equation, Laplace's Equation,  Nonhomogeneous Equations and Boundary Conditions

IX-X

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

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

IX

X

Programme Outcomes

a

X

X

X

X

X

X

X

X

X

X

b

X

X

X

c

X

X

d

X

e

X

X

X

X

X

X

f

g

h

X

X

i

X

j

X

k

X

X

X

X

X

X

X

l

X

X

X

X

X

X

X

Prepared by

Şengül Ersoy, Ph.D., Lecturer

Date

September, 2017

Signature