Issue date: 01.10.2019

Revision date:01.10.2019

Revision No:00

DF Board Decision No: -

Course Name: Differential Equations

Degree: Undergraduate

Code

Year/Semester

Local Credits

ECTS Credits

Course Implementation, Hours/Week

Course

Tutorial

Laboratory

MATH 221Y

2/4

3,5

4

3

1

-

Department

Maritime Transportation and Management Engineering

Instructors

Contact Information

Office Hours

Web page

www.pirireis.edu.tr

Course Type

 Compulsory

Course Language

English

Course Prerequisites

MATH 121

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

---

Laboratory Work

---

Computer Use

---

Other Activities

---

Assessment Criteria

Activities

Quantity

Effects on Grading, %

Attendance

Midterm

1

40

Quiz

5

10

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

14

4

56

Midterm

1

8

8

Quiz

5

3

15

Homework

3

4

12

Term Paper/Project

Laboratory Work

Practices

Tutorial

Seminar

Presentation

Field Study

Final Exam

1

12

12

Total Workload

103

Total Workload/25

103/25

Course ECTS Credits

4

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,

VI

8

Solutions About Ordinary Points , Solutions About Singular Points

9

Midterm

VI

10

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

VI

11

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

VI

12

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

VII

13

Orhogonal Functions,  Fourier Series, Fourier Sine and Cosine Series

VIII

14

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

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 legal, societal and environmental knowledge in maritime transport and in all respective modes of transport operations.

X

m

An ability to interpret and analysis of the data regarding maritime management and operations, recognition and solution of problems for decision making process.

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

c

X

X

d

e

X

X

X

X

X

X

f

g

h

X

X

i

X

j

X

k

X

l

X

m

X