Course Name : Applied Engineering Mathematics

Degree:  Bachelor

Code

Year/Semester

Local Credits

ECTS Credits

Course Implementation, Hours/Week

Course

Tutorial

Laboratory

ENG225

2/2 (Fall-Spring)

3,5

5

3

1

-

Department

Naval Architecture and  Marine 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

 ENG215

Course Category by Content, %

Basic Sciences

Engineering Science

Engineering Design

Humanities

50

50

-

-

Course Description

Vector differential Calculus. Grad, div, curl. Vector integral Calculus. Integral theorems. System of ODEs. Series solutions of ODEs. Special functions. Fourier analysis. Partial differential equations.

Course Objectives

To give an ability to apply knowledge of mathematics on engineering problems, especially how to study and solve differential equations, which model physical systems varying in space and/or time.

Course Learning Outcomes

Upon successful completion of the course students should be able to:

1. apply the knowledge of the vector calculus in solving engineering problems
2. solve  a linear   system by using elimination or operator or Laplace transform methods
3. solve linear differential equations using power series methods
4. knows the relations between the special functions and applications of special functions in engineering
5. find Fourier series expansions of periodic functions
6. 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
7. apply the knowledge of ordinary and partial differential equations in solving engineering problems

Instructional Methods and Techniques

Books, lecture and  problem solving

Tutorial Place

Classroom

Co-term Condition

Textbook

Advanced Engineering Mathematics, Erwin Kreyszig, John Wiley&Sons, 10th Edition, 2014.

Other References

1. Advanced Enginering Mathematics, 7th Edition, Cengage, Peter O’Neil,  2011.
2. Fundamentals of Differential Equations, 8th Edition, Addison Wesley, K. Nagle, A. B. Saff, E. D. Snider, 2011.
3. Thomas’ Calculus, 12th Edition, Pearson, Global Edition, George B. Thomas, Jr., Maurice D. Weir, Joel Hass.

Homework & Projects

Homework assignments based on lectures will be given regularly and quizzes  will be held.

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

3

39

Midterm

1

16

16

Quiz

5

3

15

Homework

3

5

15

Term Paper/Project

Laboratory Work

Practices

Tutorial

13

1

13

Seminar

Presentation

Field Study

Final Exam

1

24

24

Total Workload

122

Total Workload/25

122/25

Course ECTS Credits

5

Week

Topics

Course Outcomes

1

Vectors in 2-Space and 3-Space. Inner product. Vector Product. Vector and Scalar Functions and Their Fields. Vector Calculus: Derivatives. Curves. Arc Length. Curvature. Torsion.

I

2

Gradient of a Scalar Field. Directional Derivative. Divergence of a Vector Field. Curl of a Vector Field.

I

3

Line Integrals. Green’s Theorem in the Plane. Surface Integrals.

I

4

Triple Integrals. Divergence Theorem and its Applications. Stokes’s Theorem.                           

I

5

Basic Theory of System of ODEs. Wronskian. Constant-Coefficient Systems. Phase Plane Method. Criteria for Critical Points. Stability.

II

6

Differential  Operators and the Elimination Method for Systems.Solving Linear Systems with Laplace Transforms.  Nonhomogeneous Linear Systems of ODEs.         

II

7

Power Series Method. Legendre’s Equation. Legendre Polynomials  .

III-IV

8

Frobenius Method. Bessel’s Equation. Bessel Functions of the first kind, . Bessel Functions of the second kind, .                                                                             MIDTERM                                                                          

III-IV

9

Fourier Series. Even and Odd Functions. Half-Range Expansions. Sturm-Liouville Problems. Orthogonal Functions and Series. Generalized Fourier Series. Fourier Integral. Fourier Cosine and Sine Transforms. Fourier Transform.

V

10

Basic Consepts of PDEs. Wave equation: Solution of the Wave Equation, Characteristics. Solution by Separating Variables. Use of Fourier Series. Heat Equation: Solution by Fourier Series. Solution by Fourier Integrals and Transforms.     

V-VI

11

Rectangular Membrane, Two Dimensional Wave Equation.  Double Fourier Series.

V-VII

12

Laplacian in Polar Coordinates. Circular Membrane. Fourier-Bessel Series. Laplace’s Equation in Cylindrical and Spherical Coordinates.

V-VII

13

Solution of PDEs by Laplace Transforms.                                              

VI-VII

14

Review

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 engineering knowledge in fluid mechanics, structural mechanics, material selection and energy/propulsion systems in the context of marine vehicles and offshore structures.

X

Course

Outcomes

I

II

III

IV

V

VI

VII

Programme Outcomes

a

X

X

X

X

X

X

X

b

X

X

X

c

X

X

d

X

X

e

X

X

X

X

X

f

g

h

X

X

X

i

X

X

X

j

X

X

X

k

X

X

X

X

X

X

l

X

X

X

X

X

X

X

Prepared by

Şengül Ersoy, Ph.D., Lecturer

Date

February, 2018

Signature