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ISTANBUL TECHNICAL UNIVERSITY

DEPARTMENT OF MECHANICAL ENGINEERING

 

 

ENGINEERING MATHEMATICS - MAK 501E – CRN 14246

2011-2012 Fall

 

 

ANNOUNCEMENTS:

  • Attendance will be strictly controlled in this class. If you will not able to attend 70% of the courses, take the course from other available section.

 

Instructor             : Assistant Prof. Dr. Erdinç Altuğ

Phone & E-mail   : (0212) 293 13 00 / 2838  &  altuger@itu.edu.tr

Lecture hours      : To be Announced

Office                    : Room 442

Office hours         : After class or by appointment only

Prerequisites        : Undergraduate mathematics

 

Course Description :

Ordinary Differential Equations (ODEs): First-Order Differential Equations, Second-Order Linear Differential Equations, Higher-Order Linear Differential Equations, Method of Undetermined Coefficients, Method of Variation of Parameters, Series Solutions of Differential Equations (SSDEs). Special Functions; Legendre's Equations, Bessel's Equation, Sturm-Liouville Problems, Orthogonality, Eigenfunction Expansions, Laplace Transforms and Applications. Linear Algebra: Matrices, Vectors, Determinants, Linear Systems of Equations, Gauss Elimination, Eigenvalues, Eigenvectors, Grad, Div, Curl. Fourier Analysis: Series, Integrals, and Transforms. Partial Differential Equations.

 

Textbook :

Erwin Kreyszig, "Advanced Engineering Mathematics" Wiley International Edition, 9th Edition, 2006.

You may obtain a copy from pandora, bıçaklar or from bestbookbuys

 

Other References :

1.      Peter V. O’Neil, “Advanced Engineering Mathematics” Thomson Brooks/Cole, Australia, 2003.

2.      Bird J.O., May A.J.C., “Engineering Mathematics” Newnes, Oxford, 1992.

3.      Glyn James, “Advanced Modern Engineering Mathematics” Addison-Wesley Publishing Company England, 1993.

4.      Dennis G. Z.ll, Michael R. Cullen, “Advanced Engineering Mathematics” PWS-KENT Publishing Company, Boston, 1992.

5.      Stephenson G. And Radmore, P.M. “Advanced Mathematical Methods for Physics, Cambridge University Press, Cambridge, 1990.

6.      Dr. Hasan Güneş’s course notes which are available at photocopy center.

 

Objectives :

·  Provide graduate students with the advanced analytical methods that will be bases for their

research areas.

·  Use these analytical methods to obtain the closed form solutions of some of the basic

engineering problems.

 

Outcomes :

1. A sound understanding of the matrices and ability solve system of various algebraic equations.

2. A sound understanding of the important special functions and their use in the solution of

engineering problems.

3. Ability to solve nonlinear ODEs via series solution methods.

4. Ability to employ the separation of variables to solve partial differential equations.

5. Ability to select and use an appropriate integral transform technique to solve partial differential equations.

 

 

COURSE PLAN

 

Week

Date

Topics

Book Chapter

1

September 22

Introduction

Chapter 1

2

September 29

ODEs, First and Second-Order Linear Differential Equations

Chapter 1 & 2

3

October 6

ODEs, Higher-Order Linear Differential Equations

Chapter 3 and 4

4

October 13

SSDEs, Special Functions

Chapter 5

5

October 20

SSDEs, Special Functions

Chapter 5

6

October 27

Midterm Exam-1 (9:00-11:00)

-

7

November 3

Laplace Transforms and Applications

Chapter 6

8

November 10

Holiday     

-

9

November 17

Laplace Transforms and Applications

Chapter 6

10

November 24

Linear Algebra

Chapter 7-10

11

December 1

Fourier Analysis

Chapter 11

12

December 8

Fourier Analysis

Chapter 11

12

December 8

Midterm Exam-2 (18:00-20:00)

-

13

December 15

Partial Differential Equations

Chapter 12

14

December 22

Partial Differential Equations

Chapter 12

15

December 29

Partial Differential Equations

Chapter 12

 

Homeworks and Solutions:

 

 

 

Other Handouts:

 

You need this formula sheet in Final exam: Exam Sheet

 

 

Assessment Criteria :

 

 

Quantity

Total Percentage %

Midterm Exams

2

40

Homeworks or Quizzes

5

20

Final Exam

1

40

 

 

Notes:

·         Students are strongly discouraged from doing their homework assignments solely in a group framework. Homework which displays evidence of verbatim copying will receive zero credit regardless of the source of the solution.

·         In order to take the final exam you should attend at least 70% of the lectures.

 

 

[Last updated on Monday, September 05, 2011]