
ISTANBUL TECHNICAL UNIVERSITY DEPARTMENT OF MECHANICAL ENGINEERING

ANNOUNCEMENTS:

Instructor : Assistant Prof. Dr. Erdinç Altuğ
Phone & Email : (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
Ordinary Differential Equations (ODEs): FirstOrder Differential Equations, SecondOrder Linear Differential Equations, HigherOrder 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, SturmLiouville 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, 9^{th} 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” AddisonWesley Publishing Company England, 1993.
4. Dennis G. Z.ll, Michael R. Cullen, “Advanced Engineering Mathematics” PWSKENT 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 SecondOrder Linear Differential Equations 
Chapter 1 & 2 
3 
October 6 
ODEs, HigherOrder 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 Exam1 (9:0011:00) 
 
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 710 
11 
December 1 
Fourier Analysis 
Chapter 11 
12 
December 8 
Fourier Analysis 
Chapter 11 
12 
December 8 
Midterm Exam2 (18:0020:00) 
 
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:
Homeworks 
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]