PET 519E-Advanced Engineering Mathematics Midterm Mustafa Onur 16 November 2009 SOLUTIONS Duration of the exam: 2 hours and 30 minutes (14:00-16:30) Important Note: There are total of 5 questions in the exam. A student must attempt to solve all of these 5

PET 519E-Advanced Engineering Mathematics Midterm Mustafa Onur 15 December 2008 Duration of the exam: 3 hours (13:30-16:30) Important Note: There are total of 6 questions in the exam. However, Problems 5 and 6 are only optional questions. A student must a

PET 519E-Advanced Engineering Mathematics Final Exam Mustafa Onur File: pet519e_final_2007_2008_solutions.doc January 16, 2008
Solutions
Duration of the exam: 2 hours. Problem 1. (40 pts) Solve the following initial boundary value problem by using the met

NAME SURNAME Signature
CLASS HW NO Student NO CRN Instructor
PET519E 1 (Due 22/09/2008)
Prof. Mustafa Onur
Attention! Make this page a cover page to your solutions. Given Date: 15/09/2008
^ ^ ^ ^ Question 1: Two displacements are given by d=(2.1m)i+(-1.3m

NAME
M. Onur
CLASS HW NO Student NO CRN Instructor
SURNAME Hw No. Solutions Signature
PET519E 1 (Due 22/09/2008)
Prof. Mustafa Onur
Attention! Make this page a cover page to your solutions. Given Date: 15/09/2008
^ ^ Question 1 (10 points): Two displaceme

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CLASS HW NO Student NO CRN Instructor
PET519E 2
(Due 06/10/2008)
Prof. Mustafa Onur
Attention! Make this page a cover page to your solutions. Given Date: 22/09/2008 Problem 1 (5 points): Compute the vector resulting (r) from the sum

PET 519E-Advanced Engineering Mathematics Midterm Mustafa Onur 21 December 2009 SOLUTIONS Duration of the exam: 3 hours (14:00-17:00)
Problem 1. (40 pts). (a) (10 pts) Find the Laplace transform (LT) of the following function:
f (t ) = te at .
(1.1)
by us

32 Crystallographic Point Groups
Point Groups
The 32 crystallographic point groups (point groups consistent with translational symmetry) can be constructed in one of two ways: 1. From 11 initial pure rotational point groups, inversion centers can be added

MBM 501 STRUCTURE & CRYSTALLOGRAPHY OF MATERIALS Prof. Dr. M. Ltfi VEOLU
COURSE CONTENT
Introduction. Noncrystalline states. Lattices and unit cells. Crystal systems.
Bravais lattices. Coordinates of position in a unit cell. Indices of directions and
plan

MBM 501 STRUCTURE & CRYSTALLOGRAPHY OF MATERIALS Prof. Dr. M. Ltfi VEOLU
Table 8. Space Group P222
1
MBM 501 STRUCTURE & CRYSTALLOGRAPHY OF MATERIALS Prof. Dr. M. Ltfi VEOLU
Table 8. Space Group P222
2
MBM 501 STRUCTURE & CRYSTALLOGRAPHY OF MATERIALS Prof

MBM 501 STRUCTURE & CRYSTALLOGRAPHY OF MATERIALS Prof. Dr. M. Ltfi VEOLU
COURSE CONTENT
Introduction. Noncrystalline states. Lattices and unit cells. Crystal systems. Bravais lattices. Coordinates of position in a unit cell. Indices of directions and plan

MBM 501 STRUCTURE & CRYSTALLOGRAPHY OF MATERIALS Prof. Dr. M. Ltfi VEOLU
In the indexing of crystallographic planes and directions using Miller
indices, several considerations must be taken into account : 1) Planes and their negatives are identical this i

MBM 501 STRUCTURE & CRYSTALLOGRAPHY OF MATERIALS Prof. Dr. M. Ltfi VEOLU In the indexing of crystallographic planes and directions using Miller indices, several considerations must be taken into account : 1) Planes and their negatives are identical this i

Sputter Coating Techniques
Modern Surface Modification Techniques
Sputter Coating Technique
One of the most commonly used coating technique for the deposition of
thin films It is used to produce electronic and bio sensors/devices, MEMS, NEMS, decorative

Chemical Vapor Deposition Techniques
Modern Surface Modification Techniques
A) Horizontal B) Vertical C) Semi-pancake D) Barrel E) Multiple wafer
Generation of active gaseous reactant species Transport of gaseous species into the reaction chamber Gaseous

Assoc. Prof. Krat Kazmanli, PhD
Istanbul Technical University Department of Metalurgical and Materials Engineering
Modern Surface Modification Techniques ITU
"a few outer most atomic layers of a material which interacts with environment."
o Has different

PET 519E ADVANCED ENGINEERING MATHEMATICS FALL 2008 T
Instructor: Prof. Dr. Mustafa Onur. Office Hours: Friday 8:30-12:00. Class Hours: Monday 13:30-16:30 Text Books: There is no offical text for the course. We will cover some chapters from several books.

NAME SURNAME Signature
CLASS HW NO Student NO CRN Instructor
PET519E
10 (Due 08/01/2009)
Prof. Mustafa Onur
Attention! Make this page a cover page to your solutions. Given Date: 29/12/2008
Question 1. Solve the following IBVP by using separation of variab

NAME Mustafa SURNAME Onur Signature SOLUTIONS
CLASS HW NO Student NO CRN Instructor
PET519E
7 (Due 29/12/2008)
Prof. Mustafa Onur
Attention! Make this page a cover page to your solutions. Given Date: 22/12/2008
Question 1 (50 pts). Consider the following

NAME SURNAME Signature
CLASS HW NO Student NO CRN Instructor
PET519E
7 (Due 15/12/2008)
Prof. Mustafa Onur
Attention! Make this page a cover page to your solutions. Given Date: 01/12/2008
Question 1. Find the solution of the following IBVP by using method

MBM 501 STRUCTURE & CRYSTALLOGRAPHY OF MATERIALS Prof. Dr. M. Ltfi VEOLU
Symmetry
Both Bravais lattices and real crystals exhibit symmetry. A structure is said to be symmetrical when its components are arranged in such a way that certain operations can be

MBM 501 STRUCTURE & CRYSTALLOGRAPHY OF MATERIALS Prof. Dr. M. Ltfi VEOLU
Symmetry
Both Bravais lattices and real crystals exhibit symmetry. A structure is said to be symmetrical when its components are arranged in such a way that certain operations can be

MBM 501 STRUCTURE & CRYSTALLOGRAPHY OF MATERIALS
Prof. Dr. M. Ltfi VEOLU
SILICATES
The silicates are the largest, the most interesting and the most complicated class of minerals than any other minerals. Approximately 30% of all minerals are silicates and

MBM 501 STRUCTURE & CRYSTALLOGRAPHY OF MATERIALS
Prof. Dr. M. Ltfi VEOLU
Fluorite (CaF2) structure
CaF2 is a representative of many important ceramic structures, as seen in
Fig. 2.15. This is built on an f. c. c. Bravais lattice with three ions (one
Ca2+

MBM 501 STRUCTURE & CRYSTALLOGRAPHY OF MATERIALS Prof. Dr. M. Ltfi VEOLU
Compounds of the type AX The positions of the octahedral interstices are seen in the NiAs structure (Strukturbericht B8), Fig. 2.7 in which they are occupied by Ni atoms while the me

MBM 501 STRUCTURE & CRYSTALLOGRAPHY OF MATERIALS
Prof. Dr. M. Ltfi VEOLU
Compounds of the type AX
The positions of the octahedral interstices are seen in the NiAs structure
(Strukturbericht B8), Fig. 2.7 in which they are occupied by Ni atoms while the me

MBM 501 STRUCTURE & CRYSTALLOGRAPHY OF MATERIALS Prof. Dr. M. Ltfi VEOLU
Crystals may be classified according to types of atomic binding forces (atomic bonds) as follows : 1. Metallic crystals : consist of positive ions immersed in gas of negative electro

MBM 501 STRUCTURE & CRYSTALLOGRAPHY OF MATERIALS
Prof. Dr. M. Ltfi VEOLU
Crystals may be classified according to types of atomic binding forces (atomic bonds) as follows : 1. Metallic crystals : consist of positive ions immersed in gas of negative electro