COURSE INTRODUCTION AND APPLICATION INFORMATION


Course Name
Introduction to Differential Equations II
Code
Semester
Theory
(hour/week)
Application/Lab
(hour/week)
Local Credits
ECTS
MATH 208
Spring
2
2
3
6
Prerequisites
 MATH 207To attend the classes (To enrol for the course and get a grade other than NA or W)
Course Language
English
Course Type
Required
Course Level
First Cycle
Mode of Delivery -
Teaching Methods and Techniques of the Course
Course Coordinator -
Course Lecturer(s)
Assistant(s) -
Course Objectives This course aims to consider partial differential equations which are a type of differential equation that is, a relation involving an unknown function (or functions) of several independent variables and its (or their) partial derivatives with respect to those variables. Partial differential equations are used to formulate, and thus aid the solution of problems involving functions of several variables; such as the propagation of sound or heat, electrostatics, electrodynamics, fluid flow, and elasticity. Seemingly distinct physical phenomena may have identical mathematical formulations, and thus be governed by the same underlying dynamic. In this course how to model these physical phenomena and the solution methods for these models will be taught.
Learning Outcomes The students who succeeded in this course;
  • will be able to convert partial differential equations into canonical form
  • will be able to anaylze solution by method of separation of variables.
  • will be able to analyze Fourier Series for 2pi periodic functions
  • will be able to anaylze the heat equation, wave equation and their solution by method of seperation of variables.
  • will be able to anaylze the Laplace’s equation in rectangular coordinates and its solution.
  • will be able to anaylze Bessel’s Equation and Bessel’s Function. Solution of Bessel’s Equation. Legendre’s Differential Equation. Legendre Polynomials and Legendre Series Expansions.
  • will be able to analyze the Laplace’s equation in polar and spherical coordinates and their solutions.
Course Description In this course basic concepts and classification of partial differential equations will be discussed.The heat, wave and Laplace equation will be given and the solution methods will be taught.

 



Course Category

Core Courses
X
Major Area Courses
Supportive Courses
Media and Managment Skills Courses
Transferable Skill Courses

 

WEEKLY SUBJECTS AND RELATED PREPARATION STUDIES

Week Subjects Required Materials
1 Differential equations with two independent variables. Classification of partial differential equations of the second order. Canonical forms of linear equations with constant coefficients. “Equations of Mathematical Physics” by A.N. Tikhonov, A.A. Samarskii, Dover. Section 1.1, 1.2, 1.3.
2 A Model for Heat Flow. Solution by method of separation of variables. “Fundamentals of Differential Equations and Boundary Value Problems” by Nagle, Saff, Snider, 6th Edition, Pearson. Section 10.1, 10.2.
3 Fourier Series for 2pi periodic functions. Convergence of Fourier Series. Pointwise convergence of Fourier Series. Differentiation and Integration of Fourier Series. “Fundamentals of Differential Equations and Boundary Value Problems” by Nagle, Saff, Snider, 6th Edition, Pearson. Section 10.3.
4 Fourier Cosine and Sine Series. “Fundamentals of Differential Equations and Boundary Value Problems” by Nagle, Saff, Snider, 6th Edition, Pearson. Section 10.4.
5 Heat Equation. Solution by separation of variables. Existence and Uniqueness of Solutions. “Fundamentals of Differential Equations and Boundary Value Problems” by Nagle, Saff, Snider, 6th Edition, Pearson. Section 10.5.
6 The wave equation. Solution by seperation of variables. Existence and Uniqueness of Solutions. “Fundamentals of Differential Equations and Boundary Value Problems” by Nagle, Saff, Snider, 6th Edition, Pearson. Section 10.6.
7 The Laplace's equation in rectangular coordinates. Solution by separation of variables. Existence and Uniqueness of Solutions. “Fundamentals of Differential Equations and Boundary Value Problems” by Nagle, Saff, Snider, 6th Edition, Pearson. Section 10.7.
8 Bessel’s Equation and Bessel’s Function. “Partial Differential Equations with Fourier Series and Boundary Value Problems”by Nakhle H. Asmar, Pearson International Edition. Section 4.7.
9 Solution of Bessel’s Equation “Partial Differential Equations with Fourier Series and Boundary Value Problems”by Nakhle H. Asmar, Pearson International Edition. Section 4.8.
10 Laplace’s equation in polar coordinates and its solution by the method of separation of variables. “Fundamentals of Differential Equations and Boundary Value Problems” by Nagle, Saff, Snider, 6th Edition, Pearson. Section 10.7.
11 Legendre’s Differential Equation. “Partial Differential Equations with Fourier Series and Boundary Value Problems”by Nakhle H. Asmar, Pearson International Edition. Section 5.5.
12 Legendre Polynomials and Legendre Series Expansions. “Partial Differential Equations with Fourier Series and Boundary Value Problems”by Nakhle H. Asmar, Pearson International Edition. Section 5.6.
13 Associated Legendre Functions and Series Expansions. “Partial Differential Equations with Fourier Series and Boundary Value Problems”by Nakhle H. Asmar, Pearson International Edition. Section 5.7.
14 Sturm-Liouville Theory “Partial Differential Equations with Fourier Series and Boundary Value Problems”by Nakhle H. Asmar, Pearson International Edition. Section 6.1, 6.2.
15 Review for Final Exam “Fundamentals of Differential Equations and Boundary Value Problems” by Nagle, Saff, Snider, 6th Edition, Pearson. “Partial Differential Equations with Fourier Series and Boundary Value Problems”by Nakhle H. Asmar, Pearson International Edition.
16 Review of the Semester “Fundamentals of Differential Equations and Boundary Value Problems” by Nagle, Saff, Snider, 6th Edition, Pearson. “Partial Differential Equations with Fourier Series and Boundary Value Problems”by Nakhle H. Asmar, Pearson International Edition.
Course Notes/Textbooks “Fundamentals of Differential Equations and Boundary Value Problems” by Nagle, Saff, Snider, 6th Edition, Pearson. “Partial Differential Equations with Fourier Series and Boundary Value Problems”by Nakhle H. Asmar, Pearson International Edition.
Suggested Readings/Materials None

 

EVALUATION SYSTEM

Semester Activities Number Weigthing
Participation
Laboratory / Application
Field Work
Quizzes / Studio Critiques
Portfolio
Homework / Assignments
Presentation / Jury
Project
Seminar / Workshop
Oral Exam
Midterm
2
60
Final Exam
1
40
Total

Weighting of Semester Activities on the Final Grade
2
60
Weighting of End-of-Semester Activities on the Final Grade
1
40
Total

ECTS / WORKLOAD TABLE

Semester Activities Number Duration (Hours) Workload
Course Hours
(Including exam week: 16 x total hours)
16
4
64
Laboratory / Application Hours
(Including exam week: 16 x total hours)
16
Study Hours Out of Class
15
3
Field Work
Quizzes / Studio Critiques
Portfolio
Homework / Assignments
Presentation / Jury
Project
Seminar / Workshop
Oral Exam
Midterms
2
15
Final Exams
1
26
    Total
165

 

COURSE LEARNING OUTCOMES AND PROGRAM QUALIFICATIONS RELATIONSHIP

#
Program Competencies/Outcomes
* Contribution Level
1
2
3
4
5
1 To have a grasp of basic mathematics, applied mathematics and theories and applications of statistics. X
2 To be able to use theoretical and applied knowledge acquired in the advanced fields of mathematics and statistics, X
3 To be able to define and analyze problems and to find solutions based on scientific methods, X
4 To be able to apply mathematics and statistics in real life with interdisciplinary approach and to discover their potentials, X
5 To be able to acquire necessary information and to make modeling in any field that mathematics is used and to improve herself/himself, X
6 To be able to criticize and renew her/his own models and solutions, X
7 To be able to tell theoretical and technical information easily to both experts in detail and nonexperts in basic and comprehensible way, X
8

To be able to use international resources in English and in a second foreign language from the European Language Portfolio (at the level of B1) effectively and to keep knowledge up-to-date, to communicate comfortably with colleagues from Turkey and other countries, to follow periodic literature,

X
9

To be familiar with computer programs used in the fields of mathematics and statistics and to be able to use at least one of them effectively at the European Computer Driving Licence Advanced Level,

10

To be able to behave in accordance with social, scientific and ethical values in each step of the projects involved and to be able to introduce and apply projects in terms of civic engagement,

X
11 To be able to evaluate all processes effectively and to have enough awareness about quality management by being conscious and having intellectual background in the universal sense,
12

By having a way of abstract thinking, to be able to connect concrete events and to transfer solutions, to be able to design experiments, collect data, and analyze results by scientific methods and to interfere,

X
13

To be able to continue lifelong learning by renewing the knowledge, the abilities and the compentencies which have been developed during the program, and being conscious about lifelong learning,

14

To be able to adapt and transfer the knowledge gained in the areas of mathematics and statistics to the level of secondary school,

15

To be able to conduct a research either as an individual or as a team member, and to be effective in each related step of the project, to take role in the decision process, to plan and manage the project by using time effectively.

*1 Lowest, 2 Low, 3 Average, 4 High, 5 Highest

 

İzmir Ekonomi Üniversitesi | Sakarya Caddesi No:156, 35330 Balçova - İZMİR Tel: +90 232 279 25 25 | webmaster@ieu.edu.tr | YBS 2010