MATH 207 | Course Introduction and Application Information

Course Name
Introduction to Differential Equations I
Code
Semester
Theory
(hour/week)
Application/Lab
(hour/week)
Local Credits
ECTS
MATH 207
Fall
2
2
3
5

Prerequisites
None
Course Language
English
Course Type
Required
Course Level
First Cycle
Course Coordinator -
Course Lecturer(s)
Assistant(s)
Course Objectives This course is an introduction to the basic concepts, theory, methods and applications of ordinary differential equations. The aim of this course is to solve differential equations and to
develop the basics of modeling of real life problems.
Learning Outcomes The students who succeeded in this course;
  • will be able to classify the differential equations.
  • will be able to use solution methods of first order ordinary differential equations.
  • will be able to solve higher order linear differential equations with constant coefficients.
  • will be able to understand the Laplace transform method of linear differential equations.
  • will be able to analyze series solutions of linear differential equations.
  • will be able to solve systems of linear differential equations.
  • will be able to analyze approximate methods of solving first-order equations by using the method of succesive approximations and the Euler method.
Course Content In this course basic concepts of differential equations will be discussed.The types of first order ordinary differential equations will be given and the solution methods will be taught. Also, solution methods for higherorder ordinary differential equations will be analyzed.

 



Course Category

Core Courses
Major Area Courses
Supportive Courses
Media and Management Skills Courses
Transferable Skill Courses

 

WEEKLY SUBJECTS AND RELATED PREPARATION STUDIES

Week Subjects Related Preparation
1 Classification of differential equations. Exact Differential Equations. Non- Exact Differential Equations. Fundamentals of Differential Equations and Boundary Value Problems, 6th Edition by Nagle, Saff and Snider, Pearson, Addison-Wesley,Section 1.1, 2.4, 2.5.
2 Separable Differential Equations, Homogeneous Differential Equations. First - Order Linear Differential Equations. Fundamentals of Differential Equations and Boundary Value Problems, 6th Edition by Nagle, Saff and Snider, Pearson, Addison-Wesley,Section 2.2, 2.3, 2.6.
3 Bernoulli Differential Equations. Substitutions and Transformations. Equations with Linear Coefficients. Introduction to Ordinary Differential Equations by Shepley L. Ross. Fourth Edition, John Wiley and Sons, Section 2.3, 2.4.
4 Theory of Higher Order Linear Differential Equations, Linear Dependence and Independence, Representation of Solutions for Homogeneous and Nonhomogeneous Case. Fundamentals of Differential Equations and Boundary Value Problems, 6th Edition by Nagle, Saff and Snider, Pearson, Addison-Wesley,Section 6.1.
5 Reduction of Order. Homogeneous Linear Equations with Constant Coefficients. Midterm Exam 1. Introduction to Ordinary Differential Equations by Shepley L. Ross. Fourth Edition, John Wiley and Sons, Section 4.2. Fundamentals of Differential Equations and Boundary Value Problems, 6th Edition by Nagle, Saff and Snider, Pearson, Addison-Wesley,Section 4.2,4.3
6 Solution of Non-homogeneous Differential Equations: Method of Undetermined Coefficients, Method of Variation of Parameters. Fundamentals of Differential Equations and Boundary Value Problems, 6th Edition by Nagle, Saff and Snider, Pearson, Addison-Wesley,Section 4.4, 4.6,4.7.
7 Cauchy Euler Differential Equations. Laplace Transforms: Definition of the Laplace Transform, Properties of the Laplace Transform Fundamentals of Differential Equations and Boundary Value Problems, 6th Edition by Nagle, Saff and Snider, Pearson, Addison-Wesley,Section 8.5, 7.2, 7.3.
8 Inverse Laplace Transforms. Solving Initial Value Problems by Laplace Transforms. Fundamentals of Differential Equations and Boundary Value Problems, 6th Edition by Nagle, Saff and Snider, Pearson, Addison-Wesley,Section 7.4, 7.5.
9 Series Solutions of Differential Equations. Power Series Solutions: Series Solutions around an Ordinary Point. Introduction to Ordinary Differential Equations by Shepley L. Ross. Fourth Edition, John Wiley and Sons, Section 6.1.
10 Series Solutions around a Singular Point. Method of Frobenius. Midterm Exam 2. Introduction to Ordinary Differential Equations by Shepley L. Ross. Fourth Edition, John Wiley and Sons, Section 6.2.
11 Systems of Linear Differential Equations: Differential Operators and an Operator Method. Introduction to Ordinary Differential Equations by Shepley L. Ross. Fourth Edition, John Wiley and Sons, Section 7.1.
12 Basic Theory of Linear Systems in Normal Form: Two Equations in Two Unknown Functions. Homogeneous Linear Systems with Constant Coefficients: Two Equations in Two Unknown Functions. Introduction to Ordinary Differential Equations by Shepley L. Ross. 4th Edit., John Wiley and Sons, Sect. 7.3,7.4.
13 The Matrix Method for Homogeneous Linear Systems with Constant Coefficients: Two Equations in Two Unknown Functions, n Equations in n Unknown Functions. Introduction to Ordinary Differential Equations by Shepley L. Ross. 4th Edition, John Wiley and Sons, Sect. 7.6, 7.7.
14 Approximate methods of solving first-order equations: The method of successive approximations. The Euler method. The improved Euler method. Introduction to Ordinary Differential Equations by Shepley L. Ross. 4th Edition, John Wiley and Sons, Sect. 8.3, 8.4, 8.5.
15 Review of the semester.
16 Final Exam

 

Course Textbooks Fundamentals of Differential Equations and Boundary Value Problems, 6th Edition by Nagle, Saff and Snider, Pearson, Addison-Wesley,Section , Introduction to Ordinary Differential Equations" by Shepley L. Ross. Fourth Edition, John Wiley and Sons.
References None

 

EVALUATION SYSTEM

Semester Requirements Number Percentage
Participation
Laboratory / Application
Field Work
Quizzes / Studio Critiques
Homework / Assignments
Presentation / Jury
Project
Seminar / Workshop
Portfolios
Midterms / Oral Exams
2
60
Final / Oral Exam
1
40
Total

Contribution of Semester Work to Final Grade
2
60
Contribution of Final Work to Final Grade
1
40
Total

ECTS / WORKLOAD TABLE

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
16
1
Field Work
Quizzes / Studio Critiques
Homework / Assignments
Presentation / Jury
Project
Seminar / Workshop
Portfolios
Midterms / Oral Exams
2
10
Final / Oral Exam
1
30
    Total
130

 

COURSE LEARNING OUTCOMES AND PROGRAM QUALIFICATIONS RELATIONSHIP

#
Program Qualifications / Outcomes
* Level of Contribution
1
2
3
4
5
1 Adequate knowledge in Mathematics, Science and Civil Engineering; ability to use theoretical and applied information in these areas to model and solve Civil Engineering problems
2 Ability to identify, define, formulate, and solve complex Civil Engineering problems; ability to select and apply proper analysis and modeling methods for this purpose
3 Ability to design a complex system, device or product under realistic constraints and conditions, in such a way as to meet the desired result; ability to apply modern design methods for this purpose
4 Ability to devise, select, and use modern techniques and tools needed for Civil Engineering practice
5 Ability to design and conduct experiments, gather data, analyze and interpret results for investigating Civil Engineering problems
6 Ability to work efficiently in Civil Engineering disciplinary and multi-disciplinary teams; ability to work individually
7 Ability to communicate effectively in Turkish, both orally and in writing; knowledge of a minimum of two foreign languages
8 Recognition of the need for lifelong learning; ability to access information, to follow developments in science and technology, and to continue to educate him/herself
9 Awareness of professional and ethical responsibility
10 Information about business life practices such as project management, risk management, and change management; awareness of entrepreneurship, innovation, and sustainable development
11 Knowledge about contemporary issues and the global and societal effects of engineering practices on health, environment, and safety; awareness of the legal consequences of Civil Engineering solutions

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