Differential Equations (MATH 276) Course Details

Transcription

1 Differential Equations (MATH 276) Course Details Course Name Course Code Term Lecture Hours Application Hours Lab Credit ECTS Hours Differential Equations MATH 276 Spring Pre-requisite Course(s) Math 152 (Calculus II) or Math158 (Extended Calculus II) Course Language Course Type Course Level Mode of Delivery Learning and Teaching Strategies English Service Courses Taken From Other Departments Bachelor Face to Face Lecture, Question and Answer Course Coordinator Course Lecturer(s)

2 Course Assistants Course Objectives Course Learning Outcomes Course Content The course is specifically designed for engineering students as this material is applicable to many fields. The purpose of this course is to provide an understanding of ordinary differential equations (ODE's), systems of ODE s and to give methods for solving them. This course provides also a preliminary information about partial differential equations (PDE's). The students who succeeded in this course; be able to determine the existence and uniqueness of a solution and select the appropriate method for finding the solution. use appropriate methods for solution of first, second and higher order ODE s. solve differential equations using power series and Laplace transform methods. solve linear systems of ODE s by using elimination and Laplace transform methods. find Fourier series expansions of periodic functions. solve some elementary PDE s such as heat, wave and Laplace equations by the method of separation of variables technique. First Order, Higher Order Linear Ordinary Differential Equations, Series Solutions of Differential Equations, Laplace Transforms, Linear Systems of Ordinary Differential Equations, Fourier Analysis and Partial Differential Equations. Weekly Subjects and Releated Preparation Studies Week Subjects Preparation

3 1 First Order Ordinary Differential Equations: Preliminaries, pp Solutions, Existence-Uniqueness Theorem, Separable Equations, Linear Equations. 3 Bernoulli Equations, Homogeneous Equations, Exact Equations and Integrating Factors. 4 Substitutions, Higher Order Linear Ordinary Differential Equations: Basic Theory of Higher Order Linear Equations 5 Reduction of Order Method, Homogeneous Constant Coefficient Equations 6 Undetermined Coefficients Method, Variation of Parameters Method 7 Midterm 8 Cauchy-Euler Equations, Series Solutions of Ordinary Differential Equations: Power Series Solutions (Ordinary Point) 9 Power Series Solutions (Ordinary Point) (continued), Power Series Solutions (Regular-Singular Point) 10 Laplace Transforms: Basic Properties of the Laplace Transforms, Convolution 11 Solution of Differential Equations by the Laplace Transforms 12 Systems of Linear Ordinary Differential Equations: Solution of Systems of Linear ODE Using Elimination 13 Solution of Systems of Linear ODE Using Laplace Transforms pp. 1-5 pp pp pp pp pp pp pp pp pp pp pp

4 14 Fourier Analysis: Odd and Even Functions, Periodic Functions, Trigonometric Series, Fourier Series and Fourier Sine and Fourier Cosine Series for Functions of Any Period 15 Partial Differential Equations: Separation of Variables, Solution of Heat, Wave and Laplace Equations 16 Final Exam pp pp and pp Sources Course Book: Other Sources: 1. Lectures on Differential Equations, E. Akyıldız, Y. Akyıldız, Ş.Alpay, A. Erkip and A.Yazıcı,, Matematik Vakfı Yayın No:1 1. Differential Equations, 2nd Edition, Shepley L. Ross, John Wiley and Sons, Advanced Engineering Mathematics, 8th Edition, Erwin Kreyszig, John Wiley and Sons, Ordinary Differential Equations Problem Book with Solutions, Rajeh Eid, Atılım University Publications 16, Ankara, Atılım University, Evaluation System Requirements Number Percentage of Grade Attendance/Participation - - Laboratory - -

5 Application - - Field Work - - Special Course Internship - - Quizzes/Studio Critics - - Homework Assignments - - Presentation - - Project - - Seminar - - Midterms Exams/Midterms Jury 2 60 Final Exam/Final Jury 1 40 Total Percentage of Semester Work 60 Percentage of Final Work 40 Total 100 Course Category Core Courses Major Area Courses Supportive Courses X

6 Media and Managment Skills Courses Transferable Skill Courses The Relation Between Course Learning Competencies and Program Qualifications # Program Qualifications / Competencies Level of Contribution An ability to apply knowledge of computing, sciences and mathematics to solve information systems engineering problems. 2 An ability to analyze and model information systems specific problems, identify and define the appropriate requirements for their solutions. 3 An ability to design, implement and evaluate an information system, component, process or program that meets specified requirements. 4 An ability to use the modern techniques and engineering tools necessary for information system engineering practices. 5 An ability to gather/acquire, analyze, interpret data, make intelligent choices regarding the efficient use of information technology and decision models. 6 An ability to demonstrate the necessary organizational and business skills to work effectively in inter and inner disciplinary teams or individually. X X X

7 7 An ability to communicate effectively in Turkish and English. 8 Recognition of the need for, and the ability to access information, to follow recent developments in science and technology, and to engage in life-long learning. 9 An understanding of professional, legal, ethical and social issues and responsibilities related to Information Systems Engineering. 10 Skills in project and risk management, awareness about importance of entrepreneurship, innovation and long-term development, and recognition of international standards and methodologies. 11 An understanding about the impact of information systems engineering solutions in a global, environmental, societal and legal context while making decisions. 12 An ability to design, develop and operate information systems by integrating most appropriate hardware and software, arranging appropriate personnel and defining required procedures to improve the functionality and competition of public and private organizations, in a cost effective way. 13 Skills in finding solutions to business problems using information technologies. X ECTS/Workload Table Activities Number Duration (Hours) Total Workload Course Hours (Including Exam Week: 16 x Total Hours)

8 Laboratory Application Special Course Internship Field Work Study Hours Out of Class Presentation/Seminar Prepration Project Homework Assignments Quizzes/Studio Critics Prepration of Midterm Exams/Midterm Jury Prepration of Final Exams/Final Jury Total Workload 180