INTERNATIONAL BURCH UNIVERSITY
Faculty of Engineering and Natural Sciences
Department of Information Technologies
2016-2017

SYLLABUS
Code Name Level Year Semester
MTH 201 Differential Equations Undergraduate 2 Fall
Status Number of ECTS Credits Class Hours Per Week Total Hours Per Semester Language
Compulsory 4 2 + 2 100 English

 Instructor Assistant Coordinator Lejla Bandić, Research Assistant Zeljko Juric Željko Jurić, Assoc. Prof. Dr. [email protected] [email protected] no email

 Differential Equations: First-order differential equations, second-order linear equations, Wronskian, change of parameters, homogeneous and non-homogeneous equations, series solutions, Laplace transform, systems of first-order linear equations, boundary value problems, Fourier series.

COURSE OBJECTIVE
Introduce basic topics and solution techniques of differential equations.
Develop an appreciation for the development of mathematical thought and the contributions that mathematics has made to our world.
Expand understanding of advanced mathematical topics and their applications with real life problems and analyzing the results.

COURSE CONTENT
Week
Topic
1. Introduction, Types of differential equations.
2. First order Ordinary Differential Equations: Separable and homogeneous linear DE.
3. First order ODEs: Exact DE
4. First order ODEs: Solution by integrating factor.
5. First order ODEs: Linear DE
6. First order nonlinear ODEs: Special case of Bernoulli
7. Second order linear ODE: Introduction. Some definitions. Linear independency. Boundary and initial value problems
8. Exercises
9. Explicit methods: Undetermined coefficient method. Variation of parameters method.Constant coefficient higher order DE: Method of Undetermined Coefficients, Variable coefficient higher order DE
10. Cauchy-Euler Equation; application of Second order DE with constant Coefficient
11. Series solution of DE; power series
12. Bessel Equation
13. System of DE

LABORATORY/PRACTICE PLAN
Week
Topic

TEACHING/ASSESSMENT
Description
• Interactive Lectures
• Practical Sessions
• Excersises
Description (%)
Method Quantity Percentage (%)
Homework20
Midterm Exam(s)20
Attendance10
Final Exam150
Total: 100
Learning outcomes
• Solve various differential equations using various integration methods from calculus.
• Apply these solutions to various motion problems.
• Solve and apply differential equations by the method of infinite series
• Solve more complex differential equations using Laplace Transforms.
TEXTBOOK(S)
• W. E. Boyce and R. C. DiPrima, “Elementary Differential Equations and Boundary Value Problems” John Wiley and Sons, Ltd., 2001.
• Steven G. Krantz, Differential Equations Demystified, The McGraw-Hill, 2005.
• E. Kreyszig, Advanced Engineering Mathematics, John Wiley & Sons, Inc., 2006.
• Shepley L. Rose, “Differential Equations,” John Wiley & Son, Ltd.

ECTS (Allocated based on student) WORKLOAD
Activities Quantity Duration (Hour) Total Work Load
Lecture (14 weeks x Lecture hours per week)14228
Laboratory / Practice (14 weeks x Laboratory/Practice hours per week)14228
Midterm Examination (1 week)122
Final Examination(1 week)122
Preparation for Midterm Examination11010
Preparation for Final Examination11010
Assignment / Homework/ Project12020
Seminar / Presentation 0