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
    Total Workload: 100
    ECTS Credit (Total workload/25): 4