INTERNATIONAL BURCH UNIVERSITY
Faculty of Engineering and Natural Sciences
Department of Information Technologies
||Number of ECTS Credits
||Class Hours Per Week
||Total Hours Per Semester
||2 + 2
|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.
|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.
- Introduction, Types of differential equations.
- First order Ordinary Differential Equations: Separable and homogeneous linear DE.
- First order ODEs: Exact DE
- First order ODEs: Solution by integrating factor.
- First order ODEs: Linear DE
- First order nonlinear ODEs: Special case of Bernoulli
- Second order linear ODE: Introduction. Some definitions. Linear independency. Boundary and initial value problems
- Explicit methods: Undetermined coefficient method. Variation of parameters method.Constant coefficient higher order DE: Method of Undetermined Coefficients, Variable coefficient higher order DE
- Cauchy-Euler Equation; application of Second order DE with constant Coefficient
- Series solution of DE; power series
- Bessel Equation
- System of DE
- Interactive Lectures
- Practical Sessions
| Midterm Exam(s)||20|
| Final Exam||1||50|
- 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.
- 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
|Lecture (14 weeks x Lecture hours per week)||14||2||28|
|Laboratory / Practice (14 weeks x Laboratory/Practice hours per week)||14||2||28|
|Midterm Examination (1 week)||1||2||2|
|Final Examination(1 week)||1||2||2|
|Preparation for Midterm Examination||1||10||10|
|Preparation for Final Examination||1||10||10|
|Assignment / Homework/ Project||1||20||20|
|Seminar / Presentation|| || ||0|