Course Code:
MATH 245
Semester:
Fall
Course Type:
Core
P:
3
Lab:
2
Laboratuvar Saati:
0
Credits:
4
ECTS:
8
Prerequisite Courses:
Course Language:
English
Course Objectives:
Determining the type of a given first or higher order differential equation, examining the existence and uniqueness solution and being able to select the appropriate analytical technique for finding the solution if it can be obtained. Understanding the fundamental theorems of differential equations, understanding Laplace transform and application to differential equations, Finding an infinite series solution to a given differential equation
Course Content:

First order equations and various applications. Higher order linear differential equations. Power series solutions: ordinary and regular singular points. The Laplace transform: solution of initial value problems. Systems of linear differential equations: solutions by operator method, by Laplace transform.

Course Methodology:
1: Lecture, 2: Problem Solving, 3: Question-Answer, 4: Homework
Course Evaluation Methods:
A: Written examination, B: Homework

## Vertical Tabs

### Course Learning Outcomes

 Learning Outcomes Teaching Methods Assessment Methods 1) Can classify the first and higher order ordinary differential equations. 1,2,3,4 A 2) Can determine the appropriate solution method for a given differential equation. 1,2,3,4 A 3) Can investigate the existence and uniqueness of solutions for initial value problems. 1,2,3,4 A 4) Can use Laplace transforms. 1,2,3,4 A 5) Can determine an infinite series solution for a given differential equation. 1,2,3,4 A

### Course Flow

 Week Topics Study Materials 1 Introduction, Solution of Differential Equations, Classification of DEs, Initial and Boundary conditions. Separable equations. Course book, Chapter 1 , 2.2 2 Homogeneous, Linear 1st Order Differential Equations, Bernoulli, Ricatti equations 2.2,2.1,2.4 3 Clairaut Differential Equations Exact Differential Equations and Integrating Factors 2.6 4 Existence and Uniqueness Theorem for 1st order ODEs,  discontinuous coefficient, forcing function 2.4,2.8 5 Higher Order Linear ODEs Homogeneous Eqs with constant coefficients Existence and Uniqueness for general higher order equations 3.1,3.2,4.1 6 Midterm I  Fundamental Set of Solutions of linear  Homogeneous DE s, Linear Independence, Wronskian, Complex roots of the characteristic equation, Reduction of Order, - 3.2,3.3,3.4 7 Repeated roots of characteristic equation for constant coefficient homogenous equation Cauchy-Euler Equation 3.5,5.5,3.6 8 Linear Non-Homogeneous DE s (Method of Undetermined Coefficients),Variation of Parameters 4.3,3.7 9 Definition of Laplace Transform, Solution of Initial Value Problems, Step Functions 6.1,6.2,6.3 10 Midterm II, Differential Equations with discontinuous forcing functions, - 6.4 11 Impulse Function, The Convolution Integral, Review of Power Series, Ordinary Points, Singular Points 6.5,6.6,5.1 12 Series Solutions near an Ordinary Point, Regular Singular Points, Series Solutions near a Regular Singular Point, 5.2, 5.3,5.4 13 Bessel, Legendre, Hermite, Chebyshev Equation 5.5,5.6 14 System of differential equations 7.1, ch 6

### Recommended Sources

 Textbook Elementary Differential Equations and Boundary Value Problems, W. E. Boyce and R. C. DiPrima, John Wiley and Sons, 2009 Additional Resources

### Material Sharing

 Documents Assignments Exams

### Assessment

 IN-TERM STUDIES NUMBER PERCENTAGE Mid-terms 2 100 Quizzes - Assignments - Total 100 CONTRIBUTION OF FINAL EXAMINATION TO OVERALL GRADE 40 CONTRIBUTION OF IN-TERM STUDIES TO OVERALL GRADE 60 Total 100

 COURSE CATEGORY Expertise/Field Courses

### Course’s Contribution to Program

 No Program Learning Outcomes Contribution 1 2 3 4 5 1 The ability to make computation on the basic topics of mathematics such as limit, derivative, integral, logic, linear algebra and discrete mathematics which provide a basis for the fundamenral research fields in mathematics (i.e., analysis, algebra, differential equations and geometry) X 2 Acquiring fundamental knowledge on fundamental research fields in mathematics X 3 Ability form and interpret the relations between research topics in mathematics X 4 Ability to define, formulate and solve mathematical problems X 5 Consciousness of professional ethics and responsibilty X 6 Ability to communicate actively X 7 Ability of self-development in fields of interest X 8 Ability to learn, choose and use necessary information technologies X 9 Lifelong education X

### ECTS

 Activities Quantity Duration (Hour) Total Workload (Hour) Course Duration (14x Total course hours) 14 5 70 Hours for off-the-classroom study (Pre-study, practice) 14 5 70 Mid-terms (Including self study) 2 15 30 Quizzes - - - Assignments - - - Final examination (Including self study) 1 20 20 Total Work Load 190 Total Work Load / 25 (h) 7.60 ECTS Credit of the Course 8