COURSE INFORMATION FORM
Course Code and Title MAT 203 MATHEMATICS-3
H+T/C
3+0/3
ECTS Credit 4
Year / Semester
Sophomore Year / Fall Semester
Course Level
First Cycle
Course Type
Compulsory
Department
Food Engineering
Prerequisites
None
Teaching Method
Face to Face-Presentation
Period (Week-Hour) 14 week-3 hours of lectures per week
Course Language
Turkish
Course Objective
To provide students with general knowledge on formulating problems that arises
in applied sciences as mathematical models, solving such models through
analytical, qualitative and numerical methods, as well as interpreting solutions
within the concept of physical problem at hand.
Course Content
Differential equations and basic concepts, Differential equations as mathematical
model (Ordinary differential equations, order and degree of differential equations,
Derivation of differential equations). General, particular and singular solutions of
the differential equations. Existence and uniqueness theorems. Direction fields
and solution curves. Separable, homogenous, exact differential equations and
transforming to exact differential equation by using integrating factor. Linear
differential equations, Bernoulli differential equation and applications of the first
order differential equations (Population model, acceleration-velocity model,
temperature problems). Change of variables. Reducible differential equations
(single variable and non-linear differential equations). General solution of nth
order linear differential equations (linearly independent solutions, super position
principle for the homogeneous equations, particular and general solutions).
General solution of nth order constant coefficient homogenous differential
equations. Solutions of the constant coefficient non-homogenous equations.
(Undetermined coefficients, change of parameters). Initial Value Problems (IVP)
and Boundary Value Problems (BVP) (Eigen values and Eigen functions for
boundary value problems. Physical applications, mechanical vibrations, electrical
circuits). Variable coefficient homogenous and non-homogenous differential
equations (Cauchy-Euler, Legendre differential equations). Reduction of order.
Power series solutions of differential equations around ordinary points. Laplace
and inverse Laplace transformations. Solutions of constant and variable
coefficient boundary value problems and differential equations containing DiracDelta function and transformation functions by using Laplace transformations.
System of differential equations. Transformation of higher order differential
equation to the system of first order differential equations. Solutions of the
homogenous differential equations using Eigen values and eigenvectors. Solutions
of non-homogeneous constant coefficient system of differential equations.
Application of the Laplace transformation to system of differential equations.
Numerical solutions of differential equations (Euler and Runge-Kutta methods).
Assessment System
Semester Requirements
Midterm Exam
Number
1
Contribution %
40
Quiz
Homework
Attendance
Application
1
Total
40
Contribution to the Overall Success
Contribution of the Final Exam to the
60
Overall Success
100
Total
ECTS Workload Table Criteria
Number
Time (hour) Total Workload (hour)
14
3
42
Course Time
Outside Classroom Study
14
4
56
Time
Homework
Presentation/Seminar
Preparation
Midterm Exam
1
1
1
Project
Final Exam
1
2
2
Total Workload (hour)
101
Course ECTS Credit
4
Learning Outcomes
The student who accomplishes the course successfully;
1.Formulates mathematical models for a variety of problems.
2.Solves the model using analytical, qualitative and partially some numerical
methods.
3.Interprets the solution within the concept of the phenomenon being modeled.
4.Obtains solution for models studied within the scope of the course.
5.Learns the physical applications of differential equations.
6.Solves the homogeneous and inhomogeneous differential equations with
variable coefficients.
7.Solves the series solutions of differential equations around ordinary points.
8.Solves the solution of differential equations by Laplace transform method.
Course Stream
Week
Education Modules
Preliminary Documents
Studies
1.
Differential Equations and Basic Concepts, Preparation Proposed
Differential Equations as Mathematical for Lesson Sources
Model (Ordinary Differential Equations,
Order and Degree of Differential Equations,
Derivation Of Differential Equations)
2.
General, Particular and Singular Solutions of Preparation Proposed
the Differential Equations, Existence and for Lesson Sources
Uniqueness Theorems, Direction Fields and
Solution Curves
3.
Separable, Homogenous, Exact Differential Preparation Proposed
Equations and Transforming to Exact for Lesson Sources
Differential Equation by Integrating Factor
4.
Linear Differential Equations, Bernoulli Preparation Proposed
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
Differential Equation and Applications of for Lesson
The First Order Differential Equations
(Population Model, Acceleration-Velocity
Model, Temperature Problems)
Sources
Change of Variables, Reducible Differential Preparation
Equations (Single Variable and Non-Linear for Lesson
Differential Equations)
General Solution of nth Order Linear Preparation
Differential Equations (Linearly Independent for Lesson
Solutions, Super Position Principle for the
Homogeneous Equations, Particular and
General Solutions), General Solution of nth
Order Constant Coefficient Homogenous
Differential Equations
Solutions of the Constant Coefficient Non- Preparation
Homogenous
Equations
(Undetermined for Lesson
Coefficients, Change Of Parameters)
Midterm Exam
Initial Value Problems (IVP) and Boundary Preparation
Value Problems (BVP) (Eigen Values and for Lesson
Eigen Functions for Boundary Value
Problems, Physical Applications, Mechanical
Vibrations, Electrical Circuits)
Variable Coefficient Homogenous and Non- Preparation
Homogenous
Differential
Equations for Lesson
(Cauchy-Euler,
Legendre
Differential
Equations), Reduction of Order
Power Series Solutions of Differential Preparation
Equations around Ordinary Points
for Lesson
Laplace and Inverse Laplace Transformations Preparation
for Lesson
Solutions of Constant and Variable Preparation
Coefficient Boundary Value Problems and for Lesson
Differential Equations Containing DiracDelta Function and Transformation Functions
by Using Laplace Transformations
System
of
Differential
Equations, Preparation
Transformation of Higher Order Differential for Lesson
Equation to the System of First Order
Differential Equations, Solutions of the
Homogenous Differential Equations Using
Eigen Values and Eigenvectors, Solutions of
Non-Homogeneous Constant Coefficient
System of Differential Equations
Application of the Laplace Transformation to Preparation
System of Differential Equations, Numerical for Lesson
Solutions of Differential Equations (Euler
and Runge-Kutta Methods)
Proposed
Sources
Proposed
Sources
Proposed
Sources
Proposed
Sources
Proposed
Sources
Proposed
Sources
Proposed
Sources
Proposed
Sources
Proposed
Sources
Proposed
Sources
Course Sources
1.Edwards, C. H., Penney, D. E. (Çeviri Ed. Akın, Ö). 2006; Diferansiyel
Denklemler ve Sınır Değer Problemleri, Palme Yayıncılık, Ankara
2.Coşkun, H. 2002; Diferansiyel Denklemler, KTÜ Yayınları, Trabzon
3.Başarır, M., Tuncer, E. S. 2003; Çözümlü Problemlerle Diferansiyel
Denklemler, Değişim Yayınları, İstanbul
Contribution of the
Course Learning Outcomes
Course to Department
Learning Outcomes
1.Formulates mathematical models for a variety of problems.
2.Solves the model using analytical, qualitative and partially some
numerical methods.
3.Interprets the solution within the concept of the phenomenon being
modeled.
4.Obtains solution for models studied within the scope of the course.
5.Learns the physical applications of differential equations.
6.Solves the homogeneous and inhomogeneous differential equations
with variable coefficients.
7.Solves the series solutions of differential equations around ordinary
points.
8.Solves the solution of differential equations by Laplace transform
method.
Course Coordinator(s) Assist. Prof. Mehmet MERDAN
Dep.
Learn.
Outcomes
1, 2, 3, 5
1, 2, 3, 5
1, 2, 3, 5
1, 2, 3, 5
1, 2, 3, 5
1, 2, 3, 5
1, 2, 3, 5
1, 2, 3, 5