1. To provide the methods of solution of systems of linear equations and the applications of matrix and determinant.
2. To introduce the basic concepts required to understand, construct, solve and interpret differential equations and to teach methods to solve differential equations of various types.
3. To give an ability to apply knowledge of mathematics on engineering problems
Course Content
This course contains; Matrices and Systems of Linear Equations,Matrices and Systems of Linear Equations,Determinants,Vector Spaces,Vector Spaces,Eigenvalues and Eigenvectors,Eigenvalues and Eigenvectors,First order differential equations,First order differential equations,Higher order differential equations,Higher order differential equations,Higher order differential equations,Laplace Transform,Laplace Transform.
Dersin Öğrenme Kazanımları
Teaching Methods
Assessment Methods
5. Solve higher order linear differential equations with constant coefficients and construct all solutions from the linearly independent solutions ; solve initial value problems using the Laplace transform
12, 14, 9
A, E
4. Solve first order linear equations and nonlinear equations of certain types , interpret the solutions and understand the conditions for the existence and uniqueness of solutions for linear differential equations
12, 14, 9
A, E
3. Classify differential equations according to certain features
12, 14, 9
A, E
2. Learn the importance of the concepts of vector space, basis and dimension and evaluate the eigenvalues and the corresponding eigenvectors of the matrix.
12, 14, 9
A, E
1. Solve the systems of linear equations, provide arithmetic operations with matrices, compute the inverse of matrix, determine the value of determinant of a matrix and use Cramer rule to solve the systems
12, 14, 9
A, E
Teaching Methods:
12: Problem Solving Method, 14: Self Study Method, 9: Lecture Method
Assessment Methods:
A: Traditional Written Exam, E: Homework
Course Outline
Order
Subjects
Preliminary Work
1
Matrices and Systems of Linear Equations
2
Matrices and Systems of Linear Equations
3
Determinants
4
Vector Spaces
5
Vector Spaces
6
Eigenvalues and Eigenvectors
7
Eigenvalues and Eigenvectors
8
First order differential equations
9
First order differential equations
10
Higher order differential equations
11
Higher order differential equations
12
Higher order differential equations
13
Laplace Transform
14
Laplace Transform
Resources
Differential Equations & Linear Algebra Third Edition Edition, C.Henry Edwards ; David E. Penney Pearson International Education International,2011.
Course Contribution to Program Qualifications
Course Contribution to Program Qualifications
No
Program Qualification
Contribution Level
1
2
3
4
5
1
An ability to apply knowledge of mathematics, science, and engineering
X
2
An ability to identify, formulate, and solve engineering problems
X
3
An ability to design a system, component, or process to meet desired needs within realistic constraints such as economic, environmental, social, political, ethical, health and safety, manufacturability, and sustainability
X
4
An ability to use the techniques, skills, and modern engineering tools necessary for engineering practice
5
An ability to design and conduct experiments, as well as to analyze and interpret data
6
An ability to function on multidisciplinary teams
7
An ability to communicate effectively
8
A recognition of the need for, and an ability to engage in life-long learning
9
An understanding of professional and ethical responsibility
10
A knowledge of contemporary issues
11
The broad education necessary to understand the impact of engineering solutions in a global, economic, environmental, and societal context
Assessment Methods
Contribution Level
Absolute Evaluation
Rate of Midterm Exam to Success
30
Rate of Final Exam to Success
70
Total
100
ECTS / Workload Table
Activities
Number of
Duration(Hour)
Total Workload(Hour)
Course Hours
14
4
56
Guided Problem Solving
0
0
0
Resolution of Homework Problems and Submission as a Report
14
10
140
Term Project
0
0
0
Presentation of Project / Seminar
0
0
0
Quiz
0
0
0
Midterm Exam
1
22
22
General Exam
1
22
22
Performance Task, Maintenance Plan
0
0
0
Total Workload(Hour)
240
Dersin AKTS Kredisi = Toplam İş Yükü (Saat)/30*=(240/30)
8
ECTS of the course: 30 hours of work is counted as 1 ECTS credit.
Detail Informations of the Course
Course Description
Course
Code
Semester
T+P (Hour)
Credit
ECTS
LINEAR ALGEBRA and DIFFERENTIAL EQUATIONS
-
Fall Semester
4+0
4
8
Course Program
Prerequisites Courses
Recommended Elective Courses
Language of Course
English
Course Level
First Cycle (Bachelor's Degree)
Course Type
Required
Course Coordinator
Assist.Prof. Cihan Bilge KAYASANDIK
Name of Lecturer(s)
Assist.Prof. Mehmed Rafet ÖZDEMİR
Assistant(s)
Aim
1. To provide the methods of solution of systems of linear equations and the applications of matrix and determinant.
2. To introduce the basic concepts required to understand, construct, solve and interpret differential equations and to teach methods to solve differential equations of various types.
3. To give an ability to apply knowledge of mathematics on engineering problems
Course Content
This course contains; Matrices and Systems of Linear Equations,Matrices and Systems of Linear Equations,Determinants,Vector Spaces,Vector Spaces,Eigenvalues and Eigenvectors,Eigenvalues and Eigenvectors,First order differential equations,First order differential equations,Higher order differential equations,Higher order differential equations,Higher order differential equations,Laplace Transform,Laplace Transform.
Dersin Öğrenme Kazanımları
Teaching Methods
Assessment Methods
5. Solve higher order linear differential equations with constant coefficients and construct all solutions from the linearly independent solutions ; solve initial value problems using the Laplace transform
12, 14, 9
A, E
4. Solve first order linear equations and nonlinear equations of certain types , interpret the solutions and understand the conditions for the existence and uniqueness of solutions for linear differential equations
12, 14, 9
A, E
3. Classify differential equations according to certain features
12, 14, 9
A, E
2. Learn the importance of the concepts of vector space, basis and dimension and evaluate the eigenvalues and the corresponding eigenvectors of the matrix.
12, 14, 9
A, E
1. Solve the systems of linear equations, provide arithmetic operations with matrices, compute the inverse of matrix, determine the value of determinant of a matrix and use Cramer rule to solve the systems
12, 14, 9
A, E
Teaching Methods:
12: Problem Solving Method, 14: Self Study Method, 9: Lecture Method
Assessment Methods:
A: Traditional Written Exam, E: Homework
Course Outline
Order
Subjects
Preliminary Work
1
Matrices and Systems of Linear Equations
2
Matrices and Systems of Linear Equations
3
Determinants
4
Vector Spaces
5
Vector Spaces
6
Eigenvalues and Eigenvectors
7
Eigenvalues and Eigenvectors
8
First order differential equations
9
First order differential equations
10
Higher order differential equations
11
Higher order differential equations
12
Higher order differential equations
13
Laplace Transform
14
Laplace Transform
Resources
Differential Equations & Linear Algebra Third Edition Edition, C.Henry Edwards ; David E. Penney Pearson International Education International,2011.
Course Contribution to Program Qualifications
Course Contribution to Program Qualifications
No
Program Qualification
Contribution Level
1
2
3
4
5
1
An ability to apply knowledge of mathematics, science, and engineering
X
2
An ability to identify, formulate, and solve engineering problems
X
3
An ability to design a system, component, or process to meet desired needs within realistic constraints such as economic, environmental, social, political, ethical, health and safety, manufacturability, and sustainability
X
4
An ability to use the techniques, skills, and modern engineering tools necessary for engineering practice
5
An ability to design and conduct experiments, as well as to analyze and interpret data
6
An ability to function on multidisciplinary teams
7
An ability to communicate effectively
8
A recognition of the need for, and an ability to engage in life-long learning
9
An understanding of professional and ethical responsibility
10
A knowledge of contemporary issues
11
The broad education necessary to understand the impact of engineering solutions in a global, economic, environmental, and societal context
