To provide the recognition of differential equations and to give solution techniques and to give also its applications for the study of Engineering. To provide supports on studies and researches in the area of Engineering.
Course Content
This course contains; Preliminaries/Differential Equations,Definitions and Terminology, Initial-Value Problems ,Methods of Solving First Order Differential Equations: Separable Differential Equations,Linear Differential Equations,Exact Differential Equations, Making non-exact Differential Equations to Exact,Solutions by Substitutions ,Differential Equations as Mathematical Models, Linear Models ,Preliminaries: Higher Order Linear Differential Equations,Methods of Solving Higher Order Linear Differential Equations: Reduction of Order,Homogeneous Linear Equations with Constant Coefficients,Undetermined Coefficients—Superposition and Annihilator Approaches,Variation of Parameters and Cauchy-Euler Differential Equations,Definition of the Laplace Transform, Inverse Transforms,Transforms of Derivatives and Solving Initial Value Problems from Laplace Transform.
Dersin Öğrenme Kazanımları
Teaching Methods
Assessment Methods
2.Apply the methods for solving first-order differential equations.
12, 14, 6, 9
A
1. Recognize the classification of differential equations, solutions of differential equations, systems of differential equations, initial value problems and apply Existence and Uniqueness Theorem for first-order differential equations.
12, 14, 6, 9
A
3. Recognize and solve differential equations as mathematical models and higher-order linear differential equations and apply Existence and Uniqueness Theorem for higher-order equations.
12, 14, 6, 9
A
4. Recognize linearly dependent and independent solutions and Wronskian and apply the methods for solving higher-order linear differential equations.
12, 14, 6, 9
A
5. Solve Cauchy-Euler differential equations and calculate initial value problems by Laplace transforms.
12, 14, 6, 9
A
Teaching Methods:
12: Problem Solving Method, 14: Self Study Method, 6: Experiential Learning, 9: Lecture Method
Assessment Methods:
A: Traditional Written Exam
Course Outline
Order
Subjects
Preliminary Work
1
Preliminaries/Differential Equations
Book Chapter 1.1
2
Definitions and Terminology, Initial-Value Problems
Book Chapters 1.1, 1.2
3
Methods of Solving First Order Differential Equations: Separable Differential Equations
Book Chapter 2.2
4
Linear Differential Equations
Book Chapter 2.3
5
Exact Differential Equations, Making non-exact Differential Equations to Exact
Book Chapter 2.4
6
Solutions by Substitutions
Book Chapter 2.5
7
Differential Equations as Mathematical Models, Linear Models
Book Chapters 1.3, 3.1
8
Preliminaries: Higher Order Linear Differential Equations
Book Chapter 4.1
9
Methods of Solving Higher Order Linear Differential Equations: Reduction of Order
Book Chapter 4.2
10
Homogeneous Linear Equations with Constant Coefficients
Book Chapter 4.3
11
Undetermined Coefficients—Superposition and Annihilator Approaches
Book Chapters 4.4, 4.5
12
Variation of Parameters and Cauchy-Euler Differential Equations
Book Chapters 4.6, 4.7
13
Definition of the Laplace Transform, Inverse Transforms
Book Chapters 7.1, 7.2
14
Transforms of Derivatives and Solving Initial Value Problems from Laplace Transform
Book Chapter 7.2
Resources
Dennis G. Zill - A First Course in Differential Equations with Modeling Applications 11th Edition.
Course Contribution to Program Qualifications
Course Contribution to Program Qualifications
No
Program Qualification
Contribution Level
1
2
3
4
5
1
1. An ability to apply knowledge of mathematics, science, and engineering
X
2
2. An ability to identify, formulate, and solve engineering problems
X
3
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
4
4. An ability to use the techniques, skills, and modern engineering tools necessary for engineering practice
X
5
5. An ability to design and conduct experiments, as well as to analyze and interpret data
X
6
6. An ability to function on multidisciplinary teams
X
7
7. An ability to communicate effectively
8
8. A recognition of the need for, and an ability to engage in life-long learning
9
9. An understanding of professional and ethical responsibility
10
10. A knowledge of contemporary issues
11
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
3
42
Guided Problem Solving
14
1
14
Resolution of Homework Problems and Submission as a Report
14
3
42
Term Project
0
0
0
Presentation of Project / Seminar
0
0
0
Quiz
0
0
0
Midterm Exam
6
2
12
General Exam
6
2
12
Performance Task, Maintenance Plan
0
0
0
Total Workload(Hour)
122
Dersin AKTS Kredisi = Toplam İş Yükü (Saat)/30*=(122/30)
4
ECTS of the course: 30 hours of work is counted as 1 ECTS credit.
To provide the recognition of differential equations and to give solution techniques and to give also its applications for the study of Engineering. To provide supports on studies and researches in the area of Engineering.
Course Content
This course contains; Preliminaries/Differential Equations,Definitions and Terminology, Initial-Value Problems ,Methods of Solving First Order Differential Equations: Separable Differential Equations,Linear Differential Equations,Exact Differential Equations, Making non-exact Differential Equations to Exact,Solutions by Substitutions ,Differential Equations as Mathematical Models, Linear Models ,Preliminaries: Higher Order Linear Differential Equations,Methods of Solving Higher Order Linear Differential Equations: Reduction of Order,Homogeneous Linear Equations with Constant Coefficients,Undetermined Coefficients—Superposition and Annihilator Approaches,Variation of Parameters and Cauchy-Euler Differential Equations,Definition of the Laplace Transform, Inverse Transforms,Transforms of Derivatives and Solving Initial Value Problems from Laplace Transform.
Dersin Öğrenme Kazanımları
Teaching Methods
Assessment Methods
2.Apply the methods for solving first-order differential equations.
12, 14, 6, 9
A
1. Recognize the classification of differential equations, solutions of differential equations, systems of differential equations, initial value problems and apply Existence and Uniqueness Theorem for first-order differential equations.
12, 14, 6, 9
A
3. Recognize and solve differential equations as mathematical models and higher-order linear differential equations and apply Existence and Uniqueness Theorem for higher-order equations.
12, 14, 6, 9
A
4. Recognize linearly dependent and independent solutions and Wronskian and apply the methods for solving higher-order linear differential equations.
12, 14, 6, 9
A
5. Solve Cauchy-Euler differential equations and calculate initial value problems by Laplace transforms.
12, 14, 6, 9
A
Teaching Methods:
12: Problem Solving Method, 14: Self Study Method, 6: Experiential Learning, 9: Lecture Method
Assessment Methods:
A: Traditional Written Exam
Course Outline
Order
Subjects
Preliminary Work
1
Preliminaries/Differential Equations
Book Chapter 1.1
2
Definitions and Terminology, Initial-Value Problems
Book Chapters 1.1, 1.2
3
Methods of Solving First Order Differential Equations: Separable Differential Equations
Book Chapter 2.2
4
Linear Differential Equations
Book Chapter 2.3
5
Exact Differential Equations, Making non-exact Differential Equations to Exact
Book Chapter 2.4
6
Solutions by Substitutions
Book Chapter 2.5
7
Differential Equations as Mathematical Models, Linear Models
Book Chapters 1.3, 3.1
8
Preliminaries: Higher Order Linear Differential Equations
Book Chapter 4.1
9
Methods of Solving Higher Order Linear Differential Equations: Reduction of Order
Book Chapter 4.2
10
Homogeneous Linear Equations with Constant Coefficients
Book Chapter 4.3
11
Undetermined Coefficients—Superposition and Annihilator Approaches
Book Chapters 4.4, 4.5
12
Variation of Parameters and Cauchy-Euler Differential Equations
Book Chapters 4.6, 4.7
13
Definition of the Laplace Transform, Inverse Transforms
Book Chapters 7.1, 7.2
14
Transforms of Derivatives and Solving Initial Value Problems from Laplace Transform
Book Chapter 7.2
Resources
Dennis G. Zill - A First Course in Differential Equations with Modeling Applications 11th Edition.
Course Contribution to Program Qualifications
Course Contribution to Program Qualifications
No
Program Qualification
Contribution Level
1
2
3
4
5
1
1. An ability to apply knowledge of mathematics, science, and engineering
X
2
2. An ability to identify, formulate, and solve engineering problems
X
3
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
4
4. An ability to use the techniques, skills, and modern engineering tools necessary for engineering practice
X
5
5. An ability to design and conduct experiments, as well as to analyze and interpret data
X
6
6. An ability to function on multidisciplinary teams
X
7
7. An ability to communicate effectively
8
8. A recognition of the need for, and an ability to engage in life-long learning
9
9. An understanding of professional and ethical responsibility
10
10. A knowledge of contemporary issues
11
11. The broad education necessary to understand the impact of engineering solutions in a global, economic, environmental, and societal context
