DIFFERENTIAL EQUATIONS

AIM

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.

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.

1. 1

   2.Apply the methods for solving first-order differential equations.

   Taught by: Problem Solving Method, Self Study Method, Experiential Learning, Lecture Method · Assessed by: Traditional Written Exam

2. 2

   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.

   Taught by: Problem Solving Method, Self Study Method, Experiential Learning, Lecture Method · Assessed by: Traditional Written Exam

3. 3

   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.

   Taught by: Problem Solving Method, Self Study Method, Experiential Learning, Lecture Method · Assessed by: Traditional Written Exam

4. 4

   4. Recognize linearly dependent and independent solutions and Wronskian and apply the methods for solving higher-order linear differential equations.

   Taught by: Problem Solving Method, Self Study Method, Experiential Learning, Lecture Method · Assessed by: Traditional Written Exam

5. 5

   5. Solve Cauchy-Euler differential equations and calculate initial value problems by Laplace transforms.

   Taught by: Problem Solving Method, Self Study Method, Experiential Learning, Lecture Method · Assessed by: Traditional Written Exam

WEEKLY PLAN

1. WEEK 1

   Preliminaries/Differential Equations

   Preparation: Book Chapter 1.1

2. WEEK 2

   Definitions and Terminology, Initial-Value Problems

   Preparation: Book Chapters 1.1, 1.2

3. WEEK 3

   Methods of Solving First Order Differential Equations: Separable Differential Equations

   Preparation: Book Chapter 2.2

4. WEEK 4

   Linear Differential Equations

   Preparation: Book Chapter 2.3

5. WEEK 5

   Exact Differential Equations, Making non-exact Differential Equations to Exact

   Preparation: Book Chapter 2.4

6. WEEK 6

   Solutions by Substitutions

   Preparation: Book Chapter 2.5

7. WEEK 7

   Differential Equations as Mathematical Models, Linear Models

   Preparation: Book Chapters 1.3, 3.1

8. WEEK 8

   Preliminaries: Higher Order Linear Differential Equations

   Preparation: Book Chapter 4.1

9. WEEK 9

   Methods of Solving Higher Order Linear Differential Equations: Reduction of Order

   Preparation: Book Chapter 4.2

10. WEEK 10

    Homogeneous Linear Equations with Constant Coefficients

    Preparation: Book Chapter 4.3

11. WEEK 11

    Undetermined Coefficients—Superposition and Annihilator Approaches

    Preparation: Book Chapters 4.4, 4.5

12. WEEK 12

    Variation of Parameters and Cauchy-Euler Differential Equations

    Preparation: Book Chapters 4.6, 4.7

13. WEEK 13

    Definition of the Laplace Transform, Inverse Transforms

    Preparation: Book Chapters 7.1, 7.2

14. WEEK 14

    Transforms of Derivatives and Solving Initial Value Problems from Laplace Transform

    Preparation: Book Chapter 7.2

ASSESSMENT

• Rate of Midterm Exam to Success30%
• Rate of Final Exam to Success70%

WORKLOAD

READING

• Dennis G. Zill - A First Course in Differential Equations with Modeling Applications 11th Edition.

TEACHING STAFF

• Assist.Prof. Cihan Bilge GÜRBÜZCOORDINATOR
• Assist.Prof. Tuğba ASLAN KHALİFA
• Assist.Prof. Hakan Osman ÇALDAĞ