Differential Equations
ataozk@yahoo.com
Content
Objective
This course introduces undergraduate students to the theory and solution methods of ordinary differential equations (ODEs), a central tool for modeling continuously evolving phenomena in physics, engineering, biology, and economics.
Master the vocabulary and classification of ODEs (order, linearity, homogeneity)
Solve first-order equations and higher-order linear equations with constant coefficients analytically
Understand and apply existence and uniqueness theorems for solutions
Use power series, the Laplace transform, and matrix methods to solve ODEs and systems of ODEs
Develop qualitative intuition (direction fields, stability) alongside analytical computation
Prepare students for later courses in physics, mechanics, control theory, and dynamic economics that rely on ODEs
Course Content
13 different types of differential equations of first and higher order degrees.
Master the vocabulary and classification of ODEs (order, linearity, homogeneity)
Solve first-order equations and higher-order linear equations with constant coefficients analytically
Understand and apply existence and uniqueness theorems for solutions
Use power series, the Laplace transform, and matrix methods to solve ODEs and systems of ODEs
Develop qualitative intuition (direction fields, stability) alongside analytical computation
Prepare students for later courses in physics, mechanics, control theory, and dynamic economics that rely on ODEs
Course Learning Outcomes
By the end of this course, the student will be able to:
Classify a differential equation by order, linearity, and type, and select the appropriate solution method
Solve first-order equations and higher-order linear equations with constant coefficients analytically
State and apply existence and uniqueness theorems for solutions
Construct power series solutions, including by the Frobenius method
Use the Laplace transform to solve differential equations and systems, including those with discontinuous inputs
Solve linear systems of ODEs using the eigenvalue/eigenvector method
Qualitatively analyze the behavior of solutions (stability, phase portraits) without explicit solving
Model a real-world problem (physical, biological, economic) with a differential equation and interpret the resulting solution
Teaching and Learning Methods
Instruction combines lectures, recitation sessions, and independent work.
Lectures: presentation of concepts, derivations, and worked examples
Recitations: application exercises solved in groups, with collective correction
Weekly homework to consolidate the methods covered in lectures
Office hours for individual questions
Assessment: one-two midterm exam, homework/quizzes, and a final exam
References
Boyce, W. E., DiPrima, R. C. — Elementary Differential Equations and Boundary Value Problems, Wiley
Zill, D. G. — A First Course in Differential Equations with Modeling Applications, Cengage
Edwards, C. H., Penney, D. E. — Differential Equations and Boundary Value Problems: Computing and Modeling, Pearson
Simmons, G. F. — Differential Equations with Applications and Historical Notes, McGraw-Hill
Tenenbaum, M., Pollard, H. — Ordinary Differential Equations, Dover
Weekly Contents
| Week | Weekly Contents |
|---|---|
| 1 | First-order differential equations |
| 2 | The type that can be divided into variables |
| 3 | The type that can be divided into variables |
| 4 | Differential equations in the homogeneous type |
| 5 | Differential equations in the Exact type |
| 6 | Differential equations in the Linear type |
| 7 | Differential equations in the Bernoulli type |
| 8 | Differential equations in the Riccatti type |
| 9 | Differential equations in the Clairout type |
| 10 | Theorem of being and singularity with Picard's iteration method |
| 11 | The type that can be resolved according to the variable described |
| 12 | High-order differential equations |
| 13 | General solution methods characteristic according to the type of polynomial and the roots |
| 14 | Wronksien |
| Week | Weekly Contents |
|---|---|
| 1 | First-order differential equations |
| 2 | The type that can be divided into variables |
| 3 | The type that can be divided into variables |
| 4 | Differential equations in the homogeneous type |
| 5 | Differential equations in the Exact type |
| 6 | Differential equations in the Linear type |
| 7 | Differential equations in the Bernoulli type |
| 8 | Differential equations in the Riccatti type |
| 9 | Differential equations in the Clairout type |
| 10 | Theorem of being and singularity with Picard's iteration method |
| 11 | The type that can be resolved according to the variable described |
| 12 | High-order differential equations |
| 13 | General solution methods characteristic according to the type of polynomial and the roots |
| 14 | Wronksien |
Assessment System
| Activities | Number | Contribution |
|---|---|---|
| Contribution of in-term studies to overall grade | 2 | 35 |
| Contribution of final exam to overall grade | 1 | 65 |
| Total | 3 | 100 |
| Activities | Number | Contribution |
|---|---|---|
| Assignments | 0 | 0 |
| Presentation | 0 | 0 |
| Midterm Examinations (including preparation) | 2 | 95 |
| Project | 0 | 0 |
| Laboratory | 0 | 0 |
| Other Applications | 0 | 0 |
| Quiz | 1 | 5 |
| Term Paper/ Project | 0 | 0 |
| Portfolio Study | 0 | 0 |
| Reports | 0 | 0 |
| Learning Diary | 0 | 0 |
| Thesis/ Project | 0 | 0 |
| Seminar | 0 | 0 |
| Other | 0 | 0 |
| Make-up | 0 | 0 |
| Total | 3 | 100 |
Relation of Proficiency
| No | Program Learning Outcomes | Contribution | ||||
|---|---|---|---|---|---|---|
| 1 | 2 | 3 | 4 | 5 | ||
| 1 | Demonstrate a basic knowledge of different economic theories and main discussions driving current theoretical approaches | X | ||||
| 2 | Demonstrate ability to use basic qualitative and quantitative methods to asses different economic questions of applied fields | X | ||||
| 3 | Show a sound understanding of current economic discussions and problems | X | ||||
| 4 | Have an effective and clear communication in written and oral formats in different public and professional contexts. | X | ||||
| 5 | Demonstrate basic knowledge of the world economic history and a sound knowledge of the Turkish economic history | X | ||||
| 7 | Demonstrate knowledge of standard quantitative techniques and empirical models used in economics | X | ||||
| 8 | Show ability to apply basic economic theory to an applied topic | X | ||||
| 9 | Show a basic understanding of analytical methods, both theory- and model-based | X | ||||
| 10 | Show ability to use economic concepts to discuss current economic issues | X | ||||
| 11 | Reason logically and work analytically | X | ||||
| 12 | Show awareness on social aspects of the economics in different applied and theoretical fields | X | ||||
| 13 | Identify appropriate economic models to analyse problems | X | ||||
| 16 | Show understanding of basic statistical and econometric concepts and ability to apply basic concepts to own empirical work | X | ||||
| 17 | Demonstrate a sound knowledge of the current economic issues in Turkey and a general knowledge of the issues in the world economy | X | ||||
ECTS
| Activities | Number | Period | Total Workload |
|---|---|---|---|
| Class Hours | 14 | 3 | 42 |
| Working Hours out of Class | 14 | 1 | 14 |
| Assignments | 0 | 0 | 0 |
| Presentation | 0 | 0 | 0 |
| Midterm Examinations (including preparation) | 2 | 30 | 60 |
| Project | 0 | 0 | 0 |
| Laboratory | 0 | 0 | 0 |
| Other Applications | 2 | 10 | 20 |
| Final Examinations (including preparation) | 0 | 0 | 0 |
| Quiz | 1 | 10 | 10 |
| Term Paper/ Project | 0 | 0 | 0 |
| Portfolio Study | 0 | 0 | 0 |
| Reports | 0 | 0 | 0 |
| Learning Diary | 0 | 0 | 0 |
| Thesis/ Project | 0 | 0 | 0 |
| Seminar | 0 | 0 | 0 |
| Other | 0 | 0 | 0 |
| Make-up | 0 | 0 | 0 |
| Yıl Sonu | 0 | 0 | 0 |
| Hazırlık Yıl Sonu | 0 | 0 | 0 |
| Hazırlık Bütünleme | 0 | 0 | 0 |
| Total Workload | 146 | ||
| Total Workload / 25 | 5.84 | ||
| Credits ECTS | 6 | ||