### 2022　Differential Equations I

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Instructor(s)
Ninomiya Syoiti
Class Format
Lecture    (Livestream)
Media-enhanced courses
Day/Period(Room No.)
Wed3-4(S621)
Group
-
Course number
MTH.C341
Credits
1
2022
Offered quarter
1Q
Syllabus updated
2022/3/16
Lecture notes updated
-
Language used
Japanese
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### Course description and aims

After introducing some terminology and fundamental notions on differential equations, we explain elementary method for explicit solutions, general method for solving constant coefficient linear differential equations and some analysis on linear differential equations. This course is to be continued to Differential Equations II.

Differential equations are fundamental notions appearing in all fields of mathematics. Space of solutions have algebraic structure, existence theorems of solutions give various geometric and analytic objects of great interests. This course is an entry to these paths.

### Student learning outcomes

Main topic of this course is a basic theory and its applications of ordinary differential equations of one unknown variable. Ordinary differential equations describe various natural phenomena and physical laws, thus, method of solving equations and its theory are important mathematically as well as for applications. Students are expected to master fundamental properties regarding existence and uniqueness of solutions and properties of solutions.

### Keywords

differential equation, initial value problem, existence of solusions, uniqueness of the solution, regularity of solutions

### Competencies that will be developed

 ✔ Specialist skills Intercultural skills Communication skills Critical thinking skills Practical and/or problem-solving skills

### Class flow

Standard lecture course.

### Course schedule/Required learning

Course schedule Required learning
Class 1 Outline of the lecture and some examples Details will be provided during each class session
Class 2 Cauchy-Peano's theorem (existence) Details will be provided during each class session
Class 3 Uniqueness of the solution Details will be provided during each class session
Class 4 Regularity of solutions Details will be provided during each class session
Class 5 Picard's iteration Details will be provided during each class session
Class 6 Analytic methods Details will be provided during each class session
Class 7 Linear differential equations Details will be provided during each class session

### Out-of-Class Study Time (Preparation and Review)

To enhance effective learning, students are encouraged to spend approximately 100 minutes preparing for class and another 100 minutes reviewing class content afterwards (including assignments) for each class.
They should do so by referring to textbooks and other course material.

not specified

### Reference books, course materials, etc.

Coddington and Levinson, ``Theory of Ordinary Differential equations'', McGraw-Hill publ. 1955

### Assessment criteria and methods

Evaluation based on mid-term and final exams. Details will be provided in the class

### Related courses

• MTH.C342 ： Differential Equations II

### Prerequisites (i.e., required knowledge, skills, courses, etc.)

Students are expected to have passed Calculus I / Recitation, Calculus II / Recitation, Linear Algebra I / Recitation, Linear Algebra II / Recitation.