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.
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.
differential equation, initial value problem, existence of solusions, uniqueness of the solution, regularity of solutions
|✔ Specialist skills||Intercultural skills||Communication skills||Critical thinking skills||Practical and/or problem-solving skills|
Standard lecture course.
|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|
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.
Coddington and Levinson, ``Theory of Ordinary Differential equations'', McGraw-Hill publ. 1955
Evaluation based on mid-term and final exams. Details will be provided in the class
Students are expected to have passed Calculus I / Recitation, Calculus II / Recitation, Linear Algebra I / Recitation, Linear Algebra II / Recitation.