The main topic of this course is nonlinear differential equation. Other topics cover existence and uniqueness of initial value problem, continuous dependence on parameters and theory of finite dimensional dynamical system. This course is a continuation of Differential Equations I.
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.
The 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. Method of solving ordinary differential equation and theory for analyzing qualitative properties of solutions are to be discussed. Applications to science and engineering will be also discussed.
nonlinear ordinary differential equation, existence and uniqueness of solution, stability
|Intercultural skills||Communication skills||Specialist skills||Critical thinking skills||Practical and/or problem-solving skills|
Standard course lecture.
|Course schedule||Required learning|
|Class 1||nonlinear ordinary differential equation||Details will be provided during each class session|
|Class 2||existence and uniqueness of solution||Details will be provided during each class session|
|Class 3||dependence of solution on initial value and parameter||Details will be provided during each class session|
|Class 4||vector field and its flow||Details will be provided during each class session|
|Class 5||stability||Details will be provided during each class session|
|Class 6||phase space||Details will be provided during each class session|
|Class 7||Hamilton flow, gradient flow||Details will be provided during each class session|
|Class 8||examples and applications of nonlinear ordinary differential equations, comprehension check-up||Details will be provided during each class session|
Introduction to differential equations, Koji Kasahara, Asakura Shoten (Japanese)
to be determined
Evaluation based on mid-term and final exam. Details will be provided in the class.
Differential Equations I