Advanced Differential Equations
|Course code MATH3700||Units 10||Level 3000||Faculty of Science and Information TechnologySchool of Mathematical and Physical Sciences|
This course introduces students to the modern theory and methods of ordinary and partial differential equations. It builds on the classical foundations of differential equations studied in second year. Ordinary and partial differential equations form an essential part of the mathematical background required for engineering and the physical sciences. A large number of real-life problems can be modelled using differential equations, making the subject one of the most widely applicable areas of mathematics. The course concentrates on some fundamental analytical and numerical methods for applied differential equations arising from the mathematical modelling of physical, chemical and biological systems.
Available in 2015
|Objectives||On successful completion of this course, students will:|
1. Have a broad overview of ordinary and partial differential equations as well as an appreciation of the application of analysis and linear algebra in studying differential equations.
2. Have the skills to build mathematical models of relevant real-world problems based on differential equations.
3. Be able to solve these differential equations using appropriate computer software if necessary, and to interpret the solutions.
4. Understand the concepts of accuracy, consistency, stability and convergence of numerical schemes for solving differential equations.
|Content||(1) Ordinary Differential Equations|
(a) Existence and uniqueness theory for ordinary differential equations
(b) Stability theory for linear and nonlinear ordinary differential equations
(c) Stability and convergence of numerical techniques, and numerical schemes for stiff ordinary differential equations
(2) Partial Differential Equations
(a) Modelling with partial differential equations
(b) Classical solution techniques and weak solutions
(c) Numerical methods for partial differential equations
|Assumed Knowledge||MATH2800 and MATH2320|
MATH2470 and MATH2320
|Modes of Delivery||Internal Mode|
|Contact Hours||Lecture: for 3 hour(s) per Week for Full Term|
|Timetables||2015 Course Timetables for MATH3700|