Differential Equations 1
| Code | School | Level | Credits | Semesters |
| MATH2104 | Mathematical Sciences | 2 | 20 | Autumn UK |
- Code
- MATH2104
- School
- Mathematical Sciences
- Level
- 2
- Credits
- 20
- Semesters
- Autumn UK
Summary
This course provides an introduction to a range of methods for studying and solving differential equations, both ordinary and partial (ODEs and PDEs). Topics include:
- Techniques for solving homogeneous and inhomogeneous second-order ODEs
- Series solutions of second-order linear ODEs and the method of Frobenius
- Fourier series and theory
- Solutions to canonical second-order partial differential equations (1D Wave, 1D Diffusion and 2D Laplace equations)
- Sturm-Liouville theory and applications to linear PDEs
- Integral transform methods for ODEs and PDEs
- Preliminary numerical methods for solving ODEs and PDEs
Target Students
Single Honours and Joint Honours students from the School of Mathematical Sciences, Mathematical Physics students, Natural Sciences students, Liberal Arts students.
Co-requisites
Modules you must take in the same academic year, or have taken in a previous year, to enrol in this module:
Classes
- Two 2-hour lectures each week for 11 weeks
- Two 1-hour lectures each week for 11 weeks
- Two 1-hour computings each week for 11 weeks
Teaching will be through a variety of methods, ranging from traditional lectures and computing sessions, with the delivery tailored to the material on a week-by-week basis.
Assessment
- 40% Cousework: Summative assessment based on tasks distributed through the semester.
- 60% Exam (2-hour): Written examination – Autumn.
Assessed by end of autumn semester
Educational Aims
This course aims to introduce standard methods of solution for linear ordinary and partial differential equations and to introduce the idea and practice of Fourier series and integral transforms. The mathematical methods taught in this module find wide application across a range of courses in applied mathematics.Learning Outcomes
A student who completes this course successfully will be able to:
L1 – Classify differential equations and identify suitable methods of solution for many important problems arising in engineering, physics and biology.
L2 – Develop and justify a mathematical framework using suitable definitions and solution methods to solve ordinary and partial differential equations in a wide range of contexts and applications.
L3 – Present conclusions verbally and in writing using structured and mathematically rigorous arguments and contextually appropriate language and defending their arguments, results, choices or assumptions against query or criticism.
L4 – Summarise complex ideas clearly and concisely, taking due consideration of the target audience, which may include influencing, educating and/or persuading different audiences using their arguments and/or results.
L5 – Make effective use of software to carry out mathematical calculations and visualise results.