ACM10060 Applications of Differential Equations
This course introduces students to the theory of differential equations and dynamical systems and to their many applications as mathematical models. The topics covered prepare the student for more advanced subjects in ordinary differential equations (ODEs), dynamical systems theory, numerical methods and partial differential equations.
Course Outline:
A) 1st-order ODEs:
Direction fields, equilibria, bifurcations.
Linear equations: Integrating factor method.
Separable equations.
Exact equations.
B) 2nd-order ODEs:
Definitions.
Linear vs. nonlinear.
Dimensional analysis.
Examples.
C) 2nd-order linear constant-coefficient ODEs:
Homogeneous equations: Characteristic equation method (real, complex and double roots).
Non-homogeneous equations: Method of undetermined coefficients.
Examples: Forced and damped systems, mechanical oscillations, resonances, etc.
D) Systems of 2 coupled ODEs:
Linear and nonlinear.
Phase plane analysis.
Critical points and classifications in terms of eigendirections and eigenvalues.
Time permitting: Jacobi last multiplier method (integrating factor).
Time permitting: Non-autonomous systems and chaos.
Examples: Population models, the tragedy of the commons, epidemic models, etc.
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Aine is amazing. She teaches very well and gives a good understanding to how this can be used irl. the midterms do help you keep on top of the content. doing past papers and tutorial questions are of big help for the final exam
professor Áine Byrne teaches this module very well, would recommend if you have an interest in application of maths in the real world. exam is very similar to tutorials and in-class tests, super doable
Had a different prof, but I still loved this module! The 2 midterm tests were motivating enough to stay on top of the workload, so go to those tutorials and ask for help when needed. All exam questions were similar to what we had seen before
One of my favourite maths modules of first year. Bustamente is a great lecturer, he delivered the content in an engaging way and went through steps carefully. The exams are ok if you attend the tutorials.
Exams were pretty difficult but he marked them leniently
go to the tutorials and a good grade is very achievable!
Miguel Bustamante, is an entertaining lecturer. A nice module and a good grade is easily achievable
it's really interesting despite the module being quite difficult
For those interested in how to model the mathematical world, I would definitely recommend this module.
go to tutorials. exam is fine
The module is interesting if you want to gain more understanding of the real world applications of applied maths.
The methods for solving the problems encountered in this module are easy to follow. Anyone that enjoys these types of problems will find it easy.
Very enjoyable module to take. Tutorials are EXTREMELY useful for the problem sets which make up a large percentage of the assessment.
REVIEWSMODULE INFO
Subject: Applied & Computational Maths
Level: 1
Module Coordinator: Dr Áine Byrne
Trimester: Spring
Credits: 5
Module Info
Subject: Applied & Computational Maths
Level: 1
Module Coordinator: Dr Áine Byrne
Trimester: Spring
Credits: 5