# Applied Mathematics

### What is the subject about?

Leaving Certificate Applied Mathematics introduces mathematical modelling through exploration of real problems in the physical, natural, and economic worlds. Modelling requires students to turn authentic situations into mathematical structures. They then operate on those mathematical structures and generate a solution or a strategy to address the situation. The cycle of defining the problem, translating it to mathematics, calculating and evaluating the solution provides some of the most challenging, exhilarating, democratic work students will ever do in mathematics, requiring the best from all of them. Applied Mathematics is available for study at both Higher Level and Ordinary Level.

### How is the subject assessed?

I. Modelling Project(20%)

II. Written Examination (80%)

The course operates around 4 strands:

Stand 1: Mathematical modelling

– Problem solving cycle

– Formulating problems

– Translating problems into mathematics

– Computing solutions

– Evaluating solutions

Stand 2: Mathematical modelling with networks and graphs – Networks

– Matrices

– Optimisation

– Dynamic Programming

– Algorithms

– Project scheduling

Strand 3: Mathematically modelling the physical world; kinematics and dynamics

– Kinematics

– Particle motion in 2D

– Forces acting on a particle

– Work, energy, conservative forces, conservation of energy and momentum

– Circular motion

– Dimensional analysis

Strand 4: Mathematically modelling a changing world – Recurrence relations

– Real-world phenomena involving incremental change

– Solving homogenous and inhomogeneous difference equations

– Analysing real-world phenomena using continuous change

o Students who are studying Leaving Certificate higher level Mathematics should consider Applied Mathematics. This course also helps students studying Physics, due to some overlap in the course content.

o There is overlap between some parts of the Leaving Cert Physics course and the Applied Maths course, such as Linear Motion, Newton’s Laws, and Circular Motion. Thus it will also help you have a deeper understanding of these topics in Physics

o As there is a high Mathematics content in the course it will also give you a better understanding of some parts of the Higher Level Maths course; especially Trigonometry, Calculus (Differentiation and Integration)

o If you are considering studying any kind of engineering in college, Applied Maths is very important – all engineering students have to study Applied Maths in college and you will have a head start if you have the Leaving Certificate course done

### Career Opportunities

o Engineering

o Science

o Information Technology

o Architecture

o Education