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Applied maths could be defined as the use of mathematics in studying natural phenomena. The branch of applied maths studied at Leaving Cert level is Newtonian mechanics. Mechanics is the study of systems under the action of forces. Newtonian mechanics is concerned with systems that can be adequately described by Newton’s Laws of Motion. Systems that aren’t adequately described by Newtonian mechanics include systems with speeds approaching the speed of light, systems of extremely small particles and systems with a large number of particles. Hence Leaving Cert Applied Maths is the study of simple macro-systems that have moderate speeds.

Applied maths is essentially a further study of the mathematics of chapters 6 through 13 in Real World Physics; following which more specific and involved questions than those of Leaving Cert Physics may be posed and answered. The emphasis in applied maths is more on problem-solving than anything and reflecting this, the need for rote-learning is almost non-existent. The course content itself could be presented on one A4 sheet. The skills required for the course include:

• Capacity for interpretation and visualisation

• Ability for strategic problem solving

• Competency in mathematics

Anyone who is strong in higher level maths (A or B standard) and is self-motivated can achieve great success in applied maths – especially in conjunction with LC Physics. There is then a three for the price of two and a half effect as applied maths will help your physics, physics will help your applied maths and maths will help your applied maths. For those looking at the bigger picture, if you are intending on pursuing any science or engineering course in college, having done LC Applied Maths will really stand to you in your daunting first year — most 1st year physics and applied maths modules broadly cover the material of LC Applied Maths.

The statistics over the last number of years are that typically over 90% of students taking applied maths do higher level, and of these about a quarter achieve an A, over half achieve an A or B and nearly two-thirds achieve an honour. 90% of students pass. So with strong maths and good, effective application to the task at hand, good grades are there for the taking.

Some LC Applied Math Notes and some Solutions to selected problems. Section 6.2 deals with the Fundamental Theorem of Calculus and Section 6.4 has a little integration. See Chapter 10 of these LC Maths Lecture Notes for some more on integration.

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