applied maths: whats it all about?

8/13/2019 Applied Maths: Whats It All About?

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Applied Maths whats it all about?

Table of contents

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Introduction: WhatisApplied Maths?

Some commonly asked questions

Why study Applied Maths?

Do I need to be doing Physics to study Applied Maths? Whoshouldntstudy Applied Maths?

Ho likely is it that I ill get A?

Ho long is the course?

What is the !ormat o! the paper in the lea"ing cert e#am?

What te#tbook do I need?

What is the paper like at $rdinary %e"el?

Is it possible to study Applied Maths in college?

I ant to study Maths in college & should I take Applied

Maths no?

'estimonies

(elated )areers

Applied Mathematics Syllabus


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Introduction

*nlike most other sub+ects there is noApplied Mathsoption !or ,unior )ert so !or you the student it is quite

di!!icult to kno +ust hat the sub+ect is like at %ea"ing )ert le"el-

'he best ay to get a !eel !or hat the sub+ect is to attend an Applied Maths class. e usually hold a series

o! classes !or interested students in ,anuary/0ebrauary o! 1thyear !or '2 ho are interested in !inding out

more about the sub+ect- Here e start o!! looking at some typical $rdinary %e"el questions and then tacklesome Higher %e"el questions- Students are generally pleasantly surprised that they are able to do Higher

%e"el questions a!ter only one or to classes o! an introduction-

Here hoe"er e try to anser some o! your questions in ad"ance-

It is a !ascinating sub+ect hich deals ith sol"ing real3li!e problems using mathematical models- It o"erlapsith both the Mathematics course as ell as the Physics course- In particular the ne Pro+ect Maths syllabus

is "ery similar in its approach to Applied Maths- 'he emphasis is on using di!!erent mathematical models to

sol"e e"eryday problems-

*nlike any other sub+ect in the %ea"ing )ert 4ith the possible e#ception o! the ne Pro+ect Maths56

Applied Maths is aboutproblem-solving6 so i! you like a challenge then Applied Maths is !or you-

'he maths is all based around Physics problems

Applied Maths ill instil skills hich ill last a li!etime. ho to analyse a problem6 ho to represent the

problem mathematically6 ho to sol"e the maths6 and then ho to interpret your anser so that it makes

sense hen applied to real li!e situations-

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It is also 4relati"ely5 straight!orard to get a business 4or business management5 degree once you ha"e an

Science/7ngineering degree i! you so choose- It is not hoe"er straight!orard to do it the other ay

around-

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Who shouldntstudy Applied Maths?

'his sub+ect doesn9t suit students ho +ust like learning things o!! by heart-

In !act the questions are designed to catch out those "ery students and hether that is !air or not is a moot

point 3 you are being arned about it no so i! you don9t like it you kno hat to do- 2ou cannot come out

o! an Applied Maths e#am and say e ne"er did that question be!ore & sir you ne"er co"ered it ith us in

class9- It is my +ob to train9 you to tackle problems hich you ha"en9t come across be!ore-

So Applied Maths suits people ho like sol"ing pules 4e like to make it sound more impressi"e so e

call it problem sol"ing95- 'his means being able to think !or yoursel!6 and because almost all o! your

secondary3school education encourages you to learn the right anser o!! by heart9 it can make a lot o!

students uncom!ortable- 'he ability to problem3sol"e is hoe"er a "ery important skill and is highly3"alued

by many employers- It is one o! the reasons hy you o!ten see politicians and business people on the nes

saying that the country needs more scientists and engineers-

As the name suggests6 the course is mathematical in nature6 and you do need to be "ery good at maths to be

success!ul at higher le"el- In general you should be a"eraging a ;9 or higher6 and +ust because you got an

A9 in Maths in the ,unior )ert does not necessarily mean that you ill be com!ortable ith the sub+ect6 sopay attention to the problems e ill co"er belo to see i! you can !ollo them-

'he material itsel! is similar to that hich you ould study in 7ngineering in uni"ersity6 so e"en i! you are

not great at maths but ant to be an engineer you should consider taking up the sub+ect- 7"en i! you end up

taking the $rdinary %e"el e#am at the end it ill still stand to you at third le"el-

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#ow long is the course?

'he course itsel! is !airly short 4see the syllabus at the end5-

'here are ten topics but only si# questions to do on the e#am itsel! so there is enormous choice-

In !act normally e only co"er about @ topics6 and try to ensure e kno them "ery ell rather than trying

to co"er too much- It means that e are normally !inished the course by )hristmas in si#th year6 so there9s a

lot o! time !or re"ision !rom then on- 'he )hristmas e#am is itsel! usually a !ull mock paper-

What is the format of the paper in the lea$ing cert e%am?

'ime: B hours

$rdinary %e"el: si# questions to be ansered out o! nine

Higher %e"el: si# questions to be ansered out o! ten 4about C minutes per question5-

We generally aim to co"er @ 4or at most 5 topics 4here each topic corresponds to a di!!erent question5. it9s

more ad"isable to spend your time becoming competent in @ questions rather than spending time on others

and this still allos !or ample choice on the day itsel!-

'he e#am began in EFG so there are o"er 1G years o! e#am questions- We ill co"er all of these!or each

topic 4many o! them are repetiti"e5 so there should be "ery little on your lea"ing cert paper that you

ouldn9t already ha"e seen-

What is the paper li&e at 'rdinary (e$el?

Applied Maths at the $rdinary %e"el is probably the easiest sub+ect on the lea"ing cert curriculum- It is "ery

short and can easily be co"ered in one year or less- 'he questions "ary "ery little !rom year to year so ith a

+ust a little practice it should be easy to nail the A-

What te%tboo& do I need?

'here are a number o! te#tbooks a"ailable !or studying Applied Maths:

E- Fundamental AppliedMathematics 4$li"er Murphy5. a ne addition came out in GE-

- Applied Mathematics Leaving Certificate Foundation Mechanics for Third Level4e"in )onli!!e5-

An accompanying set o! solutions is a"ailable !or both o! these te#tbooks-

I don9t use a te#tbook hoe"er- I ha"e a booklet !or each topic e co"er- 'his has a short introduction to the

topic but a!ter that it9s all e#am questions6 arranged in order o! di!!iculty-

2ou don9t e"en need to buy e#am papers because all e#am questions are included in these notes 4and

anyay e#am3papers only go back EG years or so hile e you ill recei"e 1G years orth o! questions5-

;ecause some students like to ork ahead I also pro"ide a separate booklet containing all the ansers-'hese solutions/marking schemes are all a"ailable !rom -thephysicsteacher-ie

#ow li&ely is it that I will get A at #igher (e$el?

F o! students on a"erage recei"e an A in the %ea"ing )ert-

I used to think that the sub+ect as "ery di!!icult because the questions that come up on the %ea"ing )ert

e#am ere completely di!!erent e"ery year- 'hen I noticed that almost all the questions in the e#am papers

in recent years ere +ust "ariations on older questions 4some o! them JG years older>5-

So no our students co"er all questions back to EFG & that9s 1G years orth o! questions-

It may +ust be a co3incidence6 but one o! our students recently got the top mark in the country in GEE-

Any student ho can get an A Maths should certainly be getting an A in Applied Maths 4but ith much less

e!!ort>5

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Is it possible to studyApplied Mathsin college?

2ou can study Applied Maths itsel! at third le"el- It is knon as Mathsphysics9 in K*I uni"ersities and as

'heoretical Physics9 in 'rinity )ollege-

I want to study Maths in college should I ta&e Applied Maths now?

Applied Maths is an in"aluable sub+ect !or those ho plan to study pure maths in uni"ersity- Indeed many o!

those ho ha"e studied maths at uni"ersity say that Applied Maths as a more important preparation than

Maths itsel!>

I want to study )ngineering in college should I ta&e Applied Maths now?

I! you are considering studying any kind o! engineering in college6 Applied Maths is "ery important. all

engineering students ha"e to study Applied Maths in !irst year in college and you ill ha"e a head start i!

you ha"e the %ea"ing )ert course done be!orehand-

*elated (in&s

Irish Applied Maths 'eachers Association: http://-iamta-ie/

Syllabus: http://-curriculumonline-ie/uploaded!iles/PD0/lcLapmathsLsy-pd!

)areers Portal

Slss

Scoilnet

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http://www.iamta.ie/http://www.curriculumonline.ie/uploadedfiles/PDF/lc_apmaths_sy.pdfhttp://www.iamta.ie/http://www.curriculumonline.ie/uploadedfiles/PDF/lc_apmaths_sy.pdf


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*easons you should consider doing applied maths

+rom rendan Doheny

Many students study Applied Maths !or the bene!it o! their !uture maths results-

'hese are students ho are chasing the bonus C points in honours Maths and ho ill !ind maths easier

as a result o! studying Applied Maths-

Apart !rom being a terri!ic sub+ect 4hich takes ork6 like any other56 about o! J in e"ery EG students

ill achie"e an AE-

Some uni"ersities 4like *))5 are accepting a )E in either Maths $( Applied Maths-

Many students study Applied Maths to impro"e their problem sol"ing skills and so produce better HPA'

results to ensure they get into medicine-

'he single greatest obstacle !or engineering students is passing Applied Maths in college 3 not a problem

!or those ho studied it in school-

'he te#t in Italics is taken !rom quotes gi"en to The Irish Applied Maths Teachers Association (iamta.ie

Applied maths has a reputation to be compared to Shrek> 'o those that don9t kno the beast it seems like a

big ugly ogre6 but really it is quite a lean course-

As fe! schools offer Applied Maths as a scheduled class" most that ta#e it on do so outside of school hours.

This can be stressful and tiring at first but the end result is !orth an$ hardships suffered.

'here are EG questions on the paper and the candidate has only to anser si# questions-

K$ other paper o!!ers this much choice-

%etting the actual correct ans!er onl$ gives $ou a small amount of the mar#s.

In total the recall ork is minimal possibly JG !ormulae in total and the o"erlap beteen the courses less

than hal! are unique to Applied Maths Syllabus

Applied Maths !as m$ favourite sub&ect at school. It !as a course completel$ unli#e an$ other. Lateral

and logical thin#ing are needed for it and solving problems is something I have al!a$s been interested in.

The sub&ect doesnt involve enormous amounts of theor$ that $ou have to learn off b$ heart" li#e in biolog$"

but &ust encourages $ou to thin# and appl$ principles.

Is there any sub+ect that you struggle ith6 any language that you ill only manage to do ordinary le"el in?

'hen Applied Maths can help you make your points higher>

Although no points in the Leaving Cert ever come eas$" the Applied Maths e'aminers love to give a!a$

mar#s for !riting do!n basic information and appl$ing simple rules. Applied Maths ma$ seem li#e a tough

sub&ect at first" but given a little time and a good bit of practice it becomes a tremendousl$ satisf$ing andre!arding sub&ect.

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APP(I)D MAT#)MATI,- -yllabus

'rdinary and #igher (e$el ,ourses

noledge o! the rele"ant parts o! the Mathematics course is assumed-

K-;- 'hose parts o! the syllabus hich are printed in italicsbelong to the Higher %e"el course only-

'he Higher %e"el course includes the $rdinary %e"el course treated in greater depth-

E- Motion o! a particle- Displacement6 "elocity as "ectors- Applications o! the "ector addition la-

Description o! "ectors in terms o! unit perpendicular "ectors- 7lementary treatment o! relati"e motion-

- Keton9s las- Mass6 momentum- Acceleration and !orce as "ectors- *nits and dimensions-

J- Motion in a straight line under uni!orm acceleration e-g- motion under gra"ity6 motion on smooth and

rough inclined planes- Work6 potential energy6 kinetic energy6 poer- Application o! energy

conser"ation- Motion o! connected particles-

1- 7quilibrium o! a particle under concurrent !orces6 including !riction-

C- )entre o! gra"ity o! simple bodies and systems o! particles Moments and couples- 7quilibrium o! a rigid

body or bodies.

N- %iquid pressure- 'hrust on a horiontal sur!ace- Archimede9s Principle-

F- Pro+ectiles-+ro&ectiles on inclined plane.

@- Angular "elocity- *ni!orm motion in a circle ithout gra"itational !orces- )onical pendulum- )ircular

orbits-

- )onser"ation o! momentum- )ollisions- Direct collisions6 elastic 4G O e E5 and inelastic 4e Q o5-

4bliue collisions of smooth elastic spheres in t!o dimensions.

EG- *imple harmonic motion of a particle in a straight line. (Application of simple harmonic motion to

include the simple pendulum-5

55. Motion of a rigid bod$ about a fi'ed a'is6

a. Calculation of moments of inertia for a rod" rectangular lamina" circular lamina and compound

bodies formed of those. (*phere is e'cluded. Application of parallel and perpendicular a'estheorems" !ith proofs done as class!or#. Idea of radius of g$ration. Application of the conservation

of energ$ principle to a rotating bod$.

b- 4b5Application of the principle of angular momentum6 rate of change of angular momentum about

a fi'ed a'is euals the total e'ternal moment about that a'is. Compound pendulum. *imple

applications.

57. 4rdinar$ differential euations and applications6

(a first order" variables separable8

(b *econd order reducing to t$pe

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In conclusion

Applied Maths is not an easy sub+ect6 but it is a onder!ully rearding sub+ect to take on i! you are good at

maths and en+oy challenging yoursel!- It is interesting6 challenging6 educational6 and it is good !or careers-

applied maths: whats it all about?

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