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Department of Mathematics
MATHS 108 Assignment 1 Due: 4pm, Wednesday March 30st
Hand your completed assignment in to the correct box in the Student Resource Centre (G38 Building 301) before the due date. Please
use a Mathematics Department cov
MATHS 363
THE UNIVERSITY OF AUCKLAND
FIRST SEMESTER, 2015
Campus: City
MATHEMATICS
Advanced Modeling and Computation
(Time allowed: 2.0 hours)
NOTE: Do all questions. Calculators are not permitted. Show your working. Total marks 60.
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MATHS 363
DEPARTMENT OF MATHEMATICS
MATHS 190
Tutorial 9
Tutorials in Maths 190 are collaborative tutorials. You should work in groups of 2 or
3 students, discussing the situations and puzzles listed below, or issues arising from
lectures. Part of your final mark d
DEPARTMENT OF MATHEMATICS
MATHS 190
Tutorial 6
Tutorials in Maths 190 are collaborative tutorials. You should work in groups of 2 or 3 students,
discussing the situations and puzzles listed below, or issues arising from lectures. Part of your final
mark d
DEPARTMENT OF MATHEMATICS
MATHS 190
Lecture 1 Summary
In this lecture we illustrate two important observations:
Mathematics involves logical and creative thinking.
Thinking can be fun.
In Lecture 1 there are two main examples
Dodge Ball. Instructions fo
DEPARTMENT OF MATHEMATICS
MATHS 190/190G
Tutorial 4
Tutorials in Maths 190 are collaborative tutorials. You should work in groups
of 3 or 4 students, discussing the situations and questions listed below, or issues arising
from lectures. Part of your final
Department of Mathematics
MATHS 190/190G
Assignment 1
Due: 4pm, March 30th
Hand your completed assignment in to the correct box in the Student Resource Centre (G402
Building 301) before the due date. Please use a Mathematics Department cover sheet availab
Department of Mathematics
MATHS 190/190G
Assignment 2
Due: 4pm, Tuesday 3 May
Hand your completed assignment in to the correct box in the Student Resource Centre (G38
Building 301) before the due date. Please use a Mathematics Department cover sheet avail
DEPARTMENT OF MATHEMATICS
MATHS 190
Tutorial 8
Tutorials in Maths 190 are collaborative tutorials. You should work in groups of 2 or
3 students, discussing the situations and puzzles listed below, or issues arising from
lectures. Part of your final mark d
DEPARTMENT OF MATHEMATICS
MATHS 190/190G
Tutorial 3
Tutorials in Maths 190 are collaborative tutorials. You should work in groups of 2 or
3 students, discussing the situations and puzzles listed below, or issues arising from lectures.
Part of your final m
DEPARTMENT OF MATHEMATICS
MATHS 190/190G
Tutorial 2
Tutorials in Maths 190 are collaborative tutorials. You should work in groups of 2 or
3 students, discussing the situations and puzzles listed below, or issues arising from lectures.
Part of your final m
DEPARTMENT OF MATHEMATICS
MATHS 190/190G
Tutorial 1
Tutorials in Maths 190 are collaborative tutorials. You should work in groups of 3 or
4 students, discussing the situations and puzzles listed below, or issues arising from lectures.
Part of your final m
Solutions to the exercises of Chapter 3
Exercises of Section 3.1
1.
Since the space is infinitely-dimensional we cannot find eigenvalues using the
characteristic polynomial. But it is easy to find eigenvectors. Let f (x) = a0 + a1 x + . . . +
an xn with a
Decomposed Graph
This shows 3 features:
1) The Time Series Plot (you have already
discussed the Raw Data AND the Trend!)
2) Seasonal effects
3) Residuals
millions of litres
Now, get your decomposed graph for Visitors to NZ
Seasonal effects seasonal variat
13. EQUATIONS AND IDENTITIES 2, Factorj'ze the following:
EXERCISE 13A Meaning ofldentities
(a) 2x2 w 8
1. State whether the foifowing retations are an equation or . 2
. . (b) 3.3 27'
an Identity. 2
(a) x“—i=(x—I)(x+1){x3+1) (0)83 ~3
(b) X2+2X+3=4x
(c) 2(
9. Make p the subject of the formula xjp + 1) = M
8. USE OF FORMULAE
1‘ Subject of Formulae
ke h the subject of the formula.
EXERCISE 8A Change 0
1. H 721: 6(1) + C), express 317a in terms of b and c. 10' Ma E2 1_ k
x - r - - T = me2 1 + h 1
2 In the form
12. SIMULTANEOUS LINEAR EQUATIONS IN TWO UNKNOWNS
EXERCISE 12A Revision of Linear Equations in one unknown
1- Solve the foﬁowing equations: 3. If 2;: — 1 is a factor of 4x2+ kx — 1, than k =
(1) 1—73- 1»% (2) 1343213 4. Ifx+3isafactorofx2+6x+k,thenk=
2 9
d the amount at simple inte-
12. Find the simple interest an
rest of $23000 for 2 years at 12% pa.
1 is $500 the simple interest at 15% p.21.
11. USING PERCENTAGE
EXERCISE 11A Profit and Loss
1. Find the simple interest rate for a sum to three times i
Symptoms:
Pollution - With mounting evidence that diesel exhaust poses major health hazards,
Diesel-powered vehicles and equipment account for nearly half of all nitrogen oxides
(NOx), reducing diesel pollution has become a public priority.(according to U
Optimise
Department of
Information Systems
Operations Management
Create Wealth
Generate Value
Innovate
Watch: Steve Jobs' 2005 Stanford Commencement Address https:/youtu.be/UF8uR6Z6KLc
Sustain
Read: Course overview in the Course Book
Transform
Learning Ou
MECHENG 712 AEROHYDRODYNAMICS 2013
1
2. Fluid Flow Equations and 2D Flow: Problem Sheet
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
In relation to conservation of mass, sketch how you might expect the product u to vary in the x direction
across
Inner Products and
Orthogonality
5.1 Orthogonal and orthonormal bases
Read Section 62857.9 Contemporary Linear Algebra ANTON
8; BUSBY, pages 280294&406416
For assignment/test practise do ex 14&16.
Denition 5.1. (a) A basis {V1, V2, ., vn} of an n-
Futures
FIN 261
Lecture Notes Ch. 17
1
Forward Market
Spot markets are markets for immediate delivery
A spot price refers to the current market price of the
underlying asset
Forward markets are markets for deferred delivery
An agreement or commitment to b
Bonds
FIN 261
Lecture Notes Ch. 10, 11
1
Bond
Bond
Security that obligates issuer to make payments to
holder over time
Face Value, Par Value
Payment to bondholder at maturity of bond
Coupon Rate
Bonds annual interest payment per dollar of par
value
Index Model and APT
FIN 261
Lecture Notes Ch. 7
1
Single Index (Factor) Model
IndexModel:amodelofsecurityreturnsusingan
indexsuchastheS&P500torepresentcommonor
systematicrisk(factor)
Eachstockjreturnfluctuateswiththesinglefactor,
typicallyabroadmarketin
Math and Stats Review
FIN 261
1
Random Variable
Variablewhosevalueissubjectto
variationsduetochance
Examples:
Returnfromariskyinvestment
Payofffromagameinwhichyou
chooseonecaseoutoftwo
containingeithernothingor1million
dollars
Mostcommonlyusedmeasuresto
s