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Suspension bridges

The main cable of a suspension bridge naturally forms a curve called a catenary. When it is loaded with the horizontal road structure it deforms into a parabola. Unless very carefully designed, suspension bridges are susceptible to collapse from high winds or earthquakes.




Sample problem

Let N be the number of individuals in a population. One model for studying N says that the rate of increase of N depends on both N itself (since the more individuals there are the more offspring will be produced) and on some residual amount M - N (since there will be competition for resources like food); so we have
for some constant M.
Will the population die out or reach some maximum value?




Gottfried Leibniz, 1646-1716, was one of the developers of calculus — the other was Isaac Newton. They used different approaches, and different notation. Leibniz also was a pioneer of mathematical logic.

MATH102 Supplementary Calculus 1

First Semester, Second Semester, 9 points

Introduction

This 9-point half-paper covers methods and applications of calculus. It consists of the calculus component of MATH 160. Note that to go on to MATH 170, you will need both MATH 101 and MATH 102 - or their equivalent, MATH 160.

Paper details

This calculus paper is the natural continuation of 7th Form Mathematics.

Here you will study the ideas and methods of differentiation and integration, using an approach that is intuitive and avoids excess formality. Applications will include optimization, related rates, the use of differentials, finding areas, the Taylor series, solving simple differential equations, and an introduction to partial derivatives.

Potential students

MATH 102 is taken only by students who need the calculus component (but not the algebra) of MATH 160. This situation may arise when a student has transferred from another university, or is looking for a 9-point paper, or has previously taken the algebra half.

Main topics

  • Functions
  • Introduction to calculus
  • Techniques of differentiation and integration

Prerequisites

None

Required text

Calculus by James Stewart (Truncated edition)
(Available from the University Book Shop.)

Useful references

Several standard texts are suitable for reference. For example:

Calculus with Analytic Geometry by Howard Anton (Wiley)
Calculus by James Stewart (Full edition.)

Lecturers

Semester 1: Dr Mihály Kovács (room 212) and Dr Dennis McCaughan (room 218)
Semester 2: Dr Mihály Kovács (room 212) and Dr Dennis McCaughan (room 218)

Lectures

Approximately 25 lectures, Tues and Thurs.
In the first semester there are two streams, 8 am and 12 noon; in the second semester there is a single stream at 12 noon.

Tutorials

Attendance at tutorials is voluntary. An open tutorial system operates where classes run for 8 hours per week, and students may attend as many as they need to and are able to.

Internal Assessment

There are ten marked assignments which make up your internal assessment mark.
Five computer Skills Tests together make up 33.3% of your final mark.

You can check your marks by clicking on the Resources link at the top of this page.

Terms Requirement

You have to fulfil the terms requirement in order to be allowed to sit the final exam. In this paper, to pass “terms” you need to gain at least 5/10 in each of the first four Skills Tests.

Exam format

The 90-minute final exam is answered in spaces provided on the question booklet. All questions should be attempted and the number of marks available for each question is indicated on the paper. There are usually from 15 to 20 questions.

Past exams are available for download from the MATH160 resource page.

Final mark

The final mark F is calculated from:
F = max { E, (3E + A)/4 } + T
where E (exam mark) is out of 66.7, A (internal assessment) is out of 66.7, T (test mark) is out of 33.3.

The “max” corresponds to plussage: if your internal assessment mark is greater than your exam mark then it is combined in the proportion shown. If it is less then it is ignored and the exam mark itself is used.

So your internal assessment can boost your exam mark with a 1/4 weighting if that helps you. Note that the test component definitely counts and so the tests should be regarded as compulsory.

Plagiarism

Students should make sure that all submitted work is their own. “Plagiarism is a form of dishonest practice. Plagiarism is defined as copying or paraphrasing another’s work and presenting it as one’s own” (University of Otago Calendar). In practice this means that plagiarism includes any attempt in any piece of submitted work (e.g. an assignment or test) to present as one’s own work the work of another (whether of another student or a published authority). Any student found to be responsible for plagiarism in any piece of work submitted for assessment shall be subject to the University’s dishonest practice regulations which may result in various penalties, including forfeiture of marks for the piece of work submitted, a zero grade for the paper, or in extreme cases exclusion from the University. The University of Otago reserves the right to use plagiarism detection tools.

While we strive to keep details as accurate and up-to-date as possible, information given here should be regarded as provisional. Individual lecturers will confirm teaching and assessment methods.