## MATH102 Supplementary Calculus 1

First Semester | Also available: Second Semester Summer School |

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.

### ***** Not available in 2019! *****

### Paper details

This Calculus paper is the natural continuation of Year 13 Calculus.

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, solving simple differential equations, and the definition of area.

### 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 MATH 101, the Algebra half of MATH 160.

### Prerequisites

Formally MATH 102, like Math160, has no prerequisites other than “sufficient achievement in NCEA Level 3 Calculus”. However, we strongly suggest that if you have not passed the externally assessed NCEA Calculus papers “Apply differentiation methods in solving problems” (AS91578) and “Apply integration methods in solving problems” (AS91579), then you should consider taking MATH 151 before attempting any part of MATH 160.

### Main topics

- Introduction to functions of one variable
- Limits and continuity of functions
- Differentiation of functions and applications
- Integration of functions and applications

### Required texts

Recommended text: *Calculus* by James Stewart (Truncated edition)

(available from the University Book Shop); if you are planning on taking MATH 170, you should consider getting the full *Calculus, metric edition 8*.

### 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 Fabien Montiel (room 514)

### Lectures (Semester 1)

Tues, Thurs and alternate Fridays, 10 am

### Tutorials

You are required to attend one tutorial per week, and they contribute to your final grade. You will be assigned a tutorial time before the beginning of the semester, and changes to these times can be arranged with your tutor.

### Internal Assessment

There are five marked assignments which make up your assignment mark A.

After most lectures there will be an online quiz which must be completed before the beginning of the next lecture. The top 80% of your quiz grades will be used to determine your quiz mark (Q).

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:

- attend at least 5 out of the 10 tutorials
- complete at least 50% of the quizzes.

### Exam format

The 90-minute final exam consists of multiple-choice questions.

### Calculators

Calculators must not be used in the Skills Tests. In the exam, you may use any calculator from List A (Scientific Calculators) of the University of Otago's approved calculators; these are Casio FX82, Casio FX100, Sharp EL531, Casio FX570 and Casio FX95.

### Final mark

This means your internal assessment can boost your exam mark with a 1/4 weighting if that helps you. Notice how important the tests are — to gain terms and for their contribution to the final mark.

### 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 $$\frac{dN}{dt}=N(M-N)$$ for some constant $M$.Will the population die out or reach some maximum value?