## 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.

### 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

Your final mark F in the paper will be calculated according to this formula:

**F = max(0.6E + 0.25A, 0.75E + 0.1A) + 0.1Q + 0.05T**

where:

- E is the Exam mark
- A is the Assignments mark
- Q is the Quizzes mark
- T is the Tutorials mark

and all quantities are expressed as percentages.

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.

### Students must abide by the University’s Academic Integrity Policy

**Academic integrity** means being honest in your studying and assessments. It is the basis for ethical decision-making and behaviour in an academic context. Academic integrity is informed by the values of honesty, trust, responsibility, fairness, respect and courage.

**Academic misconduct** is seeking to gain for yourself, or assisting another person to gain, an academic advantage by deception or other unfair means. The most common form of academic misconduct is plagiarism.

Academic misconduct in relation to work submitted for assessment (including all course work, tests and examinations) is taken very seriously at the University of Otago.

All students have a responsibility to understand the requirements that apply to particular assessments and also to be aware of acceptable academic practice regarding the use of material prepared by others. Therefore it is important to be familiar with the rules surrounding academic misconduct at the University of Otago; they may be different from the rules in your previous place of study.

Any student involved in academic misconduct, whether intentional or arising through failure to take reasonable care, will be subject to the University’s Student Academic Misconduct Procedures which contain a range of penalties.

If you are ever in doubt concerning what may be acceptable academic practice in relation to assessment, you should clarify the situation with your lecturer before submitting the work or taking the test or examination involved.

Types of academic misconduct are as follows:

**Plagiarism**

The University makes a distinction between unintentional plagiarism (Level One) and intentional plagiarism (Level Two).

- Although not intended,
*unintentional plagiarism*is covered by the Student Academic Misconduct Procedures. It is usually due to lack of care, naivety, and/or to a lack to understanding of acceptable academic behaviour. This kind of plagiarism can be easily avoided. *Intentional plagiarism*is gaining academic advantage by copying or paraphrasing someone elses work and presenting it as your own, or helping someone else copy your work and present it as their own. It also includes self-plagiarism which is when you use your own work in a different paper or programme without indicating the source. Intentional plagiarism is treated very seriously by the University.

**Unauthorised Collaboration**

Unauthorised Collaboration occurs when you work with, or share work with, others on an assessment which is designed as a task for individuals and in which individual answers are required. This form does not include assessment tasks where students are required or permitted to present their results as collaborative work. Nor does it preclude collaborative effort in research or study for assignments, tests or examinations; but unless it is explicitly stated otherwise, each students answers should be in their own words. If you are not sure if collaboration is allowed, check with your lecturer..

**Impersonation**

Impersonationis getting someone else to participate in any assessment on your behalf, including having someone else sit any test or examination on your behalf.

**Falsiﬁcation**

Falsiﬁcationis to falsify the results of your research; presenting as true or accurate material that you know to be false or inaccurate.

**Use of Unauthorised Materials**

Unless expressly permitted, notes, books, calculators, computers or any other material and equipment are not permitted into a test or examination. Make sure you read the examination rules carefully. If you are still not sure what you are allowed to take in, check with your lecturer.

**Assisting Others to Commit Academic Misconduct**

This includes impersonating another student in a test or examination; writing an assignment for another student; giving answers to another student in a test or examination by any direct or indirect means; and allowing another student to copy answers in a test, examination or any other assessment.

### 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?