## MATH104 Supplementary Calculus 2

First Semester | Also available: Second Semester |

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

This 9-point half-paper covers methods and applications of calculus, building on MATH 160/102. It consists of the calculus component of MATH 170. However, it is not by itself a sufficient foundation for second-year calculus (MATH 203, COMO 202) - for these papers, MATH 170 is required.

### Paper details

This paper extends some of the topics covered in MATH 160, and introduces others that are new. It starts with sequences (an ordered list of numbers, possibly infinite) and series (the sum of all the numbers in a sequences). The course then introduces special functions such as the natural logarithm, hyperbolic functions, and inverse trigonometric and hyperbolic functions. After further methods of integration and applications of integration to arclength and volumes, the course concludes with the study of differential equations (and examples of their many uses).

### Potential students

MATH 104 is taken only by students who need the calculus component (but not the algebra) of MATH 170. This situation may arise when a student has transferred from another university, or is majoring in another subject which requires a knowledge of calculus but not the same level of algebra.

### Prerequisites

MATH 160 or MATH 102 or high achievement (mostly Excellences and Merits) in NCEA Level 3 Mathematics with Calculus

### Main topics

- Review of trigonometry and basic calculus
- Sequences, series and Taylor series
- Natural log, exponential, hyperbolic, inverse trigonometric and hyperbolic functions
- Methods of integration
- Arc length; volumes and surfaces of revolution
- Solving differential equations

### Text

Course materials will be available on the resource page. The book *MATH 170 Calculus Outline Notes* is available for purchase from the Print Shop.

Recommended text: *Calculus* by James Stewart, metric version, 8th edition (available from the University Book Shop). Older editions of this textbook are perfectly good.

### Useful references

Several standard texts are suitable for reference. For example:

*Calculus with Analytic Geometry*by Howard Anton (Wiley)*Calculus and Analytic Geometry*by George Thomas and Ross Finney (Addison Wesley)

### Lecturer (Semester 1)

Dr Richard Norton (Room 513)

### Lectures (Semester 1)

Tuesday, Thursday and alternate Fridays at 12 noon

### Tutorials

Attendance at tutorials is voluntary. An open system operates: tutorial classes run for up to 10 hours per week (depending on demand), and students may attend as many as they need to and are able to.

### Internal Assessment

Five computer Skills Tests make up 20% of your final mark. The other 80% comes from a mix of your final exam mark and the assignment mark which is based solely on the ten marked weekly assignments.

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:

- achieve an overall mark of at least 40% on the 10 assignments

### 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 about 15 questions.

### Final mark

So your internal assessment counts at 1/5 weighting if that helps you.