# MATH170 Mathematics 2

This paper is divided between algebra and calculus components. The algebra component covers vectors, matrices, linear transformations, eigenvalues and introduces aspects of discrete mathematics. The calculus component covers sequences and series, inverse trigonometric and hyperbolic functions, advanced integration techniques, differential equations and their applications.

If you want to know which of MATH 151, MATH 160 or MATH 170 is best for you, check out the information and placement tools at 'Which MATH 100-level paper should I take?'

Algebra and Calculus form the basic tools used to produce most mathematical frameworks for modelling quantifiable phenomena. For example, to model the movement of an object through space we need first to create an algebraic structure in which to specify where our object is, and then we can study how that position changes with time (i.e. its movement) using calculus.Many other problems arising in areas such as Economics or Chemistry, can be examined in a mathematical way using the same basic ideas. For example, we may need to minimise a manufacturing cost or the time for a chemical reaction to take place or the effects of river pollution; in each case the techniques used for the minimisation are based on a mixture of algebra and calculus theories.

This paper aims to develop skills with these tools both for use in other subjects and in preparation for further study of Mathematics.

MATH 170 is the natural continuation of MATH 160 and provides the basis for progression to 200-level Mathematics, as well as a good mathematical background to support other subjects.

Paper title Mathematics 2 MATH170 Mathematics 0.15 18 points Semester 1 (On campus) Semester 2 (On campus) \$913.95 \$4,073.40
Restriction
MATH 103, MATH 104
Recommended Preparation
MATH 160 or (MATH 101 and MATH 102)
Schedule C
Arts and Music, Science
Notes
This paper assumes material covered in MATH160 and provides essential preparation for 200-level mathematics. Students with excellent results in Year 13 mathematics are able to enrol in MATH170 without first taking MATH160.
Eligibility
This paper should appeal to a wide variety of students, including Mathematics and Statistics majors or those studying Computer Science, Physics, Chemistry, Surveying, Biological Sciences, Genetics or other disciplines with a quantitative component requiring competent manipulation of mathematical formulae and interpretation of mathematical representations of systems.
Contact
maths@otago.ac.nz
Teaching staff

Teaching staff to be advised

Paper Structure
Main topics:

Algebra:
• Algebra and geometry of 3-dimensional vectors
• Manipulation of matrices and matrix equations
• Introduction to linear transformations
• Eigenvalues and eigenvectors
• Discrete mathematics, including mathematical induction, Diophantine equations and basic counting techniques
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
Teaching Arrangements
Five lectures a fortnight in Algebra and five lectures a fortnight in Calculus
Cafeteria-style (voluntary) weekly tutorials
Textbooks

Algebra:
Course materials will be available on the resource page. A book of MATH 170 Algebra Outline Notes is available free online, and a bound, printed copy is available for purchase from the Print Shop.

Calculus:
Course materials will be available on the resource page. A book of MATH 170 Calculus Outline Notes is available free online, and a bound, printed copy is available for purchase from the Print Shop.

Supplementary text (optional), by James Stewart, metric edition 7e (available from the Book Store)

Useful references: Several standard texts are suitable for reference. For example:

• Elementary Vector Algebra by A.M. MacBeath
• Algebra, Geometry and Trigonometry by M.V. Sweet
• Elementary Linear Algebra (Applications version) by H. Anton and C. Rorres (7th edition)
• Introductory Linear Algebra (with applications) by B. Kolman (6th edition)
• Calculus with Analytic Geometry by Howard Anton (Wiley)
• Calculus and Analytic Geometry by George Thomas and Ross Finney (Addison Wesley)
Course outline
View course outline for MATH 170
Interdisciplinary perspective, Critical thinking.
Learning Outcomes

Students who successfully complete this paper will demonstrate in-depth understanding of the central concepts and theories.

## Timetable

### Semester 1

Location
Dunedin
Teaching method
This paper is taught On Campus
Learning management system
Other

#### Lecture

Stream Days Times Weeks
Attend
A1 Monday 12:00-12:50 9-13, 15-16, 18-22
Tuesday 12:00-12:50 9-13, 15-22
Wednesday 12:00-12:50 9-13, 15-22
Thursday 12:00-12:50 9-13, 15-22
Friday 12:00-12:50 9-12, 15-22

#### Tutorial

Stream Days Times Weeks
Attend one stream from
A1 Wednesday 14:00-14:50 10-13, 15-22
A2 Thursday 14:00-14:50 10-13, 15-22

### Semester 2

Location
Dunedin
Teaching method
This paper is taught On Campus
Learning management system
Other

#### Lecture

Stream Days Times Weeks
Attend
A1 Monday 12:00-12:50 28-34, 36-41
Tuesday 12:00-12:50 28-34, 36-41
Wednesday 12:00-12:50 28-34, 36-41
Thursday 12:00-12:50 28-34, 36-41
Friday 12:00-12:50 28-34, 36-41

#### Tutorial

Stream Days Times Weeks
Attend one stream from
A1 Wednesday 13:00-13:50 29-33, 36-40
A2 Wednesday 14:00-14:50 29-33, 36-40
A3 Thursday 13:00-13:50 29-33, 36-40
A4 Thursday 14:00-14:50 29-33, 36-40