MATH103-19S2 (C) Semester Two 2019

# Mathematics 1B

15 points

Details:
 Start Date: Monday, 15 July 2019 End Date: Sunday, 10 November 2019
Withdrawal Dates
Last Day to withdraw from this course:
• Without financial penalty (full fee refund): Friday, 26 July 2019
• Without academic penalty (including no fee refund): Friday, 27 September 2019

## Description

A consolidation of concepts from MATH102 and introduction to more advanced ideas in calculus and linear algebra. It is a prerequisite for many courses in mathematics and other subjects at 200-level.

MATH103 deals with techniques and ideas in calculus and algebra, and their relationships to geometry. It is designed mainly for students who have passed MATH102, and who need at least 30 points of Mathematics at the 100 level. After passing MATH103, you will be able to enrol in any 200-level mathematics course.

Topics: differential equations, sequences and mathematical induction, series and approximation, vectors and geometry, determinants, eigenvalues and eigenvectors, curves and surfaces.

## Learning Outcomes

• Students who have succeeded in this course should be able to:

Define the key concepts associated with:
• differential equations,
• convergence of sequences,
• Taylor polynomials and series,
• vectors in two and three dimensions,
• determinants, eigenvalues and eigenvectors,
• curves and surfaces.

Use techniques from the course (including the use of computer-based tools where appropriate) to:
• solve elementary first or second order differential equations.
• prove simple statements using the principle of mathematical induction,
• test sequences or series for convergence,
• find Taylor polynomials and use them to solve problems involving limits or approximation,
• describe and solve geometric problems using vectors,
• find the eigenvalues and eigenvectors of small matrices,
• parameterise and analyse curves in Cartesian and polar coordinates,
• analyse surfaces by finding their slopes and relative extrema.

Describe and interpret:
• the solutions of differential equations in a variety of contexts,
• infinite sequences and series, their limits and applications,
• the connection between vectors and the geometry of lines and planes,
• curves and surfaces and their key properties.

Identify the appropriate method of solution for differential equations.

Synthesise appropriate techniques from different sections of the course, for example combining techniques of sequences and differential equations to determine long term behaviour, or combining vector geometry with curves and surfaces.

## Restrictions

MATH109, MATH199, EMTH119

## Course Coordinator

For further information see Mathematics and Statistics Head of Department

## Textbooks / Resources

Stewart, James: Calculus Early Transcendentals. 8th edition. ISBN: 9781305272378

## Indicative Fees

Domestic fee \$764.00

International fee \$4,000.00

* All fees are inclusive of NZ GST or any equivalent overseas tax, and do not include any programme level discount or additional course-related expenses.

For further information see Mathematics and Statistics .

## All MATH103 Occurrences

• MATH103-19S1 (C) Semester One 2019 - Not Offered
• MATH103-19S2 (C) Semester Two 2019