 MATH103-18S2 (C) Semester Two 2018

# Mathematics 1B

15 points

Details:
 Start Date: Monday, 16 July 2018 End Date: Sunday, 18 November 2018
Withdrawal Dates
Last Day to withdraw from this course:
• Without financial penalty (full fee refund): Friday, 27 July 2018
• Without academic penalty (including no fee refund): Friday, 12 October 2018

## 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 algebra, calculus and statistics. 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: vectors and geometry, eigenvalues and eigenvectors, sequences and mathematical induction, series and approximation, techniques and applications of integration, differential equations, probability.

## Learning Outcomes

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

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

Use techniques from the course (including the use of MAPLE where appropriate) to:
• solve problems involving dot or cross products of vectors,
• find the eigenvalues and eigenvectors of small matrices,
• 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,
• evaluate integrals involving trigonometric functions or rational functions,
• solve elementary first or second order differential equations,
• calculate means and variances of probability distributions.

Describe and interpret:
• the connection between vectors  and the geometry of lines and planes,
• the solutions of differential equations in a variety of contexts,
• the meaning of a random variable in a variety of contexts.

Identify the appropriate method of solution for differential equations and integrals.

Synthesise appropriate techniques from different sections of the course, for example, combining techniques of integration and skill at limit evaluation to determine improper integrals.

This course will provide students with an opportunity to develop the Graduate Attributes specified below: Critically competent in a core academic discipline of their award Students know and can critically evaluate and, where applicable, apply this knowledge to topics/issues within their majoring subject.

## 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