MATH103-17S1 (C) Semester One 2017

# Mathematics 1B

 15 points, 0.1250 EFTS20 Feb 2017 - 25 Jun 2017

## Description

A consolidation of concepts from MATH102 and introduction to more advanced ideas in calculus and linear algebra. It also incorporates some study of statistics. 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 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:

## Restrictions

MATH109, MATH199, EMTH119

## Timetable 2017

Students must attend one activity from each section.

Activity Day Time Location Weeks Lecture A 01 Monday 15:00 - 16:00 A6 Lecture Theatre 20 Feb - 9 Apr 1 May - 4 Jun Lecture B 01 Tuesday 16:00 - 17:00 A4 Lecture Theatre 20 Feb - 9 Apr 1 May - 4 Jun Lecture C 01 Wednesday 11:00 - 12:00 A5 Lecture Theatre 20 Feb - 9 Apr 1 May - 4 Jun Lecture D 01 Thursday 13:00 - 14:00 A5 Lecture Theatre 20 Feb - 9 Apr 1 May - 4 Jun Tutorial A 01 Monday 12:00 - 13:00 Rutherford 533 27 Feb - 9 Apr 1 May - 4 Jun 02 Tuesday 09:00 - 10:00 Erskine 445 27 Feb - 9 Apr 1 May - 4 Jun 03 Wednesday 16:00 - 17:00 Rutherford 533 27 Feb - 9 Apr 1 May - 4 Jun 05 Tuesday 10:00 - 11:00 Erskine 239 27 Feb - 9 Apr 1 May - 4 Jun

## Examination and Formal Tests

Activity Day Time Location Weeks Test A 01 Tuesday 18:30 - 20:00 E9 Lecture Theatre 3 Apr - 9 Apr

## Assessment

Assessment Due Date Percentage
Tutorial Work 5%
Online Quizzes 15%
Test 30%
Final Examination 50%

## Textbooks

Anton, Howard., Bivens, Irl., Davis, Stephen; Calculus: Early Transcendentals; 10th edition; Wiley (9th or 8th edition also suitable).