MATH101-21S1 (C) Semester One 2021

# Methods of Mathematics

15 points

Details:
 Start Date: Monday, 22 February 2021 End Date: Sunday, 27 June 2021
Withdrawal Dates
Last Day to withdraw from this course:
• Without financial penalty (full fee refund): Sunday, 7 March 2021
• Without academic penalty (including no fee refund): Friday, 14 May 2021

## Description

Introduction to calculus, trigonometry and algebra. Emphasis on setting up mathematical models of problems, solving them and interpreting the solutions. Applications to the physical, life and earth sciences as well as to commerce and the humanities.

MATH101 covers the basic ideas of functions and their graphs, trigonometry, limits, and calculus. We introduce the concept of a mathematical model and discuss setting up mathematical models to solve problems. Examples are drawn from the physical, life and earth sciences as well as commerce and the humanities. Skills are practised in lectures, weekly tutorial sessions, and using online learning software.

Emphasis is placed on understanding through examples, and you will use the methods taught to study a variety of practical problems. In the process your algebra and calculus skills will improve, and you will gain insight into the usefulness of these techniques. The course aims to build your confidence and foster your enjoyment of mathematics.

MATH101 is for students who need some knowledge of mathematics to support other studies such as the earth and life sciences, and for students who wish to prepare for EMTH118 or MATH102. The recommended background for this course is NCEA Level 2 Mathematics or equivalent.

## Learning Outcomes

• A student who successfully completes this course will:

• understand the rules of exponents
• be able to use basic algebra to simplify expressions and rearrange equations
• be able to solve both linear and non-linear equations
• understand the concept of a function, and recognise and use function notation and operations
• be able to identify, graph and interpret polynomial, exponential, logarithmic and trigonometric relationships in both mathematical and real world contexts using appropriate applications
• be able to find the derivative and integral of polynomial, exponential, logarithmic, and trigonometric functions, including the use of product, quotient and chain rules
• understand the relationship between the processes of integration and differentiation
• be able to identify when a derivative is an appropriate mathematical model, and use it to solve optimisation problems
• be able to identify when an integral is an appropriate mathematical model, and to use it to solve appropriate real world problems
• have the ability to express mathematics in written form to communicate mathematical ideas and solutions to problems

## Timetable 2021

Students must attend one activity from each section.

Activity Day Time Location Weeks Lecture A 01 Monday 10:00 - 11:00 C1 Lecture Theatre 22 Feb - 4 Apr 3 May - 6 Jun 02 Monday 15:00 - 16:00 Rehua 005 22 Feb - 7 Mar Lecture B 01 Tuesday 09:00 - 10:00 C1 Lecture Theatre 22 Feb - 4 Apr 26 Apr - 6 Jun 02 Tuesday 11:00 - 12:00 E7 Lecture Theatre 22 Feb - 7 Mar Lecture C 01 Wednesday 11:00 - 12:00 C1 Lecture Theatre 22 Feb - 4 Apr 26 Apr - 6 Jun 02 Wednesday 13:00 - 14:00 E9 Lecture Theatre 22 Feb - 7 Mar Lecture D 01 Thursday 09:00 - 10:00 C1 Lecture Theatre 22 Feb - 4 Apr 26 Apr - 6 Jun 02 Thursday 11:00 - 12:00 E7 Lecture Theatre 22 Feb - 7 Mar Tutorial A 01 Wednesday 08:00 - 10:00 Jack Erskine 038 Lab 4 22 Feb - 4 Apr 26 Apr - 6 Jun 02 Friday 14:00 - 16:00 Jack Erskine 038 Lab 4 22 Feb - 28 Mar 26 Apr - 6 Jun 03 Wednesday 13:00 - 15:00 Jack Erskine 035 Lab 2 22 Feb - 4 Apr 26 Apr - 6 Jun 04 Wednesday 13:00 - 15:00 Jack Erskine 038 Lab 4 22 Feb - 4 Apr 26 Apr - 6 Jun 05 Wednesday 15:00 - 17:00 Jack Erskine 038 Lab 4 22 Feb - 4 Apr 26 Apr - 6 Jun 06 Wednesday 15:00 - 17:00 Jack Erskine 035 Lab 2 22 Feb - 4 Apr 26 Apr - 6 Jun 07 Friday 08:00 - 10:00 Jack Erskine 038 Lab 4 22 Feb - 28 Mar 26 Apr - 6 Jun 08 Wednesday 08:00 - 10:00 Jack Erskine 033 Lab 1 22 Feb - 4 Apr 26 Apr - 6 Jun 09 Thursday 10:00 - 12:00 Jack Erskine 038 Lab 4 22 Feb - 4 Apr 26 Apr - 6 Jun 10 Thursday 12:00 - 14:00 Jack Erskine 038 Lab 4 22 Feb - 4 Apr 26 Apr - 6 Jun 11 Thursday 14:00 - 16:00 Jack Erskine 038 Lab 4 22 Feb - 4 Apr 26 Apr - 6 Jun 12 Wednesday 13:00 - 15:00 Jack Erskine 033 Lab 1 22 Feb - 4 Apr 26 Apr - 6 Jun 13 Friday 12:00 - 14:00 Jack Erskine 033 Lab 1 22 Feb - 28 Mar 26 Apr - 6 Jun 14 Friday 08:00 - 10:00 Jack Erskine 035 Lab 2 22 Feb - 28 Mar 26 Apr - 6 Jun 15 Thursday 16:00 - 18:00 Jack Erskine 033 Lab 1 22 Feb - 4 Apr 26 Apr - 6 Jun 16 Friday 14:00 - 16:00 Jack Erskine 033 Lab 1 22 Feb - 28 Mar 26 Apr - 6 Jun 17 Friday 10:00 - 12:00 Jack Erskine 038 Lab 4 22 Feb - 28 Mar 26 Apr - 6 Jun 18 Friday 12:00 - 14:00 Jack Erskine 038 Lab 4 22 Feb - 28 Mar 26 Apr - 6 Jun 19 Wednesday 15:00 - 17:00 Jack Erskine 033 Lab 1 22 Feb - 4 Apr 26 Apr - 6 Jun 20 Friday 09:00 - 11:00 Jack Erskine 033 Lab 1 22 Feb - 28 Mar 26 Apr - 6 Jun 21 Thursday 13:00 - 15:00 Jack Erskine 035 Lab 2 22 Feb - 4 Apr 26 Apr - 6 Jun Workshop A 01 Monday 12:00 - 13:00 Jack Erskine 242 22 Feb - 4 Apr 3 May - 6 Jun 02 Monday 16:00 - 17:00 Jack Erskine 241 22 Feb - 4 Apr 3 May - 6 Jun 03 Monday 13:00 - 14:00 Jack Erskine 239 22 Feb - 4 Apr 3 May - 6 Jun 04 Friday 14:00 - 15:00 Psychology - Sociology 251 22 Feb - 28 Mar 26 Apr - 6 Jun 05 Friday 09:00 - 10:00 Jack Erskine 239 22 Feb - 28 Mar 26 Apr - 6 Jun 06 Thursday 14:00 - 15:00 Jack Erskine 239 22 Feb - 4 Apr 26 Apr - 6 Jun 07 Monday 15:00 - 16:00 Psychology - Sociology 411 22 Feb - 4 Apr 3 May - 6 Jun 08 Thursday 13:00 - 14:00 Jack Erskine 239 22 Feb - 4 Apr 26 Apr - 6 Jun 09 Friday 12:00 - 13:00 Jack Erskine 241 22 Feb - 28 Mar 26 Apr - 6 Jun 10 Thursday 10:00 - 11:00 Meremere 409 22 Feb - 4 Apr 26 Apr - 6 Jun 11 Tuesday 10:00 - 11:00 Meremere 409 22 Feb - 4 Apr 26 Apr - 6 Jun 12 Wednesday 10:00 - 11:00 Meremere 409 22 Feb - 4 Apr 26 Apr - 6 Jun 13 Tuesday 11:00 - 12:00 Meremere 409 22 Feb - 4 Apr 26 Apr - 6 Jun 14 Tuesday 12:00 - 13:00 Meremere 409 22 Feb - 4 Apr 26 Apr - 6 Jun 15 Tuesday 16:00 - 17:00 Meremere 409 22 Feb - 4 Apr 26 Apr - 6 Jun 16 Wednesday 09:00 - 10:00 Psychology - Sociology 307 22 Feb - 4 Apr 26 Apr - 6 Jun 17 Monday 08:00 - 09:00 Jack Erskine 240 22 Feb - 4 Apr 3 May - 6 Jun 18 Wednesday 12:00 - 13:00 Psychology - Sociology 411 22 Feb - 4 Apr 26 Apr - 6 Jun 19 Friday 13:00 - 14:00 Jack Erskine 240 22 Feb - 28 Mar 26 Apr - 6 Jun 20 Thursday 16:00 - 17:00 Jack Erskine 235 22 Feb - 4 Apr 26 Apr - 6 Jun 21 Wednesday 13:00 - 14:00 James Logie 105 22 Feb - 4 Apr 26 Apr - 6 Jun 22 Thursday 11:00 - 12:00 Karl Popper 413 22 Feb - 4 Apr 26 Apr - 6 Jun 23 Tuesday 13:00 - 14:00 Jack Erskine 239 22 Feb - 4 Apr 26 Apr - 6 Jun 24 Monday 12:00 - 13:00 Jack Erskine 239 22 Feb - 4 Apr 3 May - 6 Jun 25 Monday 13:00 - 14:00 Jack Erskine 241 22 Feb - 4 Apr 3 May - 6 Jun 26 Tuesday 10:00 - 11:00 Psychology - Sociology 307 22 Feb - 4 Apr 26 Apr - 6 Jun

## Examination and Formal Tests

Activity Day Time Location Weeks Test A 01 Thursday 19:00 - 20:30 C1 Lecture Theatre 29 Mar - 4 Apr 02 Thursday 19:00 - 20:30 C2 Lecture Theatre 29 Mar - 4 Apr 03 Thursday 19:00 - 20:30 C3 Lecture Theatre 29 Mar - 4 Apr 04 Thursday 19:00 - 20:30 E6 Lecture Theatre 29 Mar - 4 Apr 05 Thursday 19:00 - 20:30 E16 Lecture Theatre 29 Mar - 4 Apr

## Assessment

Core Skills Modules 5%
Weekly labs 30%
Workshops 10%
Test 15%
Final Exam 40%

Note: To pass the course you must:
• obtain at least 50% overall; and
• obtain at least 40% on the final exam; and
• pass all five core skills modules (prerequisite content).

## Textbooks / Resources

Barton, David , Cox, David; Essential maths and stats : for higher education; Pearson, 2013.

Croft, Tony , Davison, Robert; Foundation maths; 5th ed; Pearson/Education, 2010.

Haeussler, Ernest F. , Paul, Richard S., Wood, R. J; Introductory mathematical analysis for business, economics, and the life and social sciences; 13th ed; Pearson, 2014.

NCEA Level 2 and 3 textbooks are also a useful reference.