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

## 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.