# Calculus and Applications 2 KMA652

Hobart

### Introduction

Successful completion of this unit supports your development of Mathematics core knowledge and skills. Through the development of this knowledge and skills you will have the necessary mathematics content and understanding of the nature of Mathematics for contributing to your development as a mathematics teachers.

This unit is a continuation of KMA552 and KMA554, with emphasis on the application of multi-variable calculus and Fourier Series to problems in mathematics, the physical and biological sciences, economics, and engineering.

The calculus section of this unit is focussed on dealing with functions of several variables; the typical case is 𝑧𝑧 = (𝑥𝑥, 𝑦𝑦). Functions like this are important because they describe many of the situations we encounter when applying mathematics to models of the real world. The graph of the function is a surface, and so might be used to describe roof sections; aeroplane wings; temperature, stress, and pressure distributions; income as a function of various expenses; and so on. We need to be able to say how rapidly such a surface curves, and that immediately requires us to do calculus on functions of two (or more) variables. ) , (yxf z  We will also need to consider vectors that are functions of several variables. Some obvious examples of these are the velocity vector in a moving fluid, the heat-flow vector in a solid, and the electric and magnetic fields produced by an antenna. This will lead us to consider more advanced concepts such as circulation, compressibility, divergence, and curl. Understanding this material is fundamental to the study of all areas of Engineering and (continuum) Applied Mathematics, and it underpins modern continuum mechanics and electromagnetic theory. Topics will be introduced in the Cartesian (rectangular) coordinate system but we will also investigate functions, regions, and vectors defined in cylindrical and spherical coordinates.

The Fourier-Series section of this unit is concerned with how to represent periodic functions. We have previously looked at power
series as an infinite sum of terms involving increasing powers of a particular variable. A Fourier series is an infinite sum of terms
involving sine and cosine functions. This is an important concept for solving problems in acoustics, signal processing, heat-flow
theory, fluid mechanics, vibrations, electromagnetic field theory, and so on.

### Summary

Unit name Calculus and Applications 2
Unit code KMA652
Credit points 12.5
Faculty/School College of Sciences and Engineering
School of Natural Sciences
Discipline Mathematics & Physics
Coordinator

Michael Brideson

Available as student elective? No

### Availability

Location Study period Attendance options Available to
Hobart Semester 1 On-Campus Off-Campus International International Domestic Domestic

#### Key

On-campus
Off-Campus
International students
Domestic students
##### Note

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#### Key Dates

Study Period Start date Census date WW date End date
Semester 1 25/2/2019 22/3/2019 15/4/2019 2/6/2019

* The Final WW Date is the final date from which you can withdraw from the unit without academic penalty, however you will still incur a financial liability (see withdrawal dates explained for more information).

Unit census dates currently displaying for 2019 are indicative and subject to change. Finalised census dates for 2019 will be available from the 1st October 2018.

### Learning Outcomes

1. Understand the role of multi-variable calculus and Fourier Series in the fields of mathematics, the sciences and engineering (Assessed by ATs 1 and 3)
2. Exhibit knowledge of the principles and concepts of multi-variable calculus and Fourier Series (Assessed by ATs 1, 2 and 3)
3. Apply mathematical principles, concepts, techniques, and technology to solve practical and abstract problems of multivariable calculus (Assessed by ATs 1, 2 and 3)
4. Interpret and present information communicated in mathematical and plain English form (Assessed by ATs 1, 2 and 3)
5. Demonstrate personal and social responsibility in the ethical application of approaches to problem solving, selfdirected learning and group learning (Assessed by ATs 1, 2 and 3)
6. Critically reflect upon the experience of learning and applying Calculus, and evaluate how it relates to the experience of teaching Mathematics and Science in schools. (Assessed by AT 4)*

*This ILO is specific to KMA652.

### Fees

#### Domestic

Band CSP Student Contribution Full Fee Paying (domestic) Field of Education
2 2019: \$1,169.00 2019: \$2,321.00 010101

Fees for next year will be published in October. The fees above only apply for the year shown.

### Requisites

KMA552

#### Mutual Exclusions

You cannot enrol in this unit as well as the following:

KMA252 and KME271

### Teaching

Teaching Pattern 3 x 50 minute lectures weekly, 1 X 50 minute tutorial weekly,  1 x 60 minute practicals weekly Assessment Task 1: Weekly Written Assignments: 20%Assessment Task 2: Online Quizzes: 10% Assessment Task 3: Final Exam: 70% Assessment Task 4: Portfolio Entry: 10% View the lecture timetable | View the full unit timetable

#### Textbooks

Required None