# Calculus and Applications 2 KMA252

Hobart

### Introduction

This unit is a continuation of KMA152 and KMA154, with emphasis on the application of multivariable 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 ?? = ??(??, ??). 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 z ? f (x, y) is a surface, and so might be used to describe building structures; 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. 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 KMA252
Credit points 12.5
College/School College of Sciences and Engineering
School of Natural Sciences
Discipline Mathematics
Coordinator Doctor Michael Brideson
Available as student elective? Yes
Delivered By University of Tasmania
Level Intermediate

### 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
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#### Key Dates

Study Period Start date Census date WW date End date
Semester 1 22/2/2021 23/3/2021 12/4/2021 30/5/2021

* 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 2021 are indicative and subject to change. Finalised census dates for 2021 will be available from the 1st October 2020. Note census date cutoff is 11.59pm AEST (AEDT during October to March).

### Learning Outcomes

• understand the role of multi-variable calculus, vector calculus, and fourier series in the fields of mathematics, the sciences, and engineering.
• exhibit knowledge of the principles and concepts of multi-variable calculus, vector calculus, and fourier series.
• apply mathematical principles, concepts, techniques, and technology to solve practical and abstract problems of multi-variable calculus and vector calculus.
• interpret and present information communicated in mathematical and plain english form.
• demonstrate personal and social responsibility in the ethical application of approaches to problem solving, self-directed learning, and group learning.
Field of Education Commencing Student Contribution 1 Grandfathered Student Contribution 1 Approved Pathway Course Student Contribution 2 Domestic Full Fee
010101 \$493.00 \$493.00 not applicable \$2,402.00
• Available as a Commonwealth Supported Place
• HECS-HELP is available on this unit, depending on your eligibility3
• FEE-HELP is available on this unit, depending on your eligibility4

2 Information on eligibility and Approved Pathway courses can be found here
3 Please refer here for eligibility for HECS-HELP
4 Please refer here for eligibility for FEE-HELP

### Requisites

#### Prerequisites

Admission into a Masters course OR (KMA152 Mathematics 1A OR JEE103 Mathematics I) AND (KMA154 Mathematics 1B OR JEE104 Mathematics II)

#### Mutual Exclusions

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

KME771 AND KME271

### Teaching

Teaching Pattern 3x1-hr lectures, 1-hr tutorial weekly, 1- hr lab session approximately every three weeks. Assignments (20%)|Online quizzes (10%)|Examination (70%) View the lecture timetable | View the full unit timetable

#### Textbooks

Required Required readings will be listed in the unit outline prior to the start of classes. Booktopia textbook finder

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