Technology Mathematics II: Introduction

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Technology Mathematics II Introduction
Learning outcomes
Application of calculus in design, technology and
management Use of appropriate mathematics
techniques Data management, presentation and
interpretation Problem solving
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Structure of the module
Today Introduction, objectives of the module,
methods of assessment. Concept of function,
graphs, function domain. 3 February Concept of
differentiation, graphical illustration of the
function gradient, slope of curves, limit
theorem. 10 February Interpretation of the
derivative, differentiation of simple functions,
examples. 17 February Differentiation of a
product, quotient rule, differentiation of
function of a function 24 February Application
of derivatives maximum and minimum of a
function, practical examples from engineering and
life sciences. 2 March In-class test 1
Functions and differentiation rules.
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Structure of the module (cont.)
9 March Concept of integration, inverse of
differentiation, limit theorem of sums, basic
rules of integration. 16 March Integration of
elementary functions, examples 23 March Definite
and indefinite integrals, numerical integration.
30 March Practical applications of
integration. 27 March Revision, practical
applications of integration. 4 May In-class
test 2 Integration. 11 May Practical examples
from design, technology, business and management.
19 May Revision, QA session.
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Method of Assessment
2 in-class tests 02nd of March - Functions and
differentiation 04th of May - Integration 1.5-ho
ur examination (late May/early June) Weighting
50 in-class tests / 50 examination Resits Au
gust/September 2003 - 2-hour examination
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Teaching Methods
Lectures, tutorials and computer classes given in
1-hour slots in 0.16 Phoenix. Computer classes
are given on Thursdays and Fridays in C3.08
Chesham. Attendance will be recorded and absences
will be reported.
Teaching staff
Dr Kirill V. Horoshenkov K.Horoshenkov_at_bradford.a
c.uk, Room C1.11, Chesham Building Mr Zahir
Jamil Meetings by appointment via e-mail.
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Resources
Library (L51) Web-based lecture notes
www.staff.brad.ac.uk/kvhorosh Foundation
Mathematics for Engineers, by J. Berry and P.
Wainwright, MacMillan Press, 1991. Foundation
Mathematics, by A. Croft and R. Davison, Prentice
Hall, 1997. Engineering Mathematics, by K. A.
Stroud Palgrave, 2001. Practical Mathematics
using MATLAB, 2e, by Gunnar Backstrom,
Studentlitteratur, 2000.
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Lecture 1 Functions and Concept of
Differentiation
Objectives
Revisit functions Identify a function as a
rule Determine domain, range and limit of
function Construct the function graph Identify
function gradient Introduce the concept of
derivative Solve related problems in class
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The Mathematics of Change
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Real-life Examples of Functional Relations
Geometrical - relationship between the side of a
square and its area Mechanical - relationship
between space and time, i.e. the position of
a moving body at a given time Structural - relatio
nship between the load on a beam and distance
from one end Fluid - relation between the
fluid velocity and fluid pressure Financial - rela
tionship between value of investment and time.
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Concept of a Function
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Functions Domain
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Graphical Representation of a Function
y
x
0
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Example of Graphical Representation of a Function
Attenuation of sound in a sewer pipe
empty
rubber granulate
sand
sand paper
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Linear Functions
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Gradient of a Linear Function
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General Rules for the Gradient of a Linear
Function
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General Rules for the Gradient of a Linear
Function (cont.)
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Quadratic Functions
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Quadratic Functions (cont.)
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Gradient of a Quadratic Function
P2
P1
b
slope tan(q) b/a
q
a
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Other Functions
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Rate of Change
A
B
Plot the graph and find its slope and intercept
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Questions for Practice
10m
q
50m