Fundamental maths: [for engineering and science]
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Basingstoke
Palgrave Macmillan
2011
|
| Edition: | 1. publ. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XI, 380 S. graph. Darst. |
| ISBN: | 9780230252080 |
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| 100 | 1 | |a Breach, Mark |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Fundamental maths |b [for engineering and science] |c Mark Breach |
| 250 | |a 1. publ. | ||
| 264 | 1 | |a Basingstoke |b Palgrave Macmillan |c 2011 | |
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Record in the Search Index
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|---|---|
| adam_text | Titel: Fundamental maths
Autor: Breach, Mark
Jahr: 2011
Summary of Contents
1 Preliminaries
2 Fundamental arithmetic
3 Arithmetic of small quantities
4 Arithmetic of powers
5 Arithmetic calculations
6 Graphs and Charts
7 Algebra - introducing the unknown
8 Algebra - more complex forms
9 Algebra - functions
10 Algebra - working with formulae
11 Algebra - transposition of equations and inverse functions
12 Algebra - factors of expressions
13 Geometry
14 Series
15 Trigonometry
16 Graphical representation of trigonometric functions
17 Simultaneous equations
18 Quadratic equations
19 Surface areas and volumes of solids
20 Coordinate Systems
21 Areas of irregulär figures
22 Trigonometric identities
23 Logarithms and indices
24 Differentiation - basic relationships
25 Differentiation of more complex functions
1
10
25
40
48
59
68
77
88
98
108
120
131
141
150
165
172
187
198
209
232
237
250
261
273
iv Summary of Contents
26 Differentiation - uses 285
27 Integration - basic relationships 294
28 Integration - area and volume 303
29 Vectors 316
30 Matrices 327
31 Probability 346
32 Central tendency and dispersion 359
Answers 367
Index 375
Preface
1 Preliminaries
Understanding mathematics Why this book is for you How to use the book
Familiarity with numbers Choosing a calculator Tests and examinations - and
how to be good at them Summary
2 Fundamental arithmetic
The basis of all mathematics Arithmetic Operations Negative quantities Prime
numbers Factors of a number Prime factors Finding factors 2, 3 and 5
Finding factors 7 and 11 Highest common factor Lowest common multiple
Brackets Variables Order of precedence in Operations Summary
10
3 Arithmetic of small quantities
Small quantities Fractions Converting mixed numbers to and from improper
fractions Adding mixed numbers Multiplying fractions Cancelling with
fractions Dividing fractions Compound fractions Ratios Decimals Adding
and subtracting decimal numbers Multiplying and dividing decimal numbers
Converting fractions to and from decimals « Per cent Converting fractions to and
from percentages Summary
25
4 Arithmetic of powers
What is a power? - Using powers » Roots Laws of indices Fractional powers
Standard form «¦ Summary
40
5 Arithmetic calculations
Measurements - Blunders - Systematic errors * Deliberate errors - Random errors
Working with formulae « Conversions » Imperial and metric units Converting
between imperial and metric units » Summary
48
vi Contents
6 Graphs and Charts 59
Maths in pictures The Cartesian coordinate System for graphs Charts Grouped
data Summary
7 Algebra - introducing the unknown 68
What is algebra? Algebraic equations Symbols and variables Expressions,
equations, formulae and identities Simplifying equations Simplifying equations
by dividing throughout Solving simple equations Summary
8 Algebra - more complex forms 77
Multiplication and division BEDMAS for algebra Expanding brackets Nested
brackets Adding and subtracting fractions Summary
9 Algebra - functions 88
Powers, reciprocals and roots Functions Evaluating a function Composite
functions Graphical representation of functions Range and domain of a
function One-to-one and many-to-one functions Summary
10 Algebra - working with formulae 98
Laws of indices with algebra Multiplication law Division law» Power of a power
law Applications of the laws of indices Simplifying expressions with powers
A note on notation Evaluating formulae Summary
11 Algebra - transposition of equations and inverse functions 108
Transposing formulae Why transpose? Changing sides A general rule Inverse
of a function Summary
12 Algebra - factors of expressions 120
Finding factors Number of factors in a polynomial The factor theorem Finding
factors that are not obvious Simplifying more complicated expressions
Summary
13 Geometry 131
Angles Angular units » Adding angles » Angle relationships * Angle relationships
in triangles » Area of a triangle ? Pythagoras theorem - Summary
Contents vii
14 Series 141
Sequences and series - Arithmetic progression Geometrie progression The
fallacy of Zeno s arrow Summary
15 Trigonometry 150
Sine, cosine and tangent of an angle Calculator functions Finding an angle in a
right-angled triangle Finding a side of a right-angled triangle Notation and
relationship Non-right-angled triangles The sine rule The cosine rule Angular
functions in Microsoft Excel Cosecant, secant and cotangent Summary
16 Graphical representation of trigonometric functions 165
Graphs of the functions Sine Cosine Tangent Signs of trigonometric
functions Limitations of the calculator Sine rule ambiguity Summary
17 Simultaneous equations 172
What are simultaneous equations? Solving by Substitution Solving by
subtraction General Solution by formula Approximate graphical Solution
When to use each method Summary
18 Quadratic equations 187
What are quadratic equations? Factorisation The signs of a, b and c Quadratic
formula Choosing the best method Graph of y = ax2 + bx + c - Interpretation
of Solutions Summary
19 Surface areas and volumes of solids 198
Area of a triangle Heron s formula Triangle in a rectangle Area of parts of a
circle Areas and volumes of some regulär solid figures Summary
20 Coordinate Systems 209
Cartesian coordinate System applications Distance and orientation between two
points Graph of a straight line Loci Slopes of perpendicular lines Distance of
a point from a line Loci of points on a circle - Find the radius and centre of a circle
Circle defined by its diameter Circle defined by three points Area of a triangle
» Area of a many sided figure - Polar coordinates Geographica! polar coordinates
Pythagoras theorem in three dimensions - Summary
viii Contents
21 Areas of irregulär figures 232
Irregulär figures Trapezium rule Simpson s rule The better method?
Summary
22 Trigonometric identities 237
Simple relationships Sines of sum and difference of angles Cosines of sum and
difference of angles Tangents of sum and difference of angles Double angle
identities Half angle identities Square reduction identities Sum and product
identities Summary
23 Logarithms and indices 250
Bases, indices and logarithms Using logarithms Laws of logarithms
Logarithms to bases other than 10 and e What is e? Solving equations using
logarithms and powers Finding relationships by experiment Summary
24 Differentiation - basic relationships 261
Change and rate of change Gradient of a straight line graph Gradient of a non-
straight line graph Gradient of the function y = x2 - a numerical method
Gradient of the function y - x2 - an analytical method The notation of
differentiation Differentiation of powers of x Differentiation of trigonometric
functions Differentiation of a sum of expressions of a variable Differentiation of
ex and logarithm functions Differentiation of other expressions « Summary
25 Differentiation of more complex functions 273
Differentiating a product of expressions Differentiating a product of more than
two expressions Differentiating a quotient of expressions - Differentiating a
function of a function Differentiating a function of a function of a function -
Differentiating more complex functions Summary
26 Differentiation - uses 285
Stationary points Maximum or minimum? Summary
27 Integration - basic relationships 294
What is Integration? Integration as the reverse of differentiation - Area under a
curve « Rules of integration - Functions and their indefinite integrals » Summary
Contents ix
*5ä»3S«ÜSiRFS
28 Integration - area and volume 303
Definite integration and area - Area under a curve « Area between two curves «¦
Mean values « Root mean squared values (RMS) - Volume of a solid of revolution -
Volume of a solid of revolution rotated about the y-axis » Summary
29 Vectors 316
Scalar and vector Vector notation Adding and subtracting vectors Negative
forces More complex vector problems Summary
30 Matrices 327
Matrix algebra Adding and subtracting matrices Multiplying matrices Some
special matrices Determtnant of a matrix Matrix inverse Properties of the
inverse of a matrix Solutions of sets of simultaneous equations Summary
31 Probability 346
What is probability? * Multiplication law of probability - Addition law of probability
Conditional probability Probability trees Visualisation of probability
Summary
32 Central tendency and dispersion 359
Sets of data The centre of data - mean, median and mode - Standard deviation -
Distribution of data ? Standard deviation of the mean - Summary
Answers 367
Index 375
|
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| author | Breach, Mark |
| author_facet | Breach, Mark |
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| discipline | Mathematik |
| edition | 1. publ. |
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| isbn | 9780230252080 |
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| physical | XI, 380 S. graph. Darst. |
| publishDate | 2011 |
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| spelling | Breach, Mark Verfasser aut Fundamental maths [for engineering and science] Mark Breach 1. publ. Basingstoke Palgrave Macmillan 2011 XI, 380 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Mathematics Mathematik Grundlage (DE-588)4158388-7 gnd rswk-swf Mathematik (DE-588)4037944-9 gnd rswk-swf (DE-588)4151278-9 Einführung gnd-content Mathematik (DE-588)4037944-9 s Grundlage (DE-588)4158388-7 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=022538744&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Breach, Mark Fundamental maths [for engineering and science] Mathematics Mathematik Grundlage (DE-588)4158388-7 gnd Mathematik (DE-588)4037944-9 gnd |
| subject_GND | (DE-588)4158388-7 (DE-588)4037944-9 (DE-588)4151278-9 |
| title | Fundamental maths [for engineering and science] |
| title_auth | Fundamental maths [for engineering and science] |
| title_exact_search | Fundamental maths [for engineering and science] |
| title_full | Fundamental maths [for engineering and science] Mark Breach |
| title_fullStr | Fundamental maths [for engineering and science] Mark Breach |
| title_full_unstemmed | Fundamental maths [for engineering and science] Mark Breach |
| title_short | Fundamental maths |
| title_sort | fundamental maths for engineering and science |
| title_sub | [for engineering and science] |
| topic | Mathematics Mathematik Grundlage (DE-588)4158388-7 gnd Mathematik (DE-588)4037944-9 gnd |
| topic_facet | Mathematics Mathematik Grundlage Einführung |
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