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Reeds Vol 1: Mathematics for Marine Engineers [Mīkstie vāki]

, , (South Tyneside College, UK)
  • Formāts: Paperback / softback, 656 pages, height x width x depth: 232x156x38 mm, weight: 1020 g
  • Sērija : Reeds Marine Engineering and Technology Series
  • Izdošanas datums: 02-May-2019
  • Izdevniecība: Reeds
  • ISBN-10: 1472974034
  • ISBN-13: 9781472974037
  • Mīkstie vāki
  • Cena: 68,62 €*
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  • Formāts: Paperback / softback, 656 pages, height x width x depth: 232x156x38 mm, weight: 1020 g
  • Sērija : Reeds Marine Engineering and Technology Series
  • Izdošanas datums: 02-May-2019
  • Izdevniecība: Reeds
  • ISBN-10: 1472974034
  • ISBN-13: 9781472974037

This exciting new edition covers the core subject areas of arithmetic, algebra, mensuration in 2D and 3D, trigonometry and geometry, graphs, calculus and statistics and probability for Marine Engineering students for the Merchant Navy OOW qualification.

Initial examples have been designed purely to practise mathematical technique and, once these skills have been mastered, further examples focus on engineering situations where the appropriate skills may be utilised. The practical questions are primarily from a marine engineering background but questions from other disciplines, such as electrical engineering, will also be covered, and reference made to the use of advanced calculators where relevant.

Papildus informācija

Key mathematical textbook addressing the needs of the modern marine student.
Preface ix
1 Indices and Logarithms
1(8)
Indices
1(1)
Behaviour of Indices
2(3)
Logarithms
5(2)
Test Examples 1
7(2)
2 Algebra
9(24)
Simplification of Algebraic Expressions
10(5)
Highest Common Factor (HCF) and Lowest Common Multiple (LCM)
15(2)
Algebraic Fractions
17(3)
Expansions and Factors
20(1)
Polynomial Division
21(3)
Factorisation
24(3)
Evaluation
27(3)
Test Examples 2
30(3)
3 Simple Equations
33(42)
Further Examples on Simple Equations
39(2)
Summary of the Important Points
41(2)
Practical Problems Involving Simple Equations
43(2)
Further Problems
45(3)
Problems Involving Simple Equations
48(3)
Transposition of Formulae
51(15)
Partial Fractions
66(5)
Logarithmic or Indicial Equations
71(2)
Test Examples 3
73(2)
4 Simultaneous Equations
75(21)
Two Unknowns Where the Coefficients Are Whole Numbers
75(4)
Two Unknowns Where the Coefficients Are Fractions
79(1)
Two Unknowns Where the Coefficients Are Decimals
80(1)
Two Unknowns Involving Reciprocals
81(3)
Practical Problems: Simultaneous Equations in Two Unknowns
84(4)
A More Complicated Situation
88(5)
Test Examples 4
93(3)
5 Quadratic Equations
96(23)
Solution by Factorisation
96(3)
Solution by `Completing the Square'
99(3)
Solution of Quadratic Equations by Formula
102(6)
Simultaneous Equations -- One Linear and One Quadratic
108(2)
Recap: Polynomial Division
110(1)
Function Notation
111(1)
Cubic Equations
112(1)
The Factor Theorem
113(4)
Test Examples 5
117(2)
6 Graphs
119(22)
Plotting of Straight-Line Graphs
120(2)
Determining the Equation to a Straight-Line Graph
122(5)
Graphical Solution of Simultaneous Linear Equations
127(1)
Graphical Solution of Quadratic Equations
128(5)
Graphical Solution of Simultaneous Quadratic and Linear Equations
133(2)
Determination of laws
135(3)
Curve Sketching
138(1)
Test Examples 6
139(2)
7 Trigonometry and Geometry
141(54)
Measurement of Angles
141(5)
Trigonometric Ratios
146(3)
Alternative Notation for the Right-Angled Triangle, ABC
149(1)
Properties of Angles and Straight Lines
150(1)
Theorem of Pythagoras
151(6)
Examples Where Trigonometry can be Used
157(1)
Bearings
158(3)
Coordinate Systems
161(3)
The Equation of a Sine Wave
164(1)
Sinusoidal Waveforms
165(8)
Addition of Sine Waves of Equal Frequency
173(1)
Theory
174(1)
Relationships Between Sine, Cosine and Tangents of Angles
175(2)
Identities
177(2)
Introduction to Hyperbolic Functions
179(1)
Hyperbolic Identities
180(1)
Solving Equations Using Hyperbolic Functions
180(2)
Addition of sinh(ax) and cosh(ax)
182(1)
Basic Hyperbolic Trigonometric Identities
183(1)
Latitude and Longitude
183(3)
Longitude and Time
186(2)
Test Examples 7
188(2)
Circle Theorems
190(2)
Definition
192(3)
8 Solution of Triangles
195(18)
Inverse Trigonometric Functions
196(2)
Cosine Rule and the Sine Rule for Non-Right-Angled Triangles
198(1)
Plane Trigonometry -- Sine and Cosine Rules
199(3)
Application of Trigonometry
202(4)
Areas of Triangles
206(4)
Double Angles
210(1)
Test Examples 8
211(2)
9 Mensuration of Areas
213(21)
Units
213(8)
Sector of a Circle
221(1)
Segment of a Circle
222(1)
Ellipse
223(1)
Surface of a Cylinder
223(1)
Surface of a Sphere
224(8)
Test Examples 9
232(2)
10 Volume-Mass, Centre of Gravity, Moment
234(33)
Prisms
235(2)
Pyramids
237(1)
Oblique Prisms and Pyramids
238(1)
Frustums
239(25)
Test Examples 10
264(3)
11 Differential Calculus (Differentiation)
267(24)
Gradient of a Straight Line
268(1)
Infinitesimally Small Changes `d'
268(2)
Zero Gradient
270(1)
Gradient of a Curve
271(1)
Differentiation from First Principles
271(4)
General Rule for Differentiating a Power
275(1)
Differential Coefficient of a Constant
276(1)
Differential Coefficient of a Sum of Terms
276(1)
Second Differential Coefficient
277(1)
Distance, Velocity and Acceleration
278(1)
Maxima and Minima
279(6)
Differentiation of sin(x) and cos(x)
285(1)
Differentiation of ln(x) and ex
286(1)
Function Notation
287(1)
Text Examples 11
288(3)
12 Integral Calculus (Integration)
291(23)
Constant of Integration
291(1)
General Rule for Integration of Powers of x
292(1)
Integration of a Sum of Terms
293(2)
Evaluating the Constant of Integration
295(2)
Definite Integration: Area Under a Curve
297(8)
Integration as a Summation
305(5)
Test Examples 12
310(4)
13 Advanced Calculus: Methods of Differentiation
314(34)
Differentiation -- The Product Rule
314(1)
The Product Rule
314(2)
The Quotient Rule
316(5)
Methods of Integration
321(11)
Applications of Integration
332(10)
Application of Differentiation
342(3)
Test Examples 13
345(3)
14 Statistics
348(51)
Definitions
348(1)
Tabular Presentation of Data
348(2)
Frequency Distributions
350(1)
Pictorial Representation of Data
351(1)
Histograms
352(1)
Frequency Polygons
353(1)
Cumulative Frequency Curves (Ogives)
353(1)
Pie Charts
354(1)
Statistical Averages
355(1)
The Arithmetic Mean
356(2)
The Median
358(2)
The Mode
360(1)
Calculation of the Mean of a Grouped Frequency Distribution
361(5)
Measures of Dispersion
366(6)
Correlation and Regression
372(10)
Probability
382(2)
The Addition Law of Probability
384(1)
The Multiplication Law of Probability
385(1)
The Probability Tree
385(13)
Text Examples 14
398(1)
15 Selection of Examination Standard Questions
399(66)
Suggested Solutions to Examination Questions
413(52)
APPENDIX 1 ARITHMETIC
465(22)
Fractions
465(4)
Approximating and Estimating
469(1)
Ratio
470(6)
Percentages
476(2)
Constituent Parts
478(3)
Averages
481(6)
APPENDIX 2 COMPLEX NUMBERS
487(14)
Definitions
487(1)
Complex Conjugate
487(1)
Division
487(1)
Diagrammatic Representation
488(6)
Alternating Current in a Resistor
494(1)
Alternating Current in an Inductor
495(1)
Alternating Current in a Capacitor
495(1)
Inductive and Capacitive Reactance
496(1)
Complex Impedances
496(1)
Complex Number Applications
497(2)
Test Examples -- Complex
499(1)
Solutions to Test Example -- Complex
499(2)
APPENDIX 3 LAPLACE TRANSFORMS
501(31)
Definition
501(1)
Standard Laplace Transforms
502(2)
Standard Inverse Laplace Transforms
504(1)
Inverse Laplace Transforms Using Partial Fractions
505(1)
Inverse Laplace Transforms Using `Completing the Square'
506(2)
Newton's Law of Cooling
508(1)
Solving Differential Equations Using Laplace Transforms
509(16)
Test Examples -- LAPLACE
525(1)
Solutions to Test Examples -- LAPLACE
526(6)
APPENDIX 4 FOURIER ANALYSIS
532(29)
Periodic Functions
532(1)
Trigonometric Series
533(5)
Half Range Series
538(4)
Functions with Periods Other than 2π
542(1)
Fourier Coefficients
543(6)
Rectified Sinusoidal Waveforms
549(7)
Test Examples -- Fourier
556(1)
Solution to Test Examples -- Fourier
557(4)
APPENDIX 5 SOLUTIONS TO TEXT EXAMPLES
561(66)
Solutions to Test Examples 1
561(2)
Solutions to Test Examples 2
563(3)
Solutions to Test Examples 3
566(4)
Solutions to Test Examples 4
570(8)
Solutions to Test Examples 5
578(4)
Solutions to Test Examples 6
582(7)
Solutions to Test Examples 7
589(3)
Solutions to Test Examples 8
592(7)
Solutions to Test Examples 9
599(7)
Solutions to Test Examples 10
606(7)
Solutions to Test Examples 11
613(3)
Solutions to Test Examples 12
616(5)
Solutions to Test Examples 13
621(3)
Solutions to Test Examples 14
624(3)
APPENDIX 6 MATHEMATICAL FORMULAE
627(17)
Calculus formulae
629(2)
Applications of Integration
631(2)
Laplace Transforms
633(2)
Half-range series
635(1)
Trigonometry
636(6)
Normal Probabilities for Positive Values of z
642(2)
Index 644
Kevin Corner is Lecturer in Mathematics in the Marine School at South Tyneside College, UK. He has taught the subject for over 23 years and has written interactive educational material for the marine industry.