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E-raamat: Engineering Mathematics with Applications to Fire Engineering

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  • Formaat: 382 pages
  • Ilmumisaeg: 12-Jun-2018
  • Kirjastus: CRC Press
  • Keel: eng
  • ISBN-13: 9781351597609
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Engineering Mathematics with Applications to Fire EngineeringSuurem pilt
  • Formaat: 382 pages
  • Ilmumisaeg: 12-Jun-2018
  • Kirjastus: CRC Press
  • Keel: eng
  • ISBN-13: 9781351597609
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This book addresses direct application of mathematics to fire engineering problems

Gives background interpretation for included mathematical methods

Illustrates a step-by-step detailed solution to solving relevant problems

Includes pictorial representation of the problems

Discusses a comprehensive topic list in the realm of engineering mathematics topics including basic concepts of Algebra, Trigonometry and Statistics
Preface xiii
Authors xv
1 Review of Basic Concepts 1(44)
1.1 Degrees of Accuracy
1(5)
1.1.1 Rounding Numbers (Common Method)
1(1)
1.1.2 Round-to-Even Method
2(1)
1.1.3 Decimal Places
3(1)
1.1.4 Significant Places
4(2)
1.2 Scientific Notation (Standard Form)
6(3)
1.2.1 How Does Scientific Notation Work?
7(1)
1.2.2 Addition and Subtraction
7(1)
1.2.3 Multiplication
8(1)
1.2.4 Division
9(1)
1.3 Basic Algebra
9(1)
1.3.1 Algebraic Notation
9(1)
1.3.2 Evaluating Expressions
10(1)
1.4 Linear Equations
10(7)
1.4.1 Solving Linear Equations
10(3)
1.4.2 Transposing Formulae
13(4)
1.5 Linear Simultaneous Equations
17(3)
1.5.1 Elimination Method
18(2)
1.5.2 Substitution Method
20(1)
1.6 Quadratic Equations
20(3)
1.6.1 Solving Quadratic Equations Using the Formula
21(2)
1.7 Trigonometry
23(8)
1.7.1 Right-Angled Triangles
23(2)
1.7.2 Scalene Triangles (Sine and Cosine Rules)
25(3)
1.7.2.1 Sine Rule
25(2)
1.7.2.2 Cosine Rule
27(1)
1.7.3 Resultant Forces
28(1)
1.7.3.1 Adding Two Forces
28(1)
1.7.4 Basic Trigonometric Identities
29(1)
1.7.5 Radian Measure
30(1)
1.7.5.1 Radians on the Calculator
31(1)
1.8 Statistics
31(9)
1.8.1 Introduction
31(1)
1.8.2 Measures of Averages
32(4)
1.8.2.1 Data in a Frequency Table
34(1)
1.8.2.2 Grouped Data
35(1)
1.8.3 Measures of Spread
36(3)
1.8.3.1 Range
36(1)
1.8.3.2 Interquartile Range
36(1)
1.8.3.3 Standard Deviation (σ)
37(1)
1.8.3.4 Sample Standard Deviation (s)
38(1)
1.8.4 Change of Scale
39(1)
1.9 Applications
40(2)
Problems
42(3)
2 Introduction to Probability Theory 45(20)
2.1 Introduction
45(7)
2.1.1 Mutually Exclusive Events
46(1)
2.1.2 Independent Events
47(1)
2.1.3 Conditional Probability
48(1)
2.1.4 Bayes' Theorem
49(2)
2.1.4.1 Generalization of Bayes' Theorem
50(1)
2.1.5 Tree Diagrams
51(1)
2.2 Discrete Random Variables
52(3)
2.2.1 Discrete Probability Distribution
52(2)
2.2.2 Expectation Values
54(1)
2.2.3 Variance and Standard Deviation
54(1)
2.3 Continuous Random Variables
55(5)
2.3.1 Probability Density Function (pdf)
56(1)
2.3.2 Cumulative Distribution Function (cdf)
56(2)
2.3.3 Expectation of a Continuous Random Variable
58(1)
2.3.4 Variance and Standard Deviation of a Continuous Random Variable
58(2)
2.4 Applications
60(3)
Problems
63(2)
3 Vectors and Geometrical Applications 65(16)
3.1 Introduction
65(9)
3.1.1 Magnitude and Unit Vectors
66(2)
3.1.1.1 Unit Vectors
67(1)
3.1.2 Addition and Subtraction of Vectors
68(1)
3.1.3 Scalar and Vector Products
69(3)
3.1.3.1 Scalar Product (Dot Product)
69(1)
3.1.3.2 Vector Product (Cross Product)
70(1)
3.1.3.3 How to Calculate a x b
71(1)
3.1.4 Projection of Vectors
72(2)
3.2 Vector Geometry
74(4)
3.2.1 Vector Equation of a Line
74(2)
3.2.1.1 Intersection of Lines
75(1)
3.2.2 Vector Equation of Planes
76(5)
3.2.2.1 Generalizing for Any Plane in Space
77(1)
3.3 Applications
78(1)
Problems
79(2)
4 Determinants and Matrices 81(36)
4.1 Background
81(1)
4.2 Introduction to Determinants
81(6)
4.2.1 2 x 2 Determinants
83(1)
4.2.2 Properties of Determinants
83(2)
4.2.2.1 Multiplying a Determinant by a Number
84(1)
4.2.3 3 x 3 Determinants
85(2)
4.3 Introduction to Matrices
87(16)
4.3.1 Order of a Matrix
88(1)
4.3.2 Addition and Subtraction
88(1)
4.3.3 Matrix Multiplication
88(4)
4.3.3.1 Multiplying a Matrix by a Scalar
88(1)
4.3.3.2 Multiplying Two Matrices
89(1)
4.3.3.3 How to Multiply Two Matrices
89(3)
4.3.4 Special Matrices
92(2)
4.3.5 Powers of Matrices
94(1)
4.3.6 Inverse of a Square Matrix
94(2)
4.3.7 Eigenvalues and Eigenvectors
96(4)
4.3.8 Diagonal Factorization of Matrices
100(3)
4.4 Solving Systems of Linear Equations
103(7)
4.4.1 Introduction
103(1)
4.4.2 Gaussian Elimination Method
104(4)
4.4.3 Matrix Inversion Method
108(9)
4.4.3.1 Matrix Method for Solving Simultaneou Equations
108(2)
4.5 Applications
110(4)
Problems
114(3)
5 Complex Numbers 117(14)
5.1 Background
117(1)
5.2 Introduction and the Imaginary j
117(1)
5.2.1 Some Properties of j
118(1)
5.2.2 Complex Numbers
118(1)
5.3 Arithmetic Operations
118(2)
5.3.1 Addition and Subtraction
118(1)
5.3.2 Multiplication
119(1)
5.3.2.1 Conjugate Numbers
119(1)
5.3.3 Division
119(1)
5.4 Argand Diagram
120(1)
5.4.1 Drawing a Diagram of Complex Numbers
120(1)
5.5 Polar and Exponential Form
120(3)
5.5.1 Polar Form
120(2)
5.5.1.1 Multiplying and Dividing Complex Numbers in Polar Form
121(1)
5.5.2 Exponential Form
122(1)
5.5.3 Powers of Complex Numbers
122(1)
5.5.4 De Moivre's Theorem
122(1)
5.6 Roots of Equations
123(2)
5.7 Applications
125(4)
Problems
129(2)
6 Introduction to Calculus 131(40)
6.1 Differentiation
131(13)
6.1.1 Definition of a Limit
131(5)
6.1.1.1 Differentiating Fractional and Negative Powers of x
135(1)
6.1.2 Stationary Points (Maxima and Minima)
136(3)
6.1.2.1 Practical Test
137(1)
6.1.2.2 Second Derivative Method
138(1)
6.1.3 Differentiating Products and Quotients
139(2)
6.1.3.1 Products
139(1)
6.1.3.2 Quotients
140(1)
6.1.4 Standard Functions
141(2)
6.1.5 Function of a Function (Chain Rule)
143(1)
6.2 Integration
144(11)
6.2.1 Introduction and the Riemann Sum
144(2)
6.2.2 Fundamental Theorem of Calculus (Optional Section)
146(3)
6.2.2.1 How to Compute the Integral ba f(x)dx
146(3)
6.2.3 Standard Integrals and Areas under Curves
149(3)
6.2.3.1 Finding the Area under a Curve
150(2)
6.2.4 Improper Integrals
152(3)
6.3 Integration Techniques
155(9)
6.3.1 Substitution
155(2)
6.3.2 Partial Fractions
157(5)
6.3.2.1 Type 1: Different Linear Factors
158(1)
6.3.2.2 Type 2: Denominator with a Repeated Factor
159(1)
6.3.2.3 Type 3: Denominator with a Quadratic Factor
160(1)
6.3.2.4 Performing the Final Integration
161(1)
6.3.3 Integration by Parts
162(2)
6.4 Applications
164(3)
Problems
167(4)
7 Ordinary Linear Differential Equations 171(28)
7.1 Background
171(1)
7.2 Types of Differential Equations
172(2)
7.2.1 Introduction
172(1)
7.2.2 Order of a Differential Equation
173(1)
7.2.3 Degree of a Differential Equation
173(1)
7.2.4 Linearity
173(1)
7.2.5 What Is Meant by Solving Differential Equations?
174(1)
7.3 First-Order Differential Equations
174(8)
7.3.1 Simplest Situation
175(1)
7.3.2 Separating Variables
175(4)
7.3.3 Integrating Factor Technique
179(3)
7.4 Second-Order Differential Equations
182(9)
7.4.1 Complementary Function (CF)
183(2)
7.4.1.1 General Solution for the Complementary Function
183(1)
7.4.1.2 How to Find the Complementary Function
184(1)
7.4.2 Types of Solutions
185(3)
7.4.2.1 Case 1: Real and Distinct Roots m1 and m2
185(1)
7.4.2.2 Case 2: Real and Repeated Roots
186(1)
7.4.2.3 Case 3: Complex Conjugate Roots
187(1)
7.4.3 Particular Integral (PI)
188(13)
7.4.3.1 How to Find the Particular Integral
188(3)
7.5 Applications
191(6)
Problems
197(2)
8 Laplace Transforms 199(30)
8.1 Why Do We Need the Laplace Transform?
199(1)
8.2 Derivation from a Power Series
200(1)
8.3 Introduction and Standard Transforms
201(6)
8.3.1 Schematic Representation of Laplace Transforms
202(1)
8.3.2 Standard Transforms
202(3)
8.3.3 Linearity of Laplace Transforms
205(1)
8.3.4 Basic Relations
205(2)
8.4 Inverse Transforms
207(3)
8.5 Discontinuous Functions
210(3)
8.5.1 Heaviside Unit Step Function
210(2)
8.5.1.1 Calculating the Laplace Transform of H(t-c)
210(1)
8.5.1.2 Unit Step at Origin
211(1)
8.5.2 The Delta Function
212(18)
8.5.2.1 The Delta Function at the Origin
212(1)
8.6 Shift Theorems
213(1)
8.7 Method for Solving Linear Differential Equations
214(5)
8.8 Applications
219(8)
Problems
227(2)
9 Fourier Series and Fourier Transforms 229(26)
9.1 Periodic Functions
229(1)
9.2 Fourier Series
230(8)
9.2.1 Periodic Functions of Period T
230(1)
9.2.2 General Properties and Orthogonal Functions
231(1)
9.2.3 Fourier Coefficients
232(6)
9.3 Complex Form of the Fourier Series
238(4)
9.4 Fourier Transforms
242(8)
9.4.1 Nonperiodic Functions
242(1)
9.4.2 Fourier Transform Pair
242(3)
9.4.3 What Does the Fourier Transform Represent?
245(2)
9.4.4 Properties of the Fourier Transform
247(1)
9.4.4.1 Linearity Property
247(1)
9.4.5 Convolution of Two Functions
248(2)
9.5 Applications
250(3)
Problems
253(2)
10 Multivariable Calculus 255(42)
10.1 Partial Derivatives
255(14)
10.1.1 Introduction and Definition
255(4)
10.1.1.1 Partial Derivatives Defined
256(1)
10.1.1.2 Instantaneous Rate of Change
257(2)
10.1.2 Higher Derivatives
259(1)
10.1.2.1 Clairaut's Theorem
259(1)
10.1.2.2 Antiderivatives When There Are Multiple Variables
259(1)
10.1.3 Chain Rule
260(3)
10.1.3.1 Chain Rule with One Variable
260(1)
10.1.3.2 Chain Rule with Multivariables
261(2)
10.1.4 Directional Derivatives and Gradients
263(3)
10.1.5 Stationary Points (Maxima, Minima, and Saddle Points)
266(3)
10.1.5.1 Summary to Find Maximum or Minimum Points
268(1)
10.2 Higher-Order Integration
269(20)
10.2.1 Double Integrals and Fubini's Theorem
269(4)
10.2.1.1 An Application of Double Integration
272(1)
10.2.2 Double Integration Using Polar Coordinates
273(5)
10.2.2.1 Using Polar Coordinates to Calculate Double Integrals
274(4)
10.2.3 General Regions
278(3)
10.2.4 Triple Integrals
281(2)
10.2.4.1 Cartesian Coordinates
281(2)
10.2.5 3-D Coordinate Systems
283(3)
10.2.5.1 Integrals in the New Coordinate Systems
284(2)
10.2.6 General Change of Coordinate Systems
286(3)
10.3 Applications
289(6)
10.3.1 Application of Double Integration
289(3)
10.3.2 Application of Triple Integration (Center of Mass)
292(3)
Problems
295(2)
11 Vector Calculus 297(60)
11.1 Differentiation and Integration of Vectors
297(3)
11.1.1 Derivatives of Vector Functions
297(2)
11.1.2 Integrating Vector Functions
299(1)
11.2 Vector Fields
300(3)
11.3 Line Integrals
303(5)
11.3.1 The ds-Type Integral
303(2)
11.3.2 The dr-Type Integral
305(3)
11.3.3 Summary of Results
308(1)
11.4 Gradient Fields
308(8)
11.4.1 Conservative Vector Fields
310(3)
11.4.2 Testing for Conservativeness
313(3)
11.5 Green's Theorem
316(5)
11.5.1 Properties of Green's Theorem
319(2)
11.6 Divergence and Curl of Vector Fields
321(6)
11.6.1 2-Dimensional Definitions
321(2)
11.6.2 Alternative Forms of Green's Theorem
323(2)
11.6.2.1 Curl Form
323(1)
11.6.2.2 Divergence Form
324(1)
11.6.3 3-Dimensional Definitions
325(2)
11.7 Surface Integration
327(16)
11.7.1 Parametric Surfaces
327(4)
11.7.1.1 Summary of the Main Types of Surfaces
330(1)
11.7.2 Surface Integrals
331(2)
11.7.3 Tangent Planes and Normal Vectors
333(3)
11.7.3.1 Normal Vector to the Tangent Plane
334(1)
11.7.3.2 General Formula for the Normal Vector to a Surface
335(1)
11.7.4 Normal Vectors to Surfaces
336(3)
11.7.5 Applications of Surface Integrals
339(4)
11.8 Stokes' Theorem
343(4)
11.9 Divergence Theorem
347(3)
11.10 Applications
350(3)
Problems
353(4)
Answers 357(6)
Index 363
Khalid Khan, B.Sc. (Hons), M.Sc., Ph.D., received his B.Sc. (Hons) in Mathematical Physics, M.Sc. and Ph.D. in Control Systems all from the Unversity of Manchester Institute of Science and Technology in the United Kingdom. Dr Khan then spent two years as a Consultant Engineer working on safety, reliabilty and risk assessment problems in the energy industry. Subsequently, he moved abroad and after spending some period of time as an Assistant Professor of mathematics at Eitisalat University in the United Arab Emirates he returned to the United Kingdom and took up a position at the University of Central Lancashire.

Dr Khan is currently a Senior Lecturer in Engineering Mathematics in the School of Engineering at the University of Central Lancashire. He teaches on a range of mathematics modules within the Fire degree programmes and contributes to other mathematics teaching within the School and College. He is currently the course leader for the Foundation Degree in Fire Safety Engineering. Dr Khan as part of the Fire Team has been involved in the development of a range of courses in Fire Safety Engineering and Management that are currently running at one of UCLans International partnerships in Qatar.

Dr Khans research interests are in the area of mathematical modelling of system behaviour in a range of applications. His current work focuses on fire suppression using sprinkler systems and on mathematical models of collective motion of self-propelled particles in homogeneous and heterogeneous mediums. Dr Khan has currently over thirty publications and is also a member of two journal review panel boards.

Tony Graham, B.Sc. (Hons), Ph.D., is a senior lecturer and course leader at University of Central Lancashire, UK. Best known for teaching fire safety engineering to thousands of students over 24 years in different countries and for papers on compartment fire dynamics and the phenomenon of flashover fire. His teaching also includes risk engineering and engineering analysis. He has taught courses at International College of Engineering and Management in Sultanate of Oman and also in City University of Hong Kong, he is a senior fellow of Higher Education Authority and Secretary of the Combustion, Explosion and Fire Engineering research group in School of Engineering and has served on both Academic Board and Academic Standards and Quality Assurance Committee. His research was funded by Nuffield Foundation and is ongoing.

Before all of that, he read B.Sc. (Hons) Theoretical Physics at Lancaster University, and subsequently was awarded his Ph.D. in Fire Engineering in 1998 from the University of Central Lancashire. For the future, Dr Graham is looking at two books on fire engineering science and risk engineering. Dr Graham, along with beloved wife Anna and daughter Natalia now prosper in Preston, in sunny Lancashire.
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