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Essentials Engineering Mathematics Alan Jeffrey [pdf]

### Essentials Engineering Mathematics (2nd Edition) by Alan Jeffrey

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Essentials Engineering Mathematics (2nd Edition) written by Alan Jeffrey , University of Newcastle-upon-Type.

This book evolved from lectures given in Newcastle over many years, and it presents the essentials of first year engineering mathematics as simply as possible. It is intended that the book should be suitable both as a text to supplement a lecture course and also, because it contains a full set of detailed solutions to problems, as a book for private study.
The success with which the style and content of the first edition was received has persuaded me that these features should be preserved when preparing this second edition. Accordingly, the changes made to the original material have, in the main, been confined to small amendments designed to improve the understanding of some basic concepts. Typical of these amendments to the first edition is the inclusion in Section 26 of some new problems involving the mean value theorem for derivatives, an extension of the account of stationary points of functions of two variables in Section 50 to include Lagrange multipliers, and the introduction of the concept of the direction field of a first order differential equation in Section 71, now made possible by the ready availability of suitable computer software. While making these changes, the opportunity has also been taken to correct some typographical errors. More important, however, is the inclusion of a considerable amount of new material. The first is to be found in Section 85, where the reader is introduced to the delta function and its uses with the Laplace transform when solving initial value problems for linear differential equations. The second, which is far more fundamental, is the inclusion of an introductory account in Section 87 of the use of new computer software that is now widely available. The purpose of this software is to enable a computer to act in some ways like a person with pencil and paper, because it allows a computer to perform symbolic operations, like differentiation, integration, and matrix algebra, and to give the results in both symbolic and numerical form. The two examples of software described here are called MAPLE and MATLAB, each of which names is the registered trademark of a software company quoted in Section 87. In fact MAPLE, which provides the symbolic capabilities of MATLAB, was used when preparing the new material for this second edition. When symbolic software is available the reader is encouraged to take full advantage of it by using it to explore the properties of functions, mathematical operations, and differential equations, and also by using its excellent graphical output to gain a better understanding of the geometrical implications of mathematical results.

Book Detail :-
Title: Essentials Engineering Mathematics
Edition: 2nd
Author(s): Burchill, Alan; Hicks, Jeffery; Moskowitz, Jeremy
Publisher: John Wiley & Sons
Series: Serious skills
Year: 2013
Pages: 886
Type: PDF
Language: English
ISBN: 978-1-118-28940-2,978-1-118-33392-1,978-1-118-33174-3,1118289404,1118331745,1118333926
Country: UK

Alan Jeffrey, University of Newcastle, NE1 7RU Newcastle upon Tyne, United Kingdom.
Alan Jeffrey Giacomin who Ontario, Canada (1959) is a professor of Chemical Engineering at Queen's University in Kingston, Ontario and cross-appointed in the Department of Mechanical & Materials Engineering. He has been Editor-In-Chief of Physics of Fluids since 2016.[2] He holds the Tier 1 Canada Research Chair in Rheology from the Canadian government's Natural Sciences and Engineering Research Council.[3] Since 2017, Giacomin has been President of the Canadian Society of Rheology.
Giacomin graduated from St. Thomas High School (Quebec) in Pointe-Claire, Quebec. He later went to Queen's University and completed a B.Sc. Honours in chemical engineering in 1981. He then completed a M.Sc. in chemical engineering in 1983 at Queen's University. Following this, Giacomin joined Professor John Dealy's group at McGill University and completed a Ph.D. in chemical engineering in 1987.
He has been a faculty member in Mechanical Engineering at Texas A&M University and at the University of Wisconsin-Madison. At the University of Wisconsin-Madison, he directed the Rheology Research Center for 20 years. He has held visiting professorships in North America, Europe, and Asia at: Université de Sherbrooke, McGill University, École Polytechnique Fédérale de Lausanne, École des Mines de Paris, the National University of Singapore, Chung Yuan University, National Yunlin University of Science and Technology, University of Crete, Shandong University, Shanghai University, Peking University and King Mongkut's University of Technology North Bangkok.
He has served The Society of Rheology as Associate Editor for Business for the Journal of Rheology.[2] In October 2016 he gave the keynote lecture for Rheology of Complex Fluids at the 66th Annual Canadian Chemical Engineering Conference.[4] Giacomin holds Professional Engineer status in Wisconsin and Ontario.[4]

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Essentials Engineering Mathematics (2nd Edition) written by Alan Jeffrey cover the following topics.
1. Real numbers, inequalities and intervals
2. Function, domain and range
3. Basic coordinate geometry
4. Polar coordinates
5. Mathematical induction
6. Binomial theorem
7. Combination of functions
8. Symmetry in functions and graphs
9. Inverse functions
10. Complex numbers: real and imaginary forms
11. Geometry of complex numbers
12. Modulus/argument form of a complex number
13. Roots of complex numbers
14. Limits
15. One-sided limits: continuity
16. Derivatives
17. Leibniz’s formula
18. Differentials
19. Differentiation of inverse trigonometric functions
20. Implicit differentiation
21. Parametrically defined curves and parametric differentiation
22. The exponential function
23. The logarithmic function
24. Hyperbolic functions
25. Inverse hyperbolic functions
26. Properties and applications of differentiability
27. Functions of two variables
28. Limits and continuity of functions of two real variables
29. Partial differentiation
30. The total differential
31. The chain rule
32. Change of variable in partial differentiation
33. Antidifferentiation (integration)
34. Integration by substitution
35. Some useful standard forms
36. Integration by parts
37. Partial fractions and integration of rational functions
38. The definite integral 288
39. The fundamental theorem of integral calculus and the evaluation of definite integrals
40. Improper integrals
41. Numerical integration
42. Geometrical applications of definite integrals
43. Centre of mass of a plane lamina (centroid)
44. Applications of integration to he hydrostatic pressure on a plate
45. Moments of inertia
46. Sequences
47. Infinite numerical series
48. Power series
49. Taylor and Maclaurin series
50. Taylor’s theorem for functions of two variables: stationary points and their identification
51. Fourier series
52. Determinants
53. Matrices: equality, addition, subtraction, scaling and transposition
54. Matrix multiplication
55. The inverse matrix
56. Solution of a system of linear equations: Gaussian elimination
57. The Gauss/Seidel iterative method
58. The algebraic eigenvalue problem
59. Scalars, vectors and vector addition
60. Vectors in component form
61. The straight line
62. The scalar product (dot product)
63. The plane
64. The vector product (cross product)
65. Applications of the vector product
66. Differentiation and integration of vectors
67. Dynamics of a particle and the motion of a particle in a plane
68. Scalar and vector fields and the gradient of a scalar function
69. Ordinary differential equations: order and degree, initial and boundary conditions
70. First order differential equations solvable by separation of variables
71. The method of isoclines and Euler’s methods
72. Homogeneous and near homogeneous equations
73. Exact differential equations
74. The first order linear differential equation
75. The Bernoulli equation
76. The structure of solutions of linear differential equations of any order
77. Determining the complementary function for constant coefficient equations
78. Determining particular integrals of constant coefficient equations
79. Differential equations describing oscillations
80. Simultaneous first order linear constant coefficient differential equations
81. The Laplace transform and transform pairs
82. The Laplace transform of derivatives
83. The shift theorems and the Heaviside step function
84. Solution of initial value problems
85. The delta function and its use in initial value problems with the Laplace transform
86. Enlarging the list of Laplace transform pairs
87. Symbolic algebraic manipulation by computer software
Reference information
Index

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