understanding engineering mathematics, bill cox [pdf]

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Understanding Engineering Mathematics by Bill Cox

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Understanding Engineering Mathematics written by Bill Cox

This book contains most of the material covered in a typical first year mathematics course in an engineering or science programme. It devotes Chapters 1–10 to consolidating the foundations of basic algebra, elementary functions and calculusChapters 11–17 cover the range of more advanced topics that are normally treated in the first year, such As vectors and matrices, differential equations, partial differentiation and transform methods.
With widening participation in higher education, broader school curricula and the wide range of engineering programmes available, the challenges for both teachers and learners in engineering mathematics are now considerableAs a result, a substantial part of many first year engineering programmes is dedicated to consolidation of the basic mathematics material covered at pre-university levelHowever, individual students have widely varying backgrounds in mathematics and it is difficult for a single mathematics course to address everyone’s needsThis book is designed to help with this by covering the basics in a way that enables students and teachers to quickly identify the strengths and weaknesses of individual students and ‘top up’ where necessaryThe structure of the book is therefore somewhat different to the conventional textbook, and ‘To the student’ provides Some suggestions on how to use it.
Title: Understanding Engineering Mathematics
Edition:
Author(s): Bill Cox
Publisher: Newnes
Series:
Year: 2001
Pages: 545
Type: PDF
Language: English
ISBN: 9780750650984,9781417505562,0750650982
Country:
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Understanding Engineering Mathematics written by Bill Cox cover the following topics.
1. Number and Arithmetic
1.1 Review
1.2 Revision
1.3 Reinforcement
1.4 Applications
Answers to reinforcement exercises
2. Algebra
2.1 Review
2.2 Revision
2.3 Reinforcement
2.4 Applications
Answers to reinforcement exercises
3. Functions and Series
3.1 Review
3.2 Revision
3.3 Reinforcement
3.4 Applications
Answers to reinforcement exercises
4. Exponential and Logarithm Functions
4.1 Review
4.2 Revision
4.3 Reinforcement
4.4 Applications
Answers to reinforcement exercises
5. Geometry of Lines, Triangles and Circles
5.1 Review
5.2 Revision
5.3 Reinforcement
5.4 Applications
Answers to reinforcement exercises
6. Trigonometry
6.1 Review
6.2 Revision
6.3 Reinforcement
6.4 Applications
Answers to reinforcement exercises
7. Coordinate Geometry
7.1 Review
7.2 Revision
7.3 Reinforcement
7.4 Applications
Answers to reinforcement exercises
8. Techniques of Differentiation
8.1 Review
8.2 Revision
8.3 Reinforcement
8.4 Applications
Answers to reinforcement exercises
9. Techniques of Integration
9.1 Review
9.2 Revision
9.3 Reinforcement
9.4 Applications
Answers to reinforcement exercises
10. Applications of Differentiation and Integration
10.1 Review
10.2 Revision
10.3 Reinforcement
10.4 Applications
Answers to reinforcement exercises
11. vectors
11.1 Introduction – representation of a vector quantity
11.2 Vectors as arrows
11.3 Addition and subtraction of vectors
11.4 Rectangular Cartesian coordinates in three dimensions
11.5 Distance in Cartesian coordinates
11.6 Direction cosines and ratios
11.7 Angle between two lines through the origin
11.8 Basis vectors
11.9 Properties of vectors
11.10 The scalar product of two vectors
11.11 The vector product of two vectors
11.12 Vector functions
11.13 Differentiation of vector functions
11.14 Reinforcement
11.15 Applications
11.16 Answers to reinforcement exercises
12. Complex Numbers
12.1 What are complex numbers?
12.2 The algebra of complex numbers
12.3 Complex variables and the Argand plane
12.4 Multiplication in polar form
12.5 Division in polar form
12.6 Exponential form of a complex number
12.7 De Moivre’s theorem for integer powers
12.8 De Moivre’s theorem for fractional powers
12.9 Reinforcement
12.10 Applications
12.11 Answers to reinforcement exercises
13. Matrices and Determinants
13.1 An overview of matrices and determinants
13.2 Definition of a matrix and its elements
13.3 Adding and multiplying matrices
13.4 Determinants
13.5 Cramer’s rule for solving a system of linear equations
13.6 The inverse matrix
13.7 Eigenvalues and eigenvectors
13.8 Reinforcement
13.9 Applications
13.10 Answers to reinforcement exercises
14. Analysis for Engineers – Limits, Sequences, Iteration, Series and All That
14.1 Continuity and irrational numbers
14.2 Limits
14.3 Some important limits
14.4 Continuity
14.5 The slope of a curve
14.6 Introduction to infinite series
14.7 Infinite sequences
14.8 Iteration
14.9 Infinite series
14.10 Tests for convergence
14.11 Infinite power series
14.12 Reinforcement
14.13 Applications
14.14 Answers to reinforcement exercises
15. Ordinary Differential Equations
15.1 Introduction
15.2 Definitions
15.3 First order equations – direct integration and separation of variables
15.4 Linear equations and integrating factors
15.5 Second order linear homogeneous differential equations
15.6 The inhomogeneous equation
15.7 Reinforcement
15.8 Applications
15.9 Answers to reinforcement exercises
16. Functions of More than One Variable – Partial Differentiation
16.1 Introduction
16.2 Function of two variables
16.3 Partial differentiation
16.4 Higher order derivatives
16.5 The total differential
16.6 Reinforcement
16.7 Applications
16.8 Answers to reinforcement exercises
17. An Appreciation of Transform Methods
17.1 Introduction
17.2 The Laplace transform
17.3 Laplace transforms of the elementary functions
17.4 Properties of the Laplace transform
17.5 The inverse Laplace transform
17.6 Solution of initial value problems by Laplace transform
17.7 Linear systems and the principle of superposition
17.8 Orthogonality relations for trigonometric functions
17.9 The Fourier series expansion
17.10 The Fourier coefficients
17.11 Reinforcement
17.12 Applications
17.13 Answers to reinforcement exercises

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