Essentials Engineering Mathematics

Alan Jeffrey

• Publisher: CRC Press
• Year: 2004
• Print ISBN: 9781584884897
• eBook ISBN: 9781040088449
• Edition: 2
• Topic: Mathematics
• Subtopic: Applied Mathematics
• Index: Mathematics

First published in 1992, Essentials of Engineering Mathematics is a widely popular reference ideal for self-study, review, and fast answers to specific questions. While retaining the style and content that made the first edition so successful, the second edition provides even more examples, new material, and most importantly, an introduction to usi

Table of contents

• Cover
• Half Title
• Title Page
• Copyright Page
• Contents
• Preface to the Second Edition
• 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
• Symmetry in functions and graphs 8
• 9 Inverse functions
• 10 Complex numbers: real and imaginary forms
• Geometry of complex numbers 11
• Modulus-argument form of a complex number 12
• Roots of complex numbers 13
• 14 Limits
• One-sided limits: continuity 15
• Derivatives 16
• Leibniz’s formula 17
• 18 Differentials
• Differentiation of inverse trigonometric functions 19
• 20 Implicit differentiation
• Parametrically defined curves and parametric differentiation
• 22 The exponential function
• 23 The logarithmic function
• 24 Hyperbolic functions
• Inverse hyperbolic functions
• 26 Properties and applications 26 of differentiability
• Functions of two variables27
• Limits and continuity of functions of two real variables 28
• 29 Partial differentiation
• The total differential 30
• 31 The chain rule
• 32 Change of variable in partial differentiation
• Antidifferentiation (integration)33
• Integration by substitution 34
• Some useful standard forms 35
• 36 Integration by parts
• Partial fractions and integration of rational functions
• 38 The definite integral
• The fundamental theorem of integral calculus and the evaluation of definite integrals
• 40 Improper integrals
• 41 Numerical integration
• Geometrical applications of definite integrals 42
• Centre of mass of a plane lamina (centroid)
• Application of integration to the hydrostatic pressure on a plate
• 45  Moments of inertia
• Sequences
• 47  Infinite numerical series
• 48 Power series
• Taylor and Maclaurin series
• Taylor’s theorem for functions of two variables: stationary points and their identification
• 51 Fourier series
• Determinants
• 53 Matrices: equality, addition, subtraction, scaling and transposition
• 54 Matrix multiplication
• The inverse matrix
• Solution of a system of linear equations: Gaussian elimination
• The Gauss-Seidel iterative method
• 58 The algebraic eigenvalue problem
• Scalars, vectors and vector addition
• Vectors in component form
• The straight line
• The scalar product (dot product) 62
• 63 The plane
• The vector product (cross product) 64
• Applications of the vector product
• Differentiation and integration of vectors
• Dynamics of a particle and the motion of a particle in a plane
• Scalar and vector fields and the gradient of a scalar function
• Ordinary differential equations: order and degree, initial and boundary conditions
• First order differential equations solvable by separation of variables
• The method of isoclines and Euler’s methods
• Homogeneous and near homogeneous equations
• Exact differential equations
• The first order linear differential equation
• The Bernoulli equation 75
• The structure of solutions of linear differential equations of any order
• Determining the complementary function for constant coefficient equations
• Determining particular integrals of constant coefficient equations
• Differential equations describing oscillations
• Simultaneous first order linear constant coefficient differential equations 80
• The Laplace transform and transform pairs
• The Laplace transform of derivatives
• The shift theorems and the Heaviside step function 83
• Solution of initial value 84
• The delta function and its use in initial value problems with the Laplace transform
• Enlarging the list of Laplace transform pairs 86
• Symbolic algebraic manipulation by computer software
• Answers
• Reference information
• Index