Essentials Engineering Mathematics

ISBN-13: 9781584884897 / Angielski / Miękka / 2004 / 896 str.

W. H. C. Bassetti; Alan Jeffrey

Opis

This popular self-study/supplementary textbook covers in detail all mathematical requirements common to first year engineering students of every discipline. Thoroughly revised for the second edition, the book provides more worked examples and exercises, and more material on numerical computation and gives extensive problem sets at the end of each chapter. It is organized into short sections specific to certain topics, which allows students to identify subjects of interest that they can study separately, with little background reading. The author provides numerous worked examples throughout the text, and for reference, includes lists of mathematical formulae, standard integrals, and Laplace transform pairs.

Recenzje

"The book is intended for first year engineering students and presumably this choice of subjects is a reflection of the course on which the author lectured. The book fulfills this purpose in a very satisfactory manner and can be warmly recommended for this purpose. The explanations are good and there is an adequacy of worked examples. …A welcome feature is that indefinite integrals mentioned in the text all have included an arbitrary constant. …Much of the book would be found useful for those in the last years at school."
-Zentralblatt MATH

"Each of the short sections covers the amount of material one would hope to get through in a lecture or two, typically giving a short introduction to the relevant theory and several worked examples. …Jeffrey's book could be easily adopted as a course text, and the sections can be divided naturally into groups for shorter modules."
-Times Higher Education Supplement

ead> Concise explanations and a wealth of examples form an ideal study guide and reference

Spis treści

Real numbers, inequalities and intervals
Function, domain and range
Basic coordinate geometry
Polar coordinates
Mathematical induction
Binomial theorem
Combination of functions
Symmetry in functions and graphs
Inverse functions
Complex numbers; real and imaginary forms
Geometry of complex analysis
Modulus-argument form of a complex number
Roots of complex numbers
Limits
One-sided limits
Derivatives
Leibniz's formula
Differentials
Differentiation of inverse trigonometric functions
Implicit differentiation
Parametrically defined curves and parametric differentiation
The exponential function
The logarithmic function
Hyperbolic functions
Inverse hyperbolic functions
Properties and applications of differentialability
Functions of two variables
Limits and continuity of functions of two real variables
Partial differentiation
The total differential
The chain rule
Change of variable in partial differentiation
Antidifferentiation (integration)
Integration by substitution
Some useful standard forms
Integration by parts
Partial fractions and integration of rational functions
The definite integral
The fundamental theorem of integral calculus and the evaluation of definite integrals
Improper integrals
Numerical integration
Geometrical applications of definite integrals
Centre of mass of a plane lamina
Applications of integration to he hydrostatic pressure on a plate
Moments of inertia
Sequences
Infinite numerical series
Power series
Taylor and Maclaurin series
Taylor's theorem for functions of two variable: stationary points and their identification
Fourier series
Determinants
Matrices
Matrix multiplication
The inverse matrix
Solution of a system of linear equations: Gaussian elimination
The Gauss-Seidel iterative method
The algebraic eigenvalue problem
Scalars, vectors and vector addition
Vectors in component form
The straight line
The scalar product (dot product)
The plane
The vector product (cross product)
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
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 different equations
The Laplace transform and transform pairs
The Laplace transform of derivatives
The shift theorems and the Heaviside step function
Solution of initial value problems
The Delta function and its use in initial value problems with the Laplace transform
Enlarging the list of Laplace transform pairs
Symbolic Algebraic Manipulation by Computer Software
Answers
References

O autorze

Alan Jeffrey