Enhanced descriptions from Syndetics:

All students of engineering, science, and mathematics take courses on mathematical techniques or `methods', and large numbers of these students are insecure in their mathematical grounding. This book offers a course in mathematical methods for students in the first stages of a science or engineering degree. Its particular intention is to cover the range of topics typically required, while providing for students whose mathematical background is minimal. The topics covered are:* Analytic geometry, vector algebra, vector fields (div and curl), differentiation, and integration.* Complex numbers, matrix operations, and linear systems of equations.* Differential equations and first-order linear systems, functions of more than one variable, double integrals, and line integrals.* Laplace transforms and Fourier series and Fourier transforms. * Probability and statistics.The earlier part of this list consists largely of what is thought pre-university material. However, many science students have not studied mathematics to this level, and among those that have the content is frequently only patchily understood. Mathematical Techniques begins at an elementary level but proceeds to give more advanced material with a minimum of manipulative complication. Most of the concepts can be explained using quite simple examples, and to aid understanding a large number of fully worked examples is included. As far as is possible chapter topics are dealt with in a self-contained way so that a student only needing to master certain techniques can omit others without trouble. The widely illustrated text also includes simple numerical processes which lead to examples and projects for computation, and a large number of exercises (with answers) is included to reinforce understanding.

Table of contents provided by Syndetics

• Part I Elementary methods, differentiation, complex numbers
• Standard functions and techniques
• Differentiation
• Further techniques for differentiation
• Applications of differentiation
• Taylor series and approximations
• Complex numbers
• Part II Matrix algebra and vectors
• Matrix algebra
• Determinants
• Elementary operations with vectors
• The scalar product
• Vector product; derivatives of vectors
• Linear equations
• Eigenvalues and eigenvectors
• Part III Integration and differential equations
• Antidifferentiation and area
• The definite and indefinite integral
• Applications involving the integral as a sum
• Systematic techniques for integration
• Unforced linear differential equations with constant coefficients
• Forced linear differential equations
• Harmonic functions and the harmonic oscillator
• Steady forced oscillations: phasors, impedance, transfer functions
• Graphical, numerical, and other aspects of first-order equations
• Introduction to the phase plane
• Part IV Transforms and Fourier series
• The Laplace transform
• Applications of the Laplace transform
• Fourier series and Fourier transforms
• Part V Multivariable calculus
• Differentiation of functions of two variables
• Functions of two variables: geometry and formulae
• Chain rules, restricted maxima, coordinate systems
• Functions of any number of variables
• Double integration
• Line integrals
• Vector fields: divergence and curl
• Part VI Discrete mathematicsSets
• Boolean algebra: logic gates and switching functions
• Graph theory and its applications
• Difference equations
• Part VII Probability and statistics
• Probability
• Random variables and probability distributions
• Descriptive statistics
• Part VIII Projects
• Applications projects using symbolic computing
• Answers to selected problems
• Appendix
• Index
• Completely new for this second edition

Reviews provided by Syndetics

CHOICE Review

Authors Peter Smith and Dom Jordan teach in the department of mathematics at Keele University; their book is for use in a year-long course in mathematics for students of engineering and physical sciences at universities in the UK. Topics covered include differential and integral calculus, linear algebra, differential equations, Laplace and Fourier transforms, discrete mathematics, probability, and statistics. In the US, these topics would typically be discussed in as many as seven separate courses! Obviously, such a broad range of topics cannot be reviewed in depth within one 800-page book. The authors have opted for a very basic pedagogical approach, with emphasis on drill and practice. There is little in the way of in-depth exercises, modeling, or applications to other disciplines. One may compare this book with works that cover only a small part of this material but in much greater detail, such as Deborah Hughes-Hallett, Andrew M. Gleason, et al., Calculus (1994), and David C. Lay's Linear Algebra and Its Applications (2nd ed., 1997). Lower-division undergraduates. B. Borchers New Mexico Institute of Mining and Technology

Author notes provided by Syndetics

Long-standing members of Mathematics Department at Keele. Keele has a long and honourable effort to take students with non-conventional school and other qualifications on science courses. Hence the authors have a wealth of experience teaching the sort of student now entering other universities to attempt science degrees.