Mathematical techniques : an introduction for the engineering, physical, and mathematical sciences
著者
書誌事項
Mathematical techniques : an introduction for the engineering, physical, and mathematical sciences
Oxford University Press, 1997
2nd ed
- : hard
- : pbk
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注記
Includes index
内容説明・目次
- 巻冊次
-
: pbk ISBN 9780198564614
内容説明
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.
This book is intended for beginning engineering and science students (1st year) doing `maths for scientists' courses.
目次
- 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, the Z-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 mathematics. Sets. Boolean algebra: logic gates and switching functions. Graph theory and its applications. Difference equations. Part VIII: 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
- 巻冊次
-
: hard ISBN 9780198564621
内容説明
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. This book is intended for beginning engineering and science students (1st year) doing `maths for scientists' courses.
目次
- 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 mathematics
- sets
- Boolean algebra: logic gates and switching functions
- graph theory and its applications
- difference equations. Part VIII Probability and statistics
- probability
- random variables and probability distributions *
- descriptive statistics . Part VIII Projects
- applications projects using symbolic computing
- answers to selected problems.
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