# Mathematical Techniques

An Introduction for the Engineering, Physical, and Mathematical Sciences

Price: 835.00 INR

**ISBN: **

9780199560899

**Publication date: **

05/09/2008

Paperback

1008 pages

Price: 835.00 INR

**ISBN: **

9780199560899

**Publication date: **

05/09/2008

Paperback

1008 pages

Mathematical Techniques provides a complete course in mathematics, covering all the essential topics with which a physical sciences or engineering student should be familiar. By breaking the subject into small, modular chapters, the book introduces and builds on concepts in a progressive, carefully-layered way - always with an emphasis on how to use the power of mathematics to best effect, rather than on theoretical proofs of the mathematics presented. With a huge array of end of chapter problems, and new self-check questions, the fourth edition of Mathematical Techniques provides extensive opportunities for students to build their confidence in the best way possible: by using the mathematics for themselves.

**Rights: ** World Rights

Description

Mathematical Techniques provides a complete course in mathematics, covering all the essential topics with which a physical sciences or engineering student should be familiar. By breaking the subject into small, modular chapters, the book introduces and builds on concepts in a progressive, carefully-layered way - always with an emphasis on how to use the power of mathematics to best effect, rather than on theoretical proofs of the mathematics presented. With a huge array of end of chapter problems, and new self-check questions, the fourth edition of Mathematical Techniques provides extensive opportunities for students to build their confidence in the best way possible: by using the mathematics for themselves.

Table of contents

PART 1. ELEMENTARY METHODS, DIFFERENTIATION, COMPLEX NUMBERS

Chapter 1: Standard functions and techniques

Chapter 2: Differentiation

Chapter 3: Further techniques for differentiation

Chapter 4: Applications of differentiation

Chapter 5: Taylor series and approximations

Chapter 6: Complex numbers

PART 2. MATRIX AND VECTOR ALGEBRA

Chapter 7: Matrix algebra

Chapter 8: Determinants

Chapter 9: Elementary operations with vectors

Chapter 10: The scalar product

Chapter 11: Vector product

Chapter 12: Linear algebraic equations

Chapter 13: Eigenvalues and eigenvectors

PART 3. INTEGRATION AND DIFFERENTIAL EQUATIONS

Chapter 14: Antidifferentiation and area

Chapter 15: The definite and indefinite integral

Chapter 16: Applications involving the integral as a sum

Chapter 17: Systematic techniques for integration

Chapter 18: Unforced linear differential equations with constant coefficients

Chapter 19: Forced linear differential equations

Chapter 20: Harmonic functions and the harmonic oscillator

Chapter 21: Steady forced oscillations: phasors, impedance, transfer functions

Chapter 22: Graphical, numerical, and other aspects of first-order equations

Chapter 23: Nonlinear differential equations and the phase plane

PART 4. TRANSFORMS AND FOURIER SERIES

Chapter 24: The Laplace transform

Chapter 25: Laplace and z transforms: applications

Chapter 26: Fourier series

Chapter 27: Fourier transforms

PART 5. MULTIVARIABLE CALCULUS

Chapter 28: Differentiation of functions of two variables

Chapter 29: Functions of two variables: geometry and formulae

Chapter 30: Chain rules, restricted maxima, coordinate systems

Chapter 31: Functions of any number of variables

Chapter 32: Double integration

Chapter 33: Line integrals

Chapter 34: Vector fields: divergence and curl

PART 6. DISCRETE MATHEMATICS

Chapter 35: Sets

Chapter 36: Boolean algebra: logic gates and switching functions

Chapter 37: Graph theory and its applications

Chapter 38: Difference equations

PART 7. PROBABILITY AND STATISTICS

Chapter 39: Probability

Chapter 40: Random variables and probability distributions

Chapter 41: Descriptive statistics

PART 8. PROJECTS

Chapter 42: Applications projects using symbolic computing

Self-tests: ed answers

Answers to ed problems

Appendices

Further reading

Index

Features

- Short, modular chapters make the book flexible enough to be used on a wide variety of courses.
- Over 500 worked examples show how the techniques are applied and offer valuable guidance for the reader when tackling the problems.
- Self-check questions and over 2000 end of chapter problems provide extensive opportunities for students to actively master the concepts presented.
- Emphasis on methods and applications keeps students moving through the subject without being slowed down by detailed mathematical proofs.
- A series of Projects at the end of the book encourage student to use mathematical software to develop further their understanding of the concepts covered.
- The Online Resource Centre features additional resources for lecturers and students, to enhance the value of the book as a teaching and learning tool.

Description

Mathematical Techniques provides a complete course in mathematics, covering all the essential topics with which a physical sciences or engineering student should be familiar. By breaking the subject into small, modular chapters, the book introduces and builds on concepts in a progressive, carefully-layered way - always with an emphasis on how to use the power of mathematics to best effect, rather than on theoretical proofs of the mathematics presented. With a huge array of end of chapter problems, and new self-check questions, the fourth edition of Mathematical Techniques provides extensive opportunities for students to build their confidence in the best way possible: by using the mathematics for themselves.

Read MoreTable of contents

PART 1. ELEMENTARY METHODS, DIFFERENTIATION, COMPLEX NUMBERS

Chapter 1: Standard functions and techniques

Chapter 2: Differentiation

Chapter 3: Further techniques for differentiation

Chapter 4: Applications of differentiation

Chapter 5: Taylor series and approximations

Chapter 6: Complex numbers

PART 2. MATRIX AND VECTOR ALGEBRA

Chapter 7: Matrix algebra

Chapter 8: Determinants

Chapter 9: Elementary operations with vectors

Chapter 10: The scalar product

Chapter 11: Vector product

Chapter 12: Linear algebraic equations

Chapter 13: Eigenvalues and eigenvectors

PART 3. INTEGRATION AND DIFFERENTIAL EQUATIONS

Chapter 14: Antidifferentiation and area

Chapter 15: The definite and indefinite integral

Chapter 16: Applications involving the integral as a sum

Chapter 17: Systematic techniques for integration

Chapter 18: Unforced linear differential equations with constant coefficients

Chapter 19: Forced linear differential equations

Chapter 20: Harmonic functions and the harmonic oscillator

Chapter 21: Steady forced oscillations: phasors, impedance, transfer functions

Chapter 22: Graphical, numerical, and other aspects of first-order equations

Chapter 23: Nonlinear differential equations and the phase plane

PART 4. TRANSFORMS AND FOURIER SERIES

Chapter 24: The Laplace transform

Chapter 25: Laplace and z transforms: applications

Chapter 26: Fourier series

Chapter 27: Fourier transforms

PART 5. MULTIVARIABLE CALCULUS

Chapter 28: Differentiation of functions of two variables

Chapter 29: Functions of two variables: geometry and formulae

Chapter 30: Chain rules, restricted maxima, coordinate systems

Chapter 31: Functions of any number of variables

Chapter 32: Double integration

Chapter 33: Line integrals

Chapter 34: Vector fields: divergence and curl

PART 6. DISCRETE MATHEMATICS

Chapter 35: Sets

Chapter 36: Boolean algebra: logic gates and switching functions

Chapter 37: Graph theory and its applications

Chapter 38: Difference equations

PART 7. PROBABILITY AND STATISTICS

Chapter 39: Probability

Chapter 40: Random variables and probability distributions

Chapter 41: Descriptive statistics

PART 8. PROJECTS

Chapter 42: Applications projects using symbolic computing

Self-tests: ed answers

Answers to ed problems

Appendices

Further reading

Index