A Handbook of Essential Mathematical Formulae

Intended for students of mathematics as well as of engineering, physical science, economics, business studies, and computer science, this handbook contains vital information and formulas for algebra, geometry, calculus, numerical methods, and statistics. Comprehensive tables of standard derivatives and integrals, together with the tables of Laplace, Fourier, and Z transforms are included. A spiral binding that allows the handbook to lay flat for easy reference enhances the user-friendly design.

Alan Davies is a professor of mathematics at the University of Hertfordshire and has been teaching mathematics to engineers, scientists, and mathematicians for more than 30 years. He is the author of An Introduction to Computational Geometry for Curves and Surfaces. Diane Crann is a mathematics graduate with more than 10 years of experience in organizing mathematics-related activities for people of all ages, including the Royal Institution Mathematics Masterclass Series.

Algebra, Trigonometry and Geometry

1

(8)

Indices and logarithms

1

(1)

Factors and roots of equations

2

(1)

Partial fractions

2

(1)

Permutations and combinations

2

(1)

Trigonometric functions

3

(1)

Hyperbolic functions

4

(1)

Geometry

5

(1)

Conic sections

6

(1)

Mensuration

7

(1)

Complex numbers

7

(2)

Determinants and Matrices

9

(4)

Determinants

9

(1)

Matrices

10

(1)

Systems of equations

11

(1)

Eigenvalues and eigenvectors

12

(1)

Vector Algebra

13

(3)

Vector addition

13

(1)

Vector products

13

(1)

Polar coordinates in two and three dimensions

14

(2)

Calculus

16

(15)

Rules for manipulation of derivatives and integrals

16

(2)

Standard derivatives and integrals

18

(2)

Definite integrals

20

(2)

Radius of curvature of a curve

22

(1)

Stationary points

22

(1)

Limits and series

23

(1)

Multiple integration

24

(2)

Applications of integration

26

(4)

Kinematics and dynamics

30

(1)

Ordinary Differential Equations

31

(3)

First order equations

31

(1)

Second order equations

32

(1)

Higher order equations

33

(1)

Fourier Series

34

(2)

Vector Calculus

36

(4)

grad, div and curl

36

(3)

Integral theorems of the vector calculus

39

(1)

Tables of Transforms

40

(10)

The Laplace transform

40

(4)

The Z-transform

44

(1)

The Fourier transform

45

(1)

Fourier sine and cosine transforms

46

(1)

Some periodic functions: Laplace transforms and Fourier series

47

(3)

Numerical Methods

50

(10)

Interpolation

50

(1)

Finite difference operators

51

(1)

Non-linear algebraic equations

52

(1)

Numerical integration

52

(2)

Numerical solution of ordinary differential equations

54

(1)

Systems of linear equations, n x n

55

(2)

Chebyshev polynomials

57

(1)

Numerical eigenvalues and eigenvectors

57

(2)

Least squares approximation

59

(1)

Statistics

60

(4)

Sample statistics

60

(1)

Regression and correlation

61

(1)

Distributions

61

(3)

S. I. Units (Systeme International d'Unites)

64

Fundamental units

64

(1)

S. I. Prefixes and multiplication factors

65

(1)

Basic and derived units

65

(2)

Values of some physical constants

67

(1)

Useful masses

67

(2)

Astronomical constants

69

(1)

Mathematical constants

69

(1)

The Greek alphabet

70

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A Handbook of Essential Mathematical Formulae

Summary

Author Biography

Table of Contents

Supplemental Materials