Engineering Mathematics and Statistics

Pocket Handbook

Nicholas P. Cheremisinoff, Louise Ferrante

• Publisher: Routledge
• Year: 2018
• ISBN:
  9781351450973
• Edition: 1
• Topic: Mathematik
• Subtopic: Angewandte Mathematik

This pocket handbook is intended as a handy reference guide for engineers, scientists and students on widely used mathematical relationships, statistical formulas and problem-solving methods. It is a compilation of useful formulas and generalised problem-solving techniques employed by practitioners in the analysis and interpretation of scientific data and problem solving. Written in short note form, it is intended to provide the user with a quick, easy reference to information with ample references provided for further readings. Illustrated examples are included for more involved problem-solving methods. Many of the techniques are well suited to adaptatation on personal computers and there are more detailed instructions included to guide and illustrate computer aided problem solving.

Part A

Mathematics

ANGLE BETWEEN, NORM, AND DOT PRODUCT OF VECTORS

Let $\overrightarrow{a}=(a_1,a_2,\dots ,a_n)$ and $\overrightarrow{b}=(b_1,b_2,\dots ,b_n)$ be two vectors. The norm of $\overrightarrow{a}$ is denoted by |$\overrightarrow{a}$| and is calculated by the following formula:

$\left|\overrightarrow{a}\right|=\sqrt{a_1^2+a_2^2+\dots +a_n^2}$

Similarly,

$\left|\overrightarrow{b}\right|=\sqrt{b_1^2+b_2^2+\dots +b_n^2}$

The dot product of $\overrightarrow{a}$ and $\overrightarrow{b}$ is denoted by $\overrightarrow{a}\cdot \overrightarrow{b}$ and is calculated by the following formula:

$\overrightarrow{a}\cdot \overrightarrow{b}=a_1{b}_1+a_2{b}_2+\dots +a_n{b}_n$

The angle between a and b is denoted by θ and is calculated by the following formula:

$\theta ={\cos }^{-1}\left(\frac{\overrightarrow{a}\cdot \overrightarrow{b}}{\left|\overrightarrow{a}\right|\cdot \left|\overrightarrow{b}\right|}\right)$

AREA OF A TRIANGLE (a, b, c)
(refer to Figure A1)

Given three sides of a triangle this program computes the area by the following formula:

$\text{Area}=\sqrt{s(s-a)(s-b)(s-c)}$

where $s=\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.(a+b+c)$.

F...