Introductory Engineering Mathematics

✍ Scribed by Reeping, David;Reid, Kenneth

• Publisher: Momentum Press
• Year: 2017
• Tongue: English
• Series: General engineering and K-12 engineering education collection
• Edition: First edition
• Category: Library

✦ Synopsis

This text serves as a concise introduction to the ocean of information collectively known as "Engineering Mathematics." Admittedly, compiling everything into a short book that is useful to any audience is an impossible task; therefore, we picked a few main ideas holding up the mathematics within the engineering curriculum instead of stuffing all of the details into such a small package. Our strategy in writing this text was to address conceptual understanding as often as possible; the informal "meet and greets" with common mathematical objects are intended to provide an intuitive basis for the formalized study within an engineering or mathematics course. The intent is to present mathematics as a useful tool within engineering without becoming too bogged down with formalities; therefore, we do not provide rigorous proofs of major theorems. Similarly, we will refer to a particular field for additional information if desired whenever a topic is beyond the scope of the text. We do assume a level of mathematical maturity that amounts to high school Algebra. Whether you are a math or science instructor tasked to teach an engineering class, a high school student looking into engineering, or an engineering student already, we hope you are able to walk away from this text with tangible outcomes--maybe even a refined perspective on the subject.;1. Motivation for engineering mathematics -- 1.1 Abstraction in engineering -- 1.2 Engineering systems as a starting point

✦ Table of Contents

1. Motivation for engineering mathematics --
   1.1 Abstraction in engineering --
   1.2 Engineering systems as a starting point 2. Solving common engineering problems --
   2.1 Choice of coordinate systems --
   2.1.1 Rectangular coordinates --
   2.1.1.1 Moving to a third dimension --
   2.1.2 Polar coordinates --
   2.1.3 Vectors --
   2.1.3.1 Vector addition and subtraction --
   2.1.3.2 Vector multiplication --
   2.1.4 Manipulating space --
   2.1.5 Complex numbers --
   2.2 Graphical relationships --
   angles --
   2.2.1 Useful angle theorems --
   2.2.2 Ideas in trigonometry --
   2.2.2.1 Laws of sines and cosines 3. Employing functions --
   3.1 Relations to functions --
   3.1.1 Composition --
   3.1.2 Inverse functions --
   3.2 Fitting data --
   3.3 Locating roots of a function --
   3.3.1 Locating roots within a tolerance, or "getting close enough" --
   3.4 Functional behavior 4. Using calculus to solve problems --
   4.1 Differential calculus --
   4.2 Integral calculus 5. Inputs and outputs --
   5.1 Classifications --
   5.2 Common manipulations --
   5.3 Special inputs --
   5.3.1 Heaviside unit step, the step function --
   5.3.2 Dirac's Delta function: the impulse function --
   5.4 Inputs in terms of an infinite series --
   5.4.1 Power series --
   5.4.2 Fourier series 6. Engineering systems --
   6.1 A summary and where to go from here --
   Index.

✦ Subjects

calculus;first year engineering;graphing;problem solving;systems;Engineering mathematics;TECHNOLOGY & ENGINEERING--Engineering (General);TECHNOLOGY & ENGINEERING--Reference;Electronic books;TECHNOLOGY & ENGINEERING -- Engineering (General);TECHNOLOGY & ENGINEERING -- Reference