2
2.1 INTRODUCTION
· This section has been greatly enhanced, and tailored to meet our engineering requirements.
· The section outlined here is not intended to teach the elements of mathematics, but it is designed to
be a quick reference guide to support the engineer required to use techniques that may not have
been used recently.
· For those planning to write the first ABET Fundamentals of Engineering exam, the following topics
are commonly on the exam.
1.
- quadratic equation
2.
- straight line equations - slop and perpendicular
3.
- conics, circles, ellipses, etc.
4.
- matrices, determinants, adjoint, inverse, cofactors, multiplication
5.
- limits, L'Hospital's rule, small angle approximation
6.
- integration of areas
7.
- complex numbers, polar form, conjugate, addition of polar forms
8.
- maxima, minima and inflection points
9.
- first order differential equations - guessing and separation
10.
- second order differential equation - linear, homogeneous, non-homogeneous, second order
11.
- triangles, sine, cosine, etc.
12.
- integration - by parts and separation
13.
- solving equations using inverse matrices, Cramer's rule, substitution
14.
- eigenvalues, eigenvectors
15.
- dot and cross products, areas of parallelograms, angles and triple product
16.
- divergence and curl - solenoidal and conservative fields
17.
- centroids
18.
- integration of volumes
19.
- integration using Laplace transforms
20.
- probability - permutations and combinations
21.
- mean, standard deviation, mode, etc.
22.
- log properties
23.
- taylor series
24.
- partial fractions
25.
- basic coordinate transformations - cartesian, cylindrical, spherical
26.
- trig identities
27.
- derivative - basics, natural log, small angles approx., chain rule, partial fractions