THE MATHEMATICS ENGINEERS USE EVERYDAY IN INDUSTRY

W.G. STEENKENGE AVIATIONOHIO MATHEMATICS AND

SCIENCE COALITIONNOVEMBER 19, 2015

BACKGROUND

• Bachelors, Masters, and Ph.D. in Mechanical Engineering• Mathematics Courses

– High School Algebra I and II Geometry Trigonometry Solid Geometry

– Undergraduate Calculus, I, II, III Advanced Mathematics for Engineers Introduction to Mathematical Statistics Mathematics of Physics and Modern Engineering

– Graduate Advanced Calculus Introduction to Probability Theory and Its Applications Quantum Chemistry and Statistical Mechanics

– On Job Training Maximum Value Statistics Measurement and Analysis of Random Data

BACKGROUND (Concluded

• Fifty Year Career in Engineering (Aviation and Propulsion)– General Dynamics, Fort Worth, Texas (6 years)– GE Aviation, Cincinnati, Ohio (44 years)

• Lived on a Farm for 40 Years

MATHEMATICAL TOPICS

• GEOMETRY– Congruence and Similarity (Dependent on Ratio)– Proofs (Triangles, Parallel and Perpendicular Lines)– Volumes for Cylinders, Pyramids, Cones and Spheres– Intro to Right Triangles Trigonometry

Bill

X

X

X

X

Others %

68

26

63

74

MATHEMATICAL TOPICS

• Algebra II– Expressions, Equations, and Inequalities– Ratios, Proportions, Percents– Functions, Equations, and Graphs– Linear Systems– Quadratic Functions and Equations– Polynomials and Polynomial Functions– Radical Functions and Rational Exponents– Exponential and Logarithmic Functions– Rational functions– Sequences and Series– Quadratic Relations and Conic Sections– Probability and Statistics– Matrices– Periodic Functions and Trigonometry– Trigonometric Identities and Equations

• Calculus– Differential Calculus– Conic Sections– Maxima, Minima, and Inflections– Infinite Series– Differential Equations– Integral Calculus

Bill

X

X

X

X

X

X

X

X

X

X

Others %

95

100

100

74

89

84

37

68

21

37

16

79

42

32

53

X

X

X

53

0

37

11

37

42

MATHEMATICAL TOPICS (Concluded)

• Other Topics– Vector Algebra– Matrices / Matrix Algebra– Vector Field Theory– Partial Differential Equations– Complex Variables– Elementary Topology– Transformations

• Statistics– Mean– Standard Deviation– Amplitude Probability Density Function– Correlation Functions– Power Spectral Density Functions

Bill Others %

37

26

5

21

11

5

32

X

X

X

X

X

84

95

32

53

42

MY THESIS

• OF MAJOR IMPORTANCE– Expressions, Equations, and Inequalities– Ratios, Proportions, Percents– Linear Systems

• BUT USAGE WAS MUCH BROADER (74%)– Intro to Right Triangles Trigonometry– Expressions, Equations, and Inequalities– Ratios, Proportions, and Percents– Functions, Equations, and Graphs– Linear Systems– Quadratic Functions and Equations– Polynomials and Polynomial Functions– Probability and Statistics– Statistics (Mean and Standard Deviation)

04/21/23Engine Operability 7

SUMMARY

• Use of broad spectrum of mathematics strands is greater than I thought

• As a mathematics educator said to me, “To use mathematics well, you need to have a wide knowledge of the mathematical strands”

• Perhaps this statement is best supported by some recent examples from my consulting work

04/21/23Engine Operability 8

EXAMPLES OF ENGINEERING MATHEMATICS

(1 + x)-n = 1 + nx + +n(n+1)x2

2!

PROBLEM

• What is the value of 1/0.98

~1.01

• Remember the series

• Thus

• Actual answer

1/0.98 = = 1 + (.02) = 1.01 1

(1-.02)1/2

1 2

~ ~ ~

1/0.98 = 1.015 (% Error of estimate = -0.015)

INTERPOLATIONP2

B P1

Px

X1

X2

X

PROBLEM INVOLVING LOTS OF DATA