The Fundamentals of Engineering (FE) exam is given semiannually
1 Fundamentals of Engineering Exam Review Series · 1 Fundamentals of Engineering Exam Review...
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Fundamentals of Engineering Exam Review Series Mathematics Prof. Meredith Metzger Department of Mechanical Engineering University of Utah
Transcript of 1 Fundamentals of Engineering Exam Review Series · 1 Fundamentals of Engineering Exam Review...
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Fundamentals of Engineering Exam Review Series
Mathematics
Prof. Meredith Metzger Department of Mechanical Engineering
University of Utah
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Overview 2
• 110 multiple choice questions total • 5 hrs 20 min to answer questions • slightly less than 3 minutes per question
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Overview 3
• 110 multiple choice questions total • 5 hrs 20 min to answer questions • slightly less than 3 minutes per question
Discipline Number of math questions % of test
Mechanical 6-9 5.5% - 8%
Electrical & Computer 11-17 10% - 15.5%
Civil 7-11 6% - 10%
Chemical 8-12 7% - 11%
Other 12-18 11% - 16%
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Mathematics Content 4
Discipline
Algebra &
Trigon
ometry
Analy5
c Geo
metry
Calculus
Line
ar Algeb
ra
Vector Ana
lysis
Diffe
ren5
al
Equa
5ons
Num
erical
Metho
ds
Complex Num
bers
Discrete
Mathe
ma5
cs
Roots o
f Equ
a5on
s
Mechanical ✔ ✔ ✔ ✔ ✔ ✔
Electrical & Computer ✔ ✔ ✔ ✔ ✔ ✔ ✔ ✔
Civil ✔ ✔ ✔ ✔
Chemical ✔ ✔ ✔ ✔
Other ✔ ✔ ✔ ✔ ✔ ✔
5
Mathematics Content 5
Discipline
Algebra &
Trigon
ometry
Analy5
c Geo
metry
Calculus
Line
ar Algeb
ra
Vector Ana
lysis
Diffe
ren5
al
Equa
5ons
Num
erical
Metho
ds
Complex Num
bers
Discrete
Mathe
ma5
cs
Roots o
f Equ
a5on
s
Mechanical ✔ ✔ ✔ ✔ ✔ ✔
Electrical & Computer ✔ ✔ ✔ ✔ ✔ ✔ ✔ ✔
Civil ✔ ✔ ✔ ✔
Chemical ✔ ✔ ✔ ✔
Other ✔ ✔ ✔ ✔ ✔ ✔
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Permitted Calculators 6
• Casio FX-115 models
• HP 33 models
• HP 35 models
• TI-30x models
• TI-36x models
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Outline 7
I. Analytic Geometry
II. Algebra
III. Trigonometry
IV. Calculus
V. Differential Equations
VI. Linear Algebra and Vectors
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Analytic Geometry 8
• Equations and Curves
• Perimeter, Area, and Volume
• Conic Sections - Parabola - Hyperbola - Ellipse - Circle
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Straight Line (pg. 18) 9
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Straight Line 10
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Straight Line 11
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Straight Line 12
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Straight Line 13
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Straight Line 14
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Straight Line 15
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Tangent Line to Circle 16
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Tangent Line to Circle 17
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Conic Sections (pgs. 22-23) 18
Writing equations for various conic sections
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Conic Sections 19
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Conic Sections (pgs. 22-23) 20
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Conic Sections 21
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Conic Sections 22
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Conic Sections 23
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Conic Sections 24
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Conic Sections 25
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Conic Sections 26
27
Conic Sections 27
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Conic Sections 28
29 Quadratic Surface (pg. 18) & Tangent Line to Circle (pg. 23)
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Tangent Line to Circle 30
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Tangent Line to Circle 31
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Area (pgs. 20-21) 32
need to know: circle, rectangle, triangle
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Area 33
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Area 34
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Area 35
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Area 36
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Volume (pgs. 21-22) 37
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Volume 38
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Volume 39
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Volume 40
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Volume 41
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Algebra 42
• Logarithms
• Complex Numbers
• Polar Coordinates
• Roots
• Progressions and Series - Arithmetic Progression - Geometric Progression - Properties of Series - Power Series
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Logarithms (pg. 19) 43
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Logarithms 44
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Logarithms 45
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Logarithms 46
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Logarithms 47
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Logarithms 48
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Logarithms 49
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Complex Numbers (pg. 19) 50
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Complex Numbers 51
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Complex Numbers 52
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Polar Coordinates (pg. 19) 53
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Polar Coordinates 54
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Polar Coordinates 55
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Polar Coordinates 56
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Polar Coordinates 57
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Quadratic Equation (pg. 18) 58
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Roots: Quadratic Equation 59
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Roots: Quadratic Equation 60
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Progressions and Series (pg. 26) 61
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Progressions and Series 62
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Progressions and Series 63
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Progressions and Series 64
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Progressions and Series 65
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Trigonometry 66
• Degrees and Radians
• Plane Angles
• Triangles - Law of Sines - Law of Cosines
• Right Triangles
• General Triangles
• Trigonometric Identities
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Angles – Basic Knowledge 67
radians = degrees * π/180
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Triangles (pg. 19) 68
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Triangles – Basic Knowledge 69
similar triangles
sides are proportional: b/e = c/f = a/d
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Triangles 70
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Triangles 71
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Triangles 72
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Triangles 73
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Triangles 74
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Identities (pg. 20) 75
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Identities 76
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Identities 77
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Identities 78
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Identities 79
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Identities 80
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Identities 81
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Identities 82
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Identities 83
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Calculus 84
• Differential Calculus
• Critical Points
• Partial Derivatives
• Curvature
• Limits
• Integral Calculus
• Centroids and Moments of Inertia
• Taylor Series
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Differential Calculus (pg. 23) 85
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Derivative and Integral Table (pg. 25) 86
- Derivatives of polynomials missing - Product rule of differentiation - Integration by parts
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Differential Calculus 87
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Differential Calculus 88
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Differential Calculus 89
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Differential Calculus 90
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Critical Points (pg. 23) 91
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Critical Points 92
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Critical Points 93
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Critical Points 94
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Critical Points 95
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Partial Derivatives (pg. 23) 96
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Partial Derivatives 97
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Partial Derivatives 98
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Curvature (pg. 24) 99
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Curvature 100
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Curvature 101
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Limits (pg. 24) 102
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Limits 103
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Limits 104
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Integral Calculus (pg. 24) 105
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Integral Calculus 106
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Integral Calculus 107
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Derivative and Integral Table (pg. 25) 108
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Centroids and Moments of Inertia (pg. 26) 109
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Centroids and Moments of Inertia 110
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Centroids and Moments of Inertia 111
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Centroids and Moments of Inertia 112
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Centroids and Moments of Inertia 113
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Taylor Series (pg. 26) 114
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Taylor Series 115
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Taylor Series 116
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Differential Equations 117
• Ordinary Linear Differential Equations
• 1st Order Homogenous ODEs
• 2nd Order Homogenous ODEs
• 1st Order Nonhomogeneous ODEs
• Fourier Transform
• Fourier Series
• Laplace Transform
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Ordinary Linear Differential Eqn (pg. 27) 118
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Ordinary Linear Differential Eqn 119
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Ordinary Linear Differential Eqn 120
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Ordinary Linear Differential Eqn 121
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1st Order Homogeneous ODE (pg. 27) 122
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1st Order Homogeneous ODE 123
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1st Order Homogeneous ODE 124
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2nd Order Homogeneous ODE (pg. 27) 125
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2nd Order Homogeneous ODE 126
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2nd Order Homogeneous ODE 127
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1st Order Nonhomogeneous ODE (pg. 27) 128
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1st Order Nonhomogeneous ODE 129
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1st Order Nonhomogeneous ODE 130
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Fourier Series (pg. 28) 131
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Fourier Series 132
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Fourier Series 133
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Fourier Transform (pg. 27, 29) 134
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Fourier Transform 135
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Fourier Transform 136
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Laplace Transform (pg. 30) 137
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Laplace Transform 138
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Laplace Transform 139
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Laplace Transform 140
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Laplace Transform 141
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Linear Algebra & Vectors 142
• Matrix Arithmetic
• Matrix Transpose and Inverse
• Determinant of a Matrix
• Solving Systems of Linear Equations
• Vector Addition and Subtraction
• Vector Dot and Cross Products
• Vector Identities
• Gradient, Divergence, and Curl
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Matrix Arithmetic (pg. 30) 143
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Matrix Arithmetic 144
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Matrix Arithmetic 145
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Matrix Transpose and Inverse (pg. 30) 146
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Matrix Transpose and Inverse 147
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Matrix Transpose and Inverse 148
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Matrix Transpose and Inverse 149
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Matrix Transpose and Inverse 150
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Matrix Transpose and Inverse 151
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Determinants (pg. 31) 152
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Determinants 153
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Determinants 154
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Determinants 155
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Determinants 156
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Systems of Linear Equations 157
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Systems of Linear Equations 158
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Vector Addition and Subtraction (pg. 31) 159
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Vector Addition and Subtraction 160
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Vector Addition and Subtraction 161
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Vector Addition and Subtraction 162
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Vector Addition and Subtraction 163
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Vector Dot and Cross Products (pg. 31) 164
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Vector Dot and Cross Products 165
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Vector Dot and Cross Products 166
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Vector Dot and Cross Products 167
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Vector Dot and Cross Products 168
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Vector Identities (pg. 31) 169
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Vector Identities 170
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Vector Identities 171
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Gradient, Divergence, and Curl (pg. 31) 172
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Gradient, Divergence, and Curl 173
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Gradient, Divergence, and Curl 174
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Gradient, Divergence, and Curl 175
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Gradient, Divergence, and Curl 176
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Gradient, Divergence, and Curl 177
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Gradient, Divergence, and Curl 178
