1 Fundamentals of Engineering Exam Review Series

1 1 Fundamentals of Engineering Exam Review Series Mathematics Prof. Meredith Metzger Department of Mechanical Engineering University of Utah 2 Overview 2 110 multiple choice questions total 5 hrs 20 min to answer questions slightly less than 3 minutes per question 3 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 - 8% Electrical & Computer 11-17 10% - Civil 7-11 6% - 10% Chemical 8-12 7% - 11% Other 12-18 11% - 16% 4 Mathematics Content 4 Discipline Algebra & Trigonometry Analy5c Geometry Calculus Linear Algebra Vector Analysis Differen5al Equa5ons Numerical Methods Complex

2 Numbers Discrete Mathema5cs Roots of Equa5ons Mechanical Electrical & Computer Civil Chemical Other 5 Mathematics Content 5 Discipline Algebra & Trigonometry Analy5c Geometry Calculus Linear Algebra Vector Analysis Differen5al Equa5ons Numerical Methods Complex Numbers Discrete Mathema5cs Roots of Equa5ons Mechanical Electrical & Computer Civil Chemical Other 6 Permitted Calculators 6 Casio FX-115 models HP 33 models HP 35 models TI-30x models TI-36x models 7 Outline 7 I.

3 Analytic Geometry II. Algebra III. Trigonometry IV. Calculus V. Differential Equations VI. Linear Algebra and Vectors 8 Analytic Geometry 8 Equations and Curves Perimeter, Area, and Volume Conic Sections - Parabola - Hyperbola - Ellipse - Circle 9 Straight Line (pg. 18) 9 10 Straight Line 10 11 Straight Line 11 12 Straight Line 12 13 Straight Line 13 14 Straight Line 14 15 Straight Line 15 16 Tangent Line to Circle 16 17 Tangent Line to Circle 17 18 Conic Sections (pgs. 22-23) 18 Writing equations for various conic sections 19 Conic Sections 19 20 Conic Sections (pgs. 22-23) 20 21 Conic Sections 21 22 Conic Sections 22 23 Conic Sections 23 24 Conic Sections 24 25 Conic Sections 25 26 Conic Sections 26 27 Conic Sections 27 28 Conic Sections 28 29 Quadratic Surface (pg.)

4 18) & Tangent Line to Circle (pg. 23) 29 30 Tangent Line to Circle 30 31 Tangent Line to Circle 31 32 Area (pgs. 20-21) 32 need to know: circle, rectangle, triangle 33 Area 33 34 Area 34 35 Area 35 36 Area 36 37 Volume (pgs. 21-22) 37 38 Volume 38 39 Volume 39 40 Volume 40 41 Volume 41 42 Algebra 42 Logarithms Complex Numbers Polar Coordinates Roots Progressions and Series - Arithmetic Progression - Geometric Progression - Properties of Series - Power Series 43 Logarithms (pg. 19) 43 44 Logarithms 44 45 Logarithms 45 46 Logarithms 46 47 Logarithms 47 48 Logarithms 48 49 Logarithms 49 50 Complex Numbers (pg. 19) 50 51 Complex Numbers 51 52 Complex Numbers 52 53 Polar Coordinates (pg.

5 19) 53 54 Polar Coordinates 54 55 Polar Coordinates 55 56 Polar Coordinates 56 57 Polar Coordinates 57 58 Quadratic Equation (pg. 18) 58 59 Roots: Quadratic Equation 59 60 Roots: Quadratic Equation 60 61 Progressions and Series (pg. 26) 61 62 Progressions and Series 62 63 Progressions and Series 63 64 Progressions and Series 64 65 Progressions and Series 65 66 Trigonometry 66 Degrees and Radians Plane Angles Triangles - Law of Sines - Law of Cosines Right Triangles General Triangles trigonometric Identities 67 Angles Basic Knowledge 67 radians = degrees * /180 68 Triangles (pg. 19) 68 69 Triangles Basic Knowledge 69 similar triangles sides are proportional: b/e = c/f = a/d 70 Triangles 70 71 Triangles 71 72 Triangles 72 73 Triangles 73 74 Triangles 74 75 Identities (pg.

6 20) 75 76 Identities 76 77 Identities 77 78 Identities 78 79 Identities 79 80 Identities 80 81 Identities 81 82 Identities 82 83 Identities 83 84 Calculus 84 Differential Calculus Critical Points Partial Derivatives Curvature Limits Integral Calculus Centroids and Moments of Inertia Taylor Series 85 Differential Calculus (pg. 23) 85 86 Derivative and Integral Table (pg. 25) 86 - Derivatives of polynomials missing - Product rule of differentiation - Integration by parts 87 Differential Calculus 87 88 Differential Calculus 88 89 Differential Calculus 89 90 Differential Calculus 90 91 Critical Points (pg. 23) 91 92 Critical Points 92 93 Critical Points 93 94 Critical Points 94 95 Critical Points 95 96 Partial Derivatives (pg.

7 23) 96 97 Partial Derivatives 97 98 Partial Derivatives 98 99 Curvature (pg. 24) 99 100 Curvature 100 101 Curvature 101 102 Limits (pg. 24) 102 103 Limits 103 104 Limits 104 105 Integral Calculus (pg. 24) 105 106 Integral Calculus 106 107 Integral Calculus 107 108 Derivative and Integral Table (pg. 25) 108 109 Centroids and Moments of Inertia (pg. 26) 109 110 Centroids and Moments of Inertia 110 111 Centroids and Moments of Inertia 111 112 Centroids and Moments of Inertia 112 113 Centroids and Moments of Inertia 113 114 Taylor Series (pg. 26) 114 115 Taylor Series 115 116 Taylor Series 116 117 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 118 Ordinary Linear Differential Eqn (pg.

8 27) 118 119 Ordinary Linear Differential Eqn 119 120 Ordinary Linear Differential Eqn 120 121 Ordinary Linear Differential Eqn 121 122 1st Order Homogeneous ODE (pg. 27) 122 123 1st Order Homogeneous ODE 123 124 1st Order Homogeneous ODE 124 125 2nd Order Homogeneous ODE (pg. 27) 125 126 2nd Order Homogeneous ODE 126 127 2nd Order Homogeneous ODE 127 128 1st Order Nonhomogeneous ODE (pg. 27) 128 129 1st Order Nonhomogeneous ODE 129 130 1st Order Nonhomogeneous ODE 130 131 Fourier Series (pg. 28) 131 132 Fourier Series 132 133 Fourier Series 133 134 Fourier Transform (pg. 27, 29) 134 135 Fourier Transform 135 136 Fourier Transform 136 137 Laplace Transform (pg. 30) 137 138 Laplace Transform 138 139 Laplace Transform 139 140 Laplace Transform 140 141 Laplace Transform 141 142 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 143 Matrix Arithmetic (pg.

9 30) 143 144 Matrix Arithmetic 144 145 Matrix Arithmetic 145 146 Matrix Transpose and inverse (pg. 30) 146 147 Matrix Transpose and inverse 147 148 Matrix Transpose and inverse 148 149 Matrix Transpose and inverse 149 150 Matrix Transpose and inverse 150 151 Matrix Transpose and inverse 151 152 Determinants (pg. 31) 152 153 Determinants 153 154 Determinants 154 155 Determinants 155 156 Determinants 156 157 Systems of Linear Equations 157 158 Systems of Linear Equations 158 159 Vector Addition and Subtraction (pg. 31) 159 160 Vector Addition and Subtraction 160 161 Vector Addition and Subtraction 161 162 Vector Addition and Subtraction 162 163 Vector Addition and Subtraction 163 164 Vector Dot and Cross Products (pg.

10 31) 164 165 Vector Dot and Cross Products 165 166 Vector Dot and Cross Products 166 167 Vector Dot and Cross Products 167 168 Vector Dot and Cross Products 168 169 Vector Identities (pg. 31) 169 170 Vector Identities 170 171 Vector Identities 171 172 Gradient, Divergence, and Curl (pg. 31) 172 173 Gradient, Divergence, and Curl 173 174 Gradient, Divergence, and Curl 174 175 Gradient, Divergence, and Curl 175 176 Gradient, Divergence, and Curl 176 177 Gradient, Divergence, and Curl 177 178 Gradient, Divergence, and Curl 178