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1Fundamentals of Engineering ExamReview SeriesMathematicsProf. Meredith MetzgerDepartment of Mechanical EngineeringUniversity of Utah
2Overview 110 multiple choice questions total 5 hrs 20 min to answer questions slightly less than 3 minutes per question
3Overview 110 multiple choice questions total 5 hrs 20 min to answer questions slightly less than 3 minutes per questionDisciplineNumber of mathquestions% of testMechanical6-95.5% - 8%Electrical &Computer11-1710% - 15.5%Civil7-116% - 10%Chemical8-127% - 11%Other12-1811% - 16%
5onsMathematics ContentMechanical Electrical&Computer Civil Chemical Other Discipline
sofEqua5onsMechanical Electrical&Computer Civil Chemical Other lusMathematics Content
6Permitted Calculators Casio FX-115 models HP 33 models HP 35 models TI-30x models TI-36x models
7OutlineI.Analytic GeometryII. AlgebraIII. TrigonometryIV. CalculusV. Differential EquationsVI. Linear Algebra and Vectors
8Analytic Geometry Equations and Curves Perimeter, Area, and Volume Conic Sections- Parabola- Hyperbola- Ellipse- Circle
9Straight Line (pg. 18)
10Straight Line
11Straight Line
12Straight Line
13Straight Line
14Straight Line
15Straight Line
16Tangent Line to Circle
17Tangent Line to Circle
18Conic Sections (pgs. 22-23)Writing equations for various conic sections
19Conic Sections
20Conic Sections (pgs. 22-23)
21Conic Sections
22Conic Sections
23Conic Sections
24Conic Sections
25Conic Sections
26Conic Sections
27Conic Sections
28Conic Sections
29Quadratic Surface (pg. 18) &Tangent Line to Circle (pg. 23)
30Tangent Line to Circle
31Tangent Line to Circle
32Area (pgs. 20-21)need to know: circle, rectangle, triangle
33Area
34Area
35Area
36Area
37Volume (pgs. 21-22)
38Volume
39Volume
40Volume
41Volume
42Algebra Logarithms Complex Numbers Polar Coordinates Roots Progressions and Series- Arithmetic Progression- Geometric Progression- Properties of Series- Power Series
43Logarithms (pg. 19)
44Logarithms
45Logarithms
46Logarithms
47Logarithms
48Logarithms
49Logarithms
50Complex Numbers (pg. 19)
51Complex Numbers
52Complex Numbers
53Polar Coordinates (pg. 19)
54Polar Coordinates
55Polar Coordinates
56Polar Coordinates
57Polar Coordinates
58Quadratic Equation (pg. 18)
59Roots: Quadratic Equation
60Roots: Quadratic Equation
61Progressions and Series (pg. 26)
62Progressions and Series
63Progressions and Series
64Progressions and Series
65Progressions and Series
66Trigonometry Degrees and Radians Plane Angles Triangles- Law of Sines- Law of Cosines Right Triangles General Triangles Trigonometric Identities
67Angles – Basic Knowledgeradians degrees * π/180
68Triangles (pg. 19)
69Triangles – Basic Knowledgesimilar trianglessides are proportional: b/e c/f a/d
70Triangles
71Triangles
72Triangles
73Triangles
74Triangles
75Identities (pg. 20)
76Identities
77Identities
78Identities
79Identities
80Identities
81Identities
82Identities
83Identities
84Calculus Differential Calculus Critical Points Partial Derivatives Curvature Limits Integral Calculus Centroids and Moments of Inertia Taylor Series
85Differential Calculus (pg. 23)
86Derivative and Integral Table (pg. 25)- Derivatives of polynomials missing- Product rule of differentiation- Integration by parts
87Differential Calculus
88Differential Calculus
89Differential Calculus
90Differential Calculus
91Critical Points (pg. 23)
92Critical Points
93Critical Points
94Critical Points
95Critical Points
96Partial Derivatives (pg. 23)
97Partial Derivatives
98Partial Derivatives
99Curvature (pg. 24)
100Curvature
101Curvature
102Limits (pg. 24)
103Limits
104Limits
105Integral Calculus (pg. 24)
106Integral Calculus
107Integral Calculus
108Derivative and Integral Table (pg. 25)
109Centroids and Moments of Inertia (pg. 26)
110Centroids and Moments of Inertia
111Centroids and Moments of Inertia
112Centroids and Moments of Inertia
113Centroids and Moments of Inertia
114Taylor Series (pg. 26)
115Taylor Series
116Taylor Series
117Differential Equations Ordinary Linear Differential Equations 1st Order Homogenous ODEs 2nd Order Homogenous ODEs 1st Order Nonhomogeneous ODEs Fourier Transform Fourier Series Laplace Transform
118Ordinary Linear Differential Eqn (pg. 27)
119Ordinary Linear Differential Eqn
120Ordinary Linear Differential Eqn
121Ordinary Linear Differential Eqn
1221st Order Homogeneous ODE (pg. 27)
1231st Order Homogeneous ODE
1241st Order Homogeneous ODE
1252nd Order Homogeneous ODE (pg. 27)
1262nd Order Homogeneous ODE
1272nd Order Homogeneous ODE
1281st Order Nonhomogeneous ODE (pg. 27)
1291st Order Nonhomogeneous ODE
1301st Order Nonhomogeneous ODE
131Fourier Series (pg. 28)
132Fourier Series
133Fourier Series
134Fourier Transform (pg. 27, 29)
135Fourier Transform
136Fourier Transform
137Laplace Transform (pg. 30)
138Laplace Transform
139Laplace Transform
140Laplace Transform
141Laplace Transform
142Linear Algebra & Vectors 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
143Matrix Arithmetic (pg. 30)
144Matrix Arithmetic
145Matrix Arithmetic
146Matrix Transpose and Inverse (pg. 30)
147Matrix Transpose and Inverse
148Matrix Transpose and Inverse
149Matrix Transpose and Inverse
150Matrix Transpose and Inverse
151Matrix Transpose and Inverse
152Determinants (pg. 31)
153Determinants
154Determinants
155Determinants
156Determinants
157Systems of Linear Equations
158Systems of Linear Equations
159Vector Addition and Subtraction (pg. 31)
160160Vector Addition and Subtraction
161161Vector Addition and Subtraction
162162Vector Addition and Subtraction
163163Vector Addition and Subtraction
164164Vector Dot and Cross Products (pg. 31)
165165Vector Dot and Cross Products
166166Vector Dot and Cross Products
167167Vector Dot and Cross Products
168168Vector Dot and Cross Products
169169Vector Identities (pg. 31)
170170Vector Identities
171171Vector Identities
172172Gradient, Divergence, and Curl (pg. 31)
173173Gradient, Divergence, and Curl
174174Gradient, Divergence, and Curl
175175Gradient, Divergence, and Curl
176176Gradient, Divergence, and Curl
177177Gradient, Divergence, and Curl
178178Gradient, Divergence, and Curl
Review Series Mathematics Prof. Meredith Metzger Department of Mechanical Engineering University of Utah . 2 Overview 110 multiple choice questions total 5 hrs 20
