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201-Unit 1-Summer - ENGR 201 – Summer Unit 1 Study Guide...

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Unformatted text preview: ENGR 201 – Summer Unit 1 Study Guide Unit Content : Section Pages Content 13.1 906-920 Vector-Valued Functions and Motion in Space 13.3 931-936 Arc Length and The Unit Tangent Vector, g G 13.4 936-943 Curvature and The Unit Normal Vector, ¡ ¢ 13.5 943-950 Torsion and The Unit Binormal Vector, £ G , The T-N-B (Frenet) Frame, Normal, Osculating, and Rectifying Planes 10.8 734-736 Polar Vectors, Planetary Motion and Satellites 13.6 950-959 14.1 965-975 Functions of Several Variables 14.2 976-984 Limits and Continuity in Higher Dimensions Learning Objectives (part 1) : 1. Given the position vector ¤¥¦§¨ defining a curve, find © ¥¦§¨, u© ¥¦§¨u, ª ¥¦§¨, © ¥¦§ « ¨, ª ¥¦§ « ¨ , and cos ¬ (where ¬ is the angle between © ¥¦§ « ¨ and ª ¥¦§ « ¨ ) with § « specified. Show ª ¥¦§ « ¨,© ¥¦§ « ¨ , and ¬ along with the curve, ¤¥¦§¨ on a sketch. 2. Evaluate a given integral involving vector functions or solve a differential equation such as one with given ª ¥¦§¨, © ¥¦§¨ , or the force acting on a particle and the initial conditions to be used to find the velocity and/or position at any time, §. 3. Find the length of a specified portion of a given curve, ¤¥¦§¨ . 4. Find the center, radius, and equation of the osculating circle for a given curve (in the plane) at a specified point. Show that it has the same first and second derivatives as those of the curve itself at the point. Show the curve and circle on a sketch. Show the curve and circle on a sketch....
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201-Unit 1-Summer - ENGR 201 – Summer Unit 1 Study Guide...

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