## MATH 210 Calculus III  Fall, 1997 MWF 12:40 -1:50 P.M. UANX 150 / SD 017  Course Assignments

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Last updated: 11/3/97

## MATH 210: Calculus III Fall, 1997

Assignment Problem List I

 Chapter.Section (pages) Problems Interesting/optional [Review of Calc I and II] Look at Final Exams from Calc I and II 8.2 due 9-10 1-5 odd, 9, 13, 21 28, ,32, 34 9.1 all due 9-3 (i) 1-7 odd, 17-23 odd, 26, 27  (ii) 4,6,8, 11-13, 25, 28 30, 31, 33, 35,38 9.2 (554-556:tangents) due 9-5  (557-558: area) (i) 1-5, 9, 11, 15, 21, 28  (ii) 29-31, 35 (i)23, 27, 37  (ii)36,40 9.3 (560-562 middle) Due 9-8 1-5, 9, 13 15,29,30,31,32 11.1 (i) And (ii) due 10-1 (i) 1,3,5,9,11,12, 15,16,22  (ii) 24,27, 29 - 37, 44, 45 21  46, 48 11.2 due 9-10 1-3,7,8,11-17 odd, 19-21, 29 27,28,31,32,40 11..5 (i) 1-5,7,11, 17; (ii) 19-29 odd, 33,49; (iii) 51, 55-57, 63, 65, 76 11.7 Due 9-12 (i) (i)1-7, 9,10,15,17 (ii) 23,24,27,29,30,35-37 11.8 1-6

 Week/Day Monday Wednesday Friday 1 8/26 Introduction-  Begin review 8/28 Variables- relations-functions.  Visualizations: Transformations and graphs.  What is calculus? Differential Equations? 8/30 Introduction to 3-dimensional coordinate geometry and vectors. 11.1, 11.2 2 9/1 Labor Day- No Class. 9/3 1 variable controlling 2. Parametric curves and the tangent problem. 9.1 and 9.2 9/5 1 variable controlling 2 (or 3). Vector functions and tangent vectors.11.7 3 9/8 Lines: parametric and vector equations in 2 and 3 dimensions. 11.5 9/10 Lengths: segments, vectors,arcs. 9.3,11.8 9/12 Breath

Assignment Problem List II

 Chapter.Section (pages). Problems Interesting/optional 11.3  (i) due 9-19  (iii)due 9-22 (i) 1,2,6-8,13,14,19,20,25,26,51  (ii) 3-5,9,11,12,17,21-24,29,54  (iii) 37,38,43,44 47,49,53,55,56,58,61-63 11.7  (i) due 9-19  (ii)due 9-22 [Use only first two components]  (i)37-33 odd,41,43,45,49  (ii)57-61 11.8 Ex. 5 Due 9-29 21-23,27,29,30 11.9  (i) due 9-22  (ii) Read Ex.3&5 due 9-26 [Use only first two components]  (i) 1-4  (ii) 15, 16, 20, 21, 26, 27 Handout on Curvature 9-26 Find where the graph of y=ln(x) has its largest curvature. 12.1  (i) Due 10-1 (i) 1-3, 5-9 odd, 15,17  (ii) Sketch a scalar field for the integer lattice of [-2,2]x[-2,2] : 31-37,43-47 odd  (iii) 43,45,47,57  (iv) 31-37, 40-41, 59-64 12.3(i) 10-6  (ii) 10-8  (iii) 10-10 (i) 1,3-8,17,20, 28,31,50  (ii) 51-55, 57,58, 63, 68  (iii) 75,76, 78(a,c), 79 92,94,97

 Week/Day Monday Wednesday Friday 4 9/15 9/17 The Dot Product 9/19 Acceleration and speed 5 9/22 Acceleration and curvature. 9/24 Curvature Formulae 9/26 Finish up 1 variable controlling 2 6 9/29 Begin 2 controlling 1 variable.  Scalar fields and level curves. Graphs. 10/1 Partial Derivatives 10/2 More on Partial derivatives

Assignment Problem List III

 Chapter.Section (pages). Problems Interesting/optional 12.2   due 10-13 1-9 odd 12.4 (i) differentials due 10-15  (ii) Tangent planes due 10-17 (i)11-15,19,21,22,27,29,34  (ii) 1-5 12.5 (i) 1-2-1  due 10-17  (ii)2-2-1 (i) 1-4,23-25  (ii) 7-9,39,40,41,45,46 12.6 (i) Gradients and directional Derivatives  due10-22  (ii) Gradient interpreted due 10-24 (i)5,6,1,3, 9 -12  (ii) 17-19,24, 28a,30,31-33,43 12.7 (i) due 10-29  (ii) due 11-3 (i)1-11 odd  (ii)6,10,13,15, 25,27,29 33,51,52

 Week/Day Monday Wednesday Friday 6 9/29 Begin 2 controlling 1 variable.  Scalar fields and level curves. Graphs. 10/1 Partial Derivatives 10/2 More on Partial derivatives 7 10/6 Three dimensional coordinates.  Second order Partial derivatives. 10/8 Graphs of Functions with 2 controlling variables. 10/10 limits and continuity 8 10/13 Differentials, C1 and differentiable functions. 10/15 The geometry of differentiability- Tangent planes.  The Chain Rule (1-2-1) 10/17 Chain rule continued. 9Exam #1 10/20 Directional derivatives and the gradient. C1 implies differentiable. 10/22 Geometry of the gradient 10/24 Local Extremes and the gradient continued 10 10/27 Testing for extremes. Quadratic forms. (2-2-1 chain rule?) 10/29 Lagrange multiplier- extrema on compact sets. 10/31 breath- what about 4 variables: 1-3, 3-1, 2-2

Assignment Problem List IV

 Chapter.Section (pages). Problems Interesting/optional 12.8 due 11/7 1-4, 16, 17,21,22,41 17,18,23 11.2 Vectors due 11/7 5,9,13,17, 21,24 11.3 Dot Product due 11/7 5,9,10, 11,15, 21,22,27,39,41,55 45,47,54,57 11.4 Cross Product due 11/19 (i) 1-5, 9-11, 14, 19, 21, 22, 25, 26, 29  (ii) 35-37, (read example 5) 31 11.5 (i) Lines due 11/10  (ii) Planes due 11/19  (iii)Planes due  11/21 (i) 1,3,5,11,13,17  (ii) 19, 21, 23, 25, 27. 31, 35, 55  (iii) 41-43, 47, 51, 61, 63, 69 11.6 Quadratic Surfaces 1-7, 17-24, 39, 41 45, 48 11.7  due 12/1 (i) 1-6, 7-9, 15, 17  (ii) 27-29, 33, 34, 41,42, 46  (iii) 51, 57, 58, 61, 70, 71, 73 74 12.1 due 12/1 4, 29, 53-55 12.3 due 12/1 13, 15, 16, 33, 35, 49, 69, 77, 86 82 12.5 The Chain Rule due 12/1 5, 6, 13, 14, 17, 19, 35, 39 12.6 due 12/1 7, 14, 16, 22, 25, 27, 45, 49 57 13.1 (i) due 11/14  (i) due 11/17 (i) 1, 3, 5  (ii) 6-8, 10 13.2 (i) due 11/14  (ii) due  11/17 (i) 1,3, 5-8, 23  (ii) 15-17, 25-27, 35
Assignment Problem List V

 Chapter.Section (pages). Problems Interesting/optional 9.4 (i)Polar Coordinates 12-5  (ii) Curves sketching 12-5  (iii) Tangents 12-5 (i)1-4,7-9,13-15, 17-21,25-27,31-35  (ii) 37-53 odd  (iii) 63-71 odd 59,60,62,75,77,78,84 9.5 arc length p576-7 12-8 43-47 odd 11.6 Quadric surfaces 12-5 1-5 odd,17-24 11.10 (i) cylindrical coordinates  12-10  (ii)spherical coordinate 12-12 (i) 1-9 odd, 51-53 (a)  (ii)13-27 odd, 33-37, 51-53(b) 13.3 integration over regions in the plane(i) 12-5  (ii)12-10 (i) 1-5, 7-13 odd, 19,21  (ii)33-35, 39,41 31 13.4 integration in polar coordinates 12- 10 1-9 odd,14, 15, 19,25 32 13.7 Triple intergrals (rectangular) (i)12-10 (ii) 12-12 (i)1-11 odd, 17  (ii) 25,  37 find mass only, 47 13.8 Triple intergrals (cylindrical & polar) 12-12 1-3, 5,7 , 15,17,33,35

 Week/Day Monday Wednesday Friday 11 11-3 LaGrange Multiplier, extremes, and odds and ends; start integration on rectangles 11-5 11-7 12 11-10 Dot products in 3 dimensions. Planes and normal vectors. Integration over rectangles 11-12 integration over rectangles and iterated integrals 11-14Cross products Beginning-basic properties. 13 11-17 Finish cross product- applications to planes and volumes. Curves in 3 dimensions: tangents, velocity, acceleration. 11-19 More integration. Arc length in 3 -D. Functions of 3 variables. Visualizations. Partial Derivatives. The differential. Differentiability. The Chain Rule. The gradient. 11-21  Integration over compact regions.The gradient in 3D. Extremes for Functions of 3 variables. 14 11-24 No class- holiday 11-26 No class- holiday 11-28 No class- holiday 15 Exam #2 12-2,12-3 12-1 Quadratic Surfaces 12-3 More Integration in the plane.  Polar coordinates- curves in the plane. 12-5 Integration with polar coordinates. 16Team Assignment #2 due 12-8 Talks 12/11 6:30 12-8 Properties of integration in the plane.The integral of e^(-x^2). Cylindrical  coordinates.  Begin integration in 3D 12-10 More integration in 2 and 3 dimensions.  Begin spherical coordinates. 12-12 Integration in spherical coordinates