## MATH 210 Calculus III  Spring, 2001 MWF 15:00 -16:10  SH 128 / [F FR 204A]  Course Assignments

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Last updated: 1/20/01

MATH 210: Calculus III Spring,2001
 Week /Day Monday Wednesday Friday 1 1/22 Introduction-  Begin review Variables- relations-functions.  What is calculus? Differential Equations? 1/24  Introduction to 3-dimensional coordinate geometry. 13.1 1/26  Introduction to vectors. 13.2 2 1/29 Visualizations: Transformations and graphs. 1/31 More on vectors and functions "1 variable controlling 2," 2 controlling 1". 2/2Parametric curves . 11.1 and 3 2/5 Lines: parametric and vector equations 2 &3 dim. 13.5 The tangent problem 11.2 "1 variable controlling 2 (or 3)." 2/7  Vector functions, tangent vectors and velocity. 14.1, 14.2 2/9 Lengths: segments, vectors, arcs. 11.3, 14.3 speed
 Week/Day Monday Wednesday Friday 4 2/12 Smooth curces. Differential equations and integrals of vector functions. 2/14  Acceleration 14.4 and Curvature Formulae 14.3 2/16  The Dot Product. 13.3. 5 2/19 More on dot products. 2/21Finish up 1 variable controlling 2 and 3.  Calculus for r'(t). Curvature Formulae 14.3 2/23Begin "2 controlling 1 variable". Graphs.  Scalar fields 6 2/26 Graphs and level curves of Functions with 2 controlling variables. Begin Partial Derivatives 2/28 Second order Partial derivatives. Start Tangent Planes 3/2  Tangent Planes, Differentials.  Start limits and continuity

Assignment Problem List I

Not yet complete.

 Chapter.Section (pages) Due Problems Interesting/optional Review of Calc I and II] 1/24 Look at Final Exams from Calc I and II 11.1 2/2 Read- Consider what this has to do with vectors. (i) 2/5 (ii) ? (i) 1-7 odd, 17,19,23, 22, 28  (ii) 4,6,8, 11-13, 25, 40 34, 35, 37,42,43 11.2 (i) (682-685:tangents)  (ii) (iii) (685-687: area) (i)2/7 (ii) 2/9 (iii)2/19 (i) 1,3,5,6,8 (ii) 9, 11,13, 15, 25, 32 (iii) 33- 35, 39 (i) (ii) (iii) 11.3 arc length (689-691 middle) 2/12 1-5, 9, 15 13.1 (i)  1/26 And (ii) 1/29 (i) 1, 3, 4, 7, 11, 13, 15, 23-29 odd (ii) 5, 6, 21, 31,33,35-37 (i) 19 13.2 (i) 1/31 (ii) 1/31 (i) 7-9,13,14 (ii)17,19,21,23-25,  29 13.5 (i) (ii) read pages 848-849 to example 4 (iii) (i) 2/7 (ii) 2/21 (iii) (iv) (i) 2-5,7,11, 17; (ii) 19-25 odd (iii)27, 29, 31,49;  (iv) 51, 53-55, 61, 63 14.1 (i)2/9 (ii)2/12 (i) 3,4,7-13, 16, 17,21,23 (ii) 24,25, 28 (ii)33 14.2 vector derivatives and  tangent vectors  integrals and de's (i) 2/9  more (ii) 2/12 (iii) 2/14 (iv)2/23? (i) 1,3-5,9,13,14 (ii) 17-19, 27, 29 (iii) 33-39 odd, 38, 40 (iv)41,42,44,45,49 14.3 (i) arc length (883-885) (ii) Curvature I (885-Ex.3) (iii) Example 5 (i)2/14 (ii) 2/23 (iii) (i)1-6 (ii)11b,13 b,18 (iii)21-23,29,31,32 14.4 velocity and acceleration(891-895) (i) 2/16 (i)1-7 odd, 9-13, 15,17-19 13.3 dot product (i)2/19 (ii) 2/21 (iii)2/21 (i) 1,3,4,8-10,15,16, 23, 24, 29, 30 (ii) 5-7, 11, 17, 18, 21, 25-28, 31, 54 (iii) 39,40,45,46 49,51, 53, 55, 56, 58, 61-63 15.1 (i) 2/26 (ii) 2/26 (iii)2/28 (iv) 3/2 (i) 1,2, 5-9 odd, 15,17  (ii) Sketch a scalar field for the integer lattice of [-2,2]x[-2,2] : 21-27,35-41 odd  (iii) 30, 35-37,43, 51-56  (iv) 9, 19, 33, 34, 61,65 15.2 3/9 Read the examples. 3,4, 5-11odd, 21,25, 27 15.3 (i)2/28 (ii)3/2 (iii) 3/5 (i) 3,11-25 odd (ii) 6, 20,22, 32, 35, 37, 43, 45,46, 51, 56 (iii) 63, 65, 66, 68(a,c), 69, 76 87 15.4 (i) 3/5 (ii) 3/5 (iii) 3/9 (i) 1-5,7 (ii) 23-27,29, 17,18,31,36 (iii) 11, 12, 35, 37 (iii)41,42 15.5 (i) 1-2-1 p952-3 (Ex. 2) (ii) 2-2-1 p953-956 (iii) implicit... p956-7 (i)3/9 (ii)3/12 (iii)3/12 (i) 1-4, 13, 33 (ii)  7-11 odd, 19,20, 37, 41 (iii) 25-31 odd 3/14-3/15  Exam #1 covers Assigned Material through 3/12. 11.1-11.3, 13.1,13.2,13.3,13.5, 14.1-14.4. 15.1-15.5. 15.6 (i) 3/14 (ii) 3/16 (i)7,8, 3,5, 11 -14  (ii) 21-23,27, 32a,34,35,45 15.7 (i) 3/26 (ii)3/26 (i)5-13 odd  (ii)6,14,15,17, 27,29,31 15.8 pp985-989 4/2 1-9 odd,23-31 odd 13.6 4/6 (i) 9-15 odd, 21-28, 37-39, 41,43 47,49 16.1 4/9 Read  4/11 (i) & (ii) (i)Look at 3a,5,9 (will not be collected till 4/11) (ii) 11-13, 17,18 16.2 4/13 (i) 4/16 (ii) (i)1-11 odd, 4, 8, 25 (ii) 13-15, 18, 29 13.4 4/13 Read section. (i) 4/16 (ii) 4/18 (i) 1-9 odd, 13, 15 (ii) 23, 29,30, 33, 41,42,43 18 16.3 (i) 4/18 (ii) 4/20 (iii) 4/23 (i)1-9 odd, 8 (ii) 11-15 odd, 12,19, 33-35 (iii) 39-43 odd, 44, 45 16.5 1034-1038 (probability) 5/4 23, 25 11.4 (i) 4/23 (ii)4/25 (iii)4/25 (i) 1-3,5,7-11, 15-17, 31-35 (ii)33-45 odd, 56 (iii) 57-65 odd (ii) 71-73,81 4/27 Examination #2 (In-class) Covers material assigned through 4/23. 15.5-15.8, 13.6, 16.1-16.3, 13.4 11.5 p707 polar coordinates 4/30 45-49 odd 13.7 Cylindrical and spherical coordinates. 5/4 Read 5/7 Do problems 3-9 odd, 13-19 odd, 31,35,36,9, 40, 49-51, 16.4 Integration in polar coordinates. Read 4/25 (i)4/30 (ii)5/2 (i)1-11 odd (ii) 15-17, 19-23 odd, 27, 33 16.7 Integration in 3 space (rectangular). (i) 5/2 (ii) 5/4 (i)1-11 odd, 17 (ii) 25,  37 find mass only, 47 16.8 Integration in 3 space (Cylindrical and polar) (i)5/7 (ii) 5/9 (i)1,2, 5,7 , 15 (ii) 3,17,33,35

 Week/Day Monday Wednesday Friday 7 3/5 Limits and Continuity. Closeness, Approximations... concepts and defintions. 3/7 Differentials, C1 and differentiable functions.The geometry of differentiability- Tangent planes.  The Chain Rule (1-2-1) 3/9 Chain rule continued. 2-2-1 chain rule 8Exam #1 3/12 Directional derivatives and the gradient. Geometry of the gradient. 3/14 Local Extremes and the gradient continued. 3/16  Testing for extremes. 9 3/19 No Class (Break) 3/21 3/23 10 3/26 Quadratic forms. extrema on compact sets. C1 implies differentiable? Mixed partials are equal.? 3/28 Finish discussion of the discriminant test. LaGrange Multiplier, extremes, and odds and ends. 3/30 No Class 11 4/2 What about 4 variables: 1-3, 3-1, 2-2  Quadric Surfaces 13.6 4/4 Quadric Surfaces 13.6 The area problem.11.2(?) 4/6Linear regression and "least squares." 15.7 problem 51. 12 4/9 Start Integration over rectangles 4/11 More on Integration and iterated integrals. Fubini's Theorem. Cross products. Beginning-basic properties. 4/13 More cross product- applications volumes.
 Week/Day Monday Wednesday Friday 13 4/16 Integration over compact regions.More on planes and normal vectors with cross products.. 4/18  More Integration in the plane. Cross Product Application to tangent plane. 4/20 Properties of integration in the plane. Polar coordinates- curves in the plane. Tangents. 14Exam #2 4/23 More Polar coordinates. 4/25  Integration with polar coordinates. 4/27 Exam #2 (in class) 15 4/30 The integral of e^(-x^2). Application of integration in the plane to mass and probability. Arc length in Polar coordinates. Integration in 3D. Cartesian coordinates. 5/2 More integration in 2 and 3 dimensions and probability. Cylindrical  coordinates. 5/4 Begin spherical coordinates Integration in Cylindrical. 16 Talks Cancelled. 5/7 More Integration in Cylindrical and spherical coordinates 5/9 Integration over curves and surfaces.? Vector fields and line integrals? 5/11Review.!?

Assignment Problem List II

Not yet revised from 3rd Edition

 Chapter.Section (pages). Problems Interesting/optional 11.9  (i) (ii) Read Ex.3&5 [Use only first two components]  (i) 1-4  (ii) 15, 16, 20, 21, 26, 27

Assignment Problem List IV

 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 11.10 (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 integrals (rectangular) (i)12-10 (ii) 12-12 (i)1-11 odd, 17 (ii) 25,  37 find mass only, 47 13.8 Triple integrals (cylindrical & polar) 12-12 1-3, 5,7 , 15,17,33,35

Assignment Problem List V

 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 11.7  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 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