## MATH 210 Calculus III  Spring, 2002 MWF 12:00 -1:10  SH 128  Course Assignments

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Last updated: 3-25-02

MATH 210: Calculus III Spring,2002
 Week /Day Monday Wednesday Friday 1 1/23 Introduction-  Begin review Variables- relations-functions. 1/25 What is calculus? Differential Equations? Introduction to 3-dimensional coordinate geometry. 13.1 Introduction to vectors. 13.2 "1 variable controlling 2"  11.1 Parametric curves . 2 1/28 Visualizations: Transformations and graphs. 1/30 More on vectors and functions "1 variable controlling 2," 2 controlling 1". Lines: parametric and vector equations 2 &3 dim. 13.5 The tangent problem 11.2 "1 variable controlling 2 (or 3)." 2/1 Vector functions, tangent vectors and velocity. 14.1, 14.2
 Week/Day Monday Wednesday Friday 3 2/4 Tangent lines, Lengths: segments, vectors, arcs. 11.2, 11.3, 14.3 speed 2/6  Smooth curves.  Differential equations and integrals of vector functions. Acceleration 14.4  Arc length as an integral of speed. 2/8 The Dot Product. 13.3. 4 2/11 More on dot products. 2/13 Finish up 1 variable controlling 2 and 3.  Calculus for r'(t). Curvature Formulae 14.3 2/15 Begin "2 controlling 1 variable". Graphs.  Scalar fields 5 2/18 Graphs and level curves of Functions with 2 controlling variables. Begin Partial Derivatives 2/20 Second order Partial derivatives. Start limits and continuity 2/22 Start Tangent Planes, Differentials.
 Week/Day Monday Wednesday Friday 6 2-25 Limits and Continuity. Closeness, Approximations... concepts and definitions. 2-27 Differentials, C1 and differentiable functions.The geometry of differentiability- Tangent planes. 3-1 The Chain Rule (1-2-1) 2-2-1 chain rule 7 3-4 Directional derivatives and the gradient. Geometry of the gradient. 3-6 Local Extremes and the gradient continued. 3-8 Testing for extremes. 8 Exam #1 Self Scheduled for Thursday 3-14 3-11 Extrema on compact sets. 3-13 Breath. 3-15 Quadratic forms. Finish discussion of the discriminant test. 9 3-18 No Class (Break) 3-20 3-22 10 3-25 LaGrange Multiplier, extremes, and odds and ends. 3-27 Quadric Surfaces 13.6 3-29What about 4 variables: 1-3, 3-1, 2-2  Linear regression and "least squares."15.7 problem 51. 11 4-1 NO Classs  C.C. Day 4-3 Finish 2-2 Transformations and vector fields. Briefly 2-3 visualized. Start Integration over rectangles The area problem.11.2(?) 4-6More on Integration and iterated integrals. Fubini's Theorem. 12 4-8  Beginning-basic properties.applications volumes. Integration over compact regions. 4-10 More Integration over compact regions.Properties of integration in the plane. 4-12 .Cross products. More on planes and normal vectors with cross products..

 Week/Day Monday Wednesday Friday 13 4-15 More Integration in the plane. Cross Product Application to tangent plane.Begin Polar coordinates 4-17 Polar coordinates- curves in the plane. Tangents. 4-19 Arc length in Polar coordinates. Integration with polar coordinates. 14 Exam #2 Thursday 4-25 4-22  The integral of e^(-x^2). Application of integration in the plane to mass and probability. Begin Integration in 3D. Cartesian coordinates. 4-24 More integration in 2 and 3 dimensions and probability. 4-26 Cylindrical  coordinates. Integration in Cylindrical. 15 4-29  Begin spherical coordinates More Integration in Cylindrical and spherical coordinates 5- 1 Integration in spherical coordinates. 5-3  Integration surface Area Vector fields and line integrals 16 Talks 5-6Talks 5-8 Integration Over curves. Vector fields and line integrals 5-1 0 Review.!? Green's theorem? What are limits? C1 implies differentiable? Mixed partials are equal.?

Assignment Problem List I

Not yet complete.

 Chapter.Section (pages) Date Due: Problems Interesting/optional Review of Calc I and II] 1-25 Look at Final Exams from Calc I and II 11.1 Read- Consider what this has to do with vectors. 1/25(i) 2/1 (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) 2/6 (i) (i) 1,3,5,6,8 (ii) 9, 11,13, 15, 25, 32 (iii) 33- 35, 39 11.3 arc length (689-691 middle) 2/8 1-5, 9, 15 13.1 1/28(i) 1/30(ii) (i) 1, 3, 4, 7, 11, 13, 15, 23-29 odd (ii) 5, 6, 21, 31,33,35-37 (i) 19 13.2 1/28(i) 1/30 (ii) (i) 7-9,13,14 (ii)17,19,21,23-25,  29 13.5 (i) pages 846-848 (ii) read pages 848-849 to example 4 (iii) 2/1(i)*2/13 (15?) (ii)2/15  (iii) (i) 2-5,7,11, 17 (ii) 19-25 odd (iii)27, 29, 31,49; (iv) 51, 53-55, 61, 63 14.1 2/1(i) (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 2/4 (i) 2/6 (ii)  2/8 (iii) (i) 1,3-5,9,13,14 (ii) 17-19, 27, 29 (iii) integrals33-39 odd, 38, 40 (iv)41,42,44,45,49 14.3 (i) arc length (883-885) (ii) Curvature I (p885and Ex.3) (iii) Example 5 2/8(i) 2/15 (ii) (i)1-6 arc length (ii)11b,13 b curvature (iii)21-23,29,31,32 (ii)18 14.4 velocity and acceleration (891-895) 2/8 (i)1-7 odd, 9-13, 15,17-19 13.3 dot product 2/11(i) 2 dim 2/13(ii) 3 dim 2/15(iii) (i) 1,3,4,8-10,15,16, 23, 24, 29 (ii) 5-7, 11, 17, 18, 21, 25-28, 30, 31, 54 (iii) 39,40,45,46 49,51, 53, 55, 56, 58, 61-63 15.1 2/18(i), (ii) 2/20(iii),(iv) (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 (Graphs) (iv) 9, 19, 33, 34, 61,65 15.2 2/22 read only. 3/1 3,4, 5-11odd, 21,25, 27 15.3 (i) read pp929-932 2/20(i)Read only 2/22 (i)  2/25 (ii).2/27 (iii) (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 2/25 (i) 3/1 (ii) 3/1 (iii) (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 3/4 (i) 3/4 (ii) 3/6 (iii) (i) 1-4, 13, 33 (ii)  7-11 odd, 19,20, 37, 41 (iii) 25-31 odd Exam #1 covers Assigned Material through 3/8. including: 11.1-11.3, 13.1,13.2,13.3,13.5, 14.1-14.4. 15.1-15.5. 15.6 (i) read pp960-963 3/6(i)Read only. 3/8(i) 3/11 (ii) (i)7,8, 3,5, 11 -14 (ii) 21-23,27, 32a,34,35,45 15.7 3/8 3/11 (i) 3/13 (ii) (i)5-13 odd  (ii)6,14,15,17, 27,29,31 15.8 pp985-989 3/27 1-9 odd,23-31 odd 13.6 3/29 (i) 9-15 odd, 21-28, 37-39, 41,43 47,49 16.1 (i) pp 1001-1005 (ii) 1006-1008 4/5 (i)  4/8 (ii) (i) 3a,5,9  (ii) 11-13, 17,18 16.2 4/8 (i) 4/10 (ii) (i)1-11 odd, 4, 8, 25 (ii) 13-15, 18, 29 13.4 4/15 (i) 4/17 (ii) (i) 1-9 odd, 13, 15, 23 (ii)29,30, 33, 41,42,43 18 16.3 4/12 (i) 4/19 (ii) 4/22 (iii) (i)1-9 odd, 8, 11-15 odd (ii) 12,19, 33-35 (iii) 39-43 odd, 44, 45 16.5 1034-1038 (probability) 4/24 23, 25 11.4 4/19 (i) and (ii) 4/22 (iii) (i) 1-3,5,7-11, 15-17, 31-35 (ii)33-45 odd, 56 (iii) 57-65 odd (ii) 71-73,81 Examination #2 Self Scheduled 4/25: Covers material assigned through ***4-22***. 15.5-15.8, 13.6, 16.1-16.3, 13.4, 11.4, 16.4? + TBA 11.5 p707 polar coordinates (Arc length) 4/22 45-49 odd 13.7 Cylindrical and spherical coordinates. 5/1 3-9 odd, 13-19 odd, 31,35,36,9, 40, 49-51, 16.4 Integration in polar coordinates. 4/22 (i) 4/24 (ii) (i)1-11 odd (ii) 15-17, 19-23 odd, 27, 33 16.7 Integration in 3 space (rectangular). 4/29 (i) 5/1 (ii) (i)1-11 odd, 17 (ii) 25,  37 find mass only, 47 16.8 Integration in 3 space (Cylindrical and polar) 5/1 (i) 5/3 (ii) (i)1,2, 5,7 , 15 (ii) 3,17,33,35 16.6 Surface area 5/6 1-7 odd 17.1 Vector Fields 5/6 1-7 odd, 15-18,21,27,29-32 17.2 Line Integrals 5/8 1-7 odd,17, 23 17.2 FT for Line Integrals 5/8 Read