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

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Last updated: 2-04-02

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 Tangent Planes 2/22 Tangent Planes, Differentials. Start limits and continuity

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) integrals 33-39 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 3,4, 5-11odd, 21,25, 27 15.3 (i) read pp929-932 2/20(i)Read only. (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) 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) 1-4, 13, 33 (ii)  7-11 odd, 19,20, 37, 41 (iii) 25-31 odd Exam #1 covers Assigned Material through ***. 11.1-11.3, 13.1,13.2,13.3,13.5, 14.1-14.4. 15.1-15.5. 15.6 (i)7,8, 3,5, 11 -14  (ii) 21-23,27, 32a,34,35,45 15.7 (i)5-13 odd  (ii)6,14,15,17, 27,29,31 15.8 pp985-989 1-9 odd,23-31 odd 13.6 (i) 9-15 odd, 21-28, 37-39, 41,43 47,49 16.1 (i)Look at 3a,5,9 (will not be collected till 4/11) (ii) 11-13, 17,18 16.2 (i)1-11 odd, 4, 8, 25 (ii) 13-15, 18, 29 13.4 (i) 1-9 odd, 13, 15 (ii) 23, 29,30, 33, 41,42,43 18 16.3 (i)1-9 odd, 8 (ii) 11-15 odd, 12,19, 33-35 (iii) 39-43 odd, 44, 45 16.5 1034-1038 (probability) 23, 25 11.4 (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 45-49 odd 13.7 Cylindrical and spherical coordinates. 3-9 odd, 13-19 odd, 31,35,36,9, 40, 49-51, 16.4 Integration in polar coordinates. (i)1-11 odd (ii) 15-17, 19-23 odd, 27, 33 16.7 Integration in 3 space (rectangular). (i)1-11 odd, 17 (ii) 25,  37 find mass only, 47 16.8 Integration in 3 space (Cylindrical and polar) (i)1,2, 5,7 , 15 (ii) 3,17,33,35

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

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