MATH 210 Calculus III 
Spring, 2003 MTRF 10:00 -10:50  SH 116 
Course Assignments



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Last updated: 2-6-03 


MATH 210: Calculus III Spring,2002
Tentative Daily Topic Schedule
Week
/Day
Monday Tuesday Thursday Friday
1 1/21 Introduction- 
Begin review
Variables- relations-functions. 
What is calculus? Differential Equations?
1/23 Introduction to 3-dimensional coordinate geometry.   1/24 13.1
Introduction to vectors.
2  1/27 13.2 "1 variable controlling 2" 
11.1 Parametric curves .  Visualizations: Transformations and graphs. 
 1/28 More on vectors and functions
"1 variable controlling 2," 2 controlling 1".
1/30 More on vector algebra.  1/31 Lines: parametric and vector equations 2 &3 dim. 13.5
Week/Day Monday Tuesday Thursday  Friday
3 2/3 The tangent problem 11.2
"1 variable controlling 2 (or 3)." Vector functions, tangent vectors and velocity. 14.1, 14.2
2/4Tangent lines, Lengths: segments, vectors, arcs. 11.2, 11.3, 14.3 speed  2/6 Smooth curves. Acceleration 14.4 
Arc length as an integral of speed.
 2/7 Differential equations and integrals of vector functions.

Summary #1 Due 2-11
2/10 The Dot Product. 13.3. 2/11 More on dot products. 
Finish up 1 variable controlling 2 and 3. The calculus of the"vector" derivative
2/13 More on dot products 2/14  The Calculus for r'(t).
5 2/17 Curvature Formulae 14.3 2/18 Begin "2 controlling 1 variable". 
Scalar fields.Graphs and level curves of 
2/20 2/21 Begin Partial Derivatives
Tentative Daily Topic Schedule
Week/Day Monday Tuesday Thursday Friday
6
Summary #2 Due 2-25
2-24 Second order Partial derivatives. Linear (Affine)Functions- lines, planes and vectors.  2-25 More on Planes and "Tangent Planes". What is continuity? What does differentiable mean? 2/27  Differentials.Concepts and definitions.  2/28 [Limits and Continuity. Closeness, Approximations. ?] 
Differentials, C1 and differentiable functions.The geometry of differentiability- Tangent planes. 
3-3 The Chain Rule (1-2-1)  chain rule 3-4Chain Rule(2-2-1)  Directional derivatives and the gradient. 3-6 Geometry of the gradient.  3-7 More on gradient.
8 Summary #3 Due 3-10
Exam #1 Self Scheduled for Wednesday 3-12
3-10 Finish Gradient and level curve/surfaces. 
Extremes..
3-11.Testing for extremes. Extrema on compact sets 3-13 More Extremes and odds and ends. 3-14  Finish discussion of the discriminant test. Quadratic forms. 
9 3-17 No Class (Break) 3-18 3-20 3-21
10 3-24  LaGrange Multiplier 3-25 Linear regression and "least squares." 15.7 problem 51.  3-27 Quadric Surfaces 13.6 What about 4 variables: 1-3, 3-1, 2-2 ? 
5 variables? 2-3, 3-2?
3-28 Breath?
11Summary #4 Due 4-3 3-31  NO Classs  C.C. Day 4-1Start Integration over rectangles  4-3 More on Integration and iterated integrals.  4-4 Average Value 
The area problem.11.2(?)
Fubini's Theorem.
12 4-7  Beginning-basic properties.applications volumes. Integration over compact regions. 4-8 More Integration over compact regions.Properties of integration in the plane. 4-10 Cross products 4-11 .. More on planes and normal vectors with cross products.. 
Tentative Daily Topic Schedule
Week/Day Monday Tuesday Thursday Friday
13 4-14 More Integration in the plane. 
Cross Product 
Application to tangent plane.
4-15 Begin Polar coordinates  4-17 Polar coordinates- curves in the plane. Tangents. 4-18 Arc length in Polar coordinates 
Begin Integration with polar coordinates.
14 Exam #2 
4-23
4-21  More Integration with Polar Coordinates.
The integral of exp(-x2). 
.
4-22 Begin Integration in 3D. Cartesian coordinates 4-24 Applications of integration in the plane and space to mass. Start Cylindrical  coordinates.   4-25 No class!
15 4-28 
Integration in Cylindrical. Begin spherical coordinates
4-29 More Integration in Cylindrical and spherical coordinates  5-1 Integration in spherical coordinates. Integration surface Area.
Briefly 2-3 visualized. 
5-2 More work on integration and shperical coordinaates.
16 Talks  5-5 Vector fields and line integrals 
2-2 Transformations and vector fields.
5-6 Integration Over curves. Vector fields and line integrals
 
5-8 Talks 5-9 Talks
Green's theorem?Review.!?

Assignment Problem List I ( as of 1-30-03)
Chapter.Section (pages)
Date Due
Problems
Interesting/optional
Review of Calc I and II 1-23&24 Look at Final Exams from Calc I and II
11.1 Read- Consider what this has to do with vectors. 1-27 Read only
1-28(i)
1-30 (ii)
(i) 1-7 odd, 17,19,23, 22, 28 
(ii) 4,6,8, 11-13, 25, 40 
(ii)34, 35, 37,42,43
11.2 (i) (682-685:tangents) 
(ii) Re-read 682-685
(iii) (685-687: area) 
1-31& 2-3 
Read (i) only
2-4 (i)
2-7(ii)
(i) 1,3,5,6,8
(ii) 9, 11,13, 15, 25, 32
(iii) 33- 35, 39
11.3 arc length (689-691 middle)  2-7  1-5, 9, 15
13.1  1-24 Read only
1-27 (i)
1-28 (ii)
(i) 1, 3, 4, 7, 11, 13, 15, 23-29 odd
(ii) 5, 6, 21, 31,33,35-37
(i) 19
13.2  1-31(i) and (ii) (i) 7-9,13,14
(ii)17,19,21,23-25,  29
 
13.5 (i) pages 846-848 (lines in space)
(ii) read pages 848-849 to example 4
(iii)
2-3(i)
2-24Read(ii)
2-25 (ii)
(i) 2-4,7,11 Changed 1-31(1:48pm)
(ii)  5,17,19-25 odd
(iii)27, 29, 31,49;
(iv) 51, 53-55, 61, 63
 
14.1  2-4 Read Only
2-6(i)
2-7(ii)
(i) 3,4,7-13, 16, 17,21,23
(ii) 24,25, 28
(ii)33
14.2 (i)and (ii)vector derivatives and  tangent vectors p877-879
integrals and de's p 881
2-6(i)
2-7 (ii)
2-10 (iii)
2-17(iv)
(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
2-10(i)
2-18(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) 2-11 (i)1-7 odd, 9-13, 15,17-19  
13.3 dot product 2-11(i)
2-13(ii)
2-14 (iii)
(i) 1,3,4,8-10,15,16, 23, 24, 29
(ii) 5-7, 11, 17, 18, 21, 25-28, 30, 31
(iii) 39,40,45,46, 54
49,51, 53, 55, 56, 58, 61-63
15.1(i) pp907-910
(ii)pp910-917
2-20(i)
2-20(ii)
2-21(iii)
2-24(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 (i) pp921-926 2-28(i)Read ONLY
3-3 (i)
3-4 (ii)
(i)3,4, 5-11odd
(ii) 17, 21,25, 27,31
15.3 (i) read pp929-932
(ii) read pp933-934
(iii) read pp 935-936 2nd order
(iv) read pp 937-939
2-24(i)
2-25(ii)
2-25(iii)
2-27(iv)
(i) 3,11-25 odd
(ii) 6, 20,22, 32, 35, 37
(iii) 43, 45,46, 51, 56
(iv) 63, 65, 66, 68(a,c), 69, 76
 87
15.4 (i) read 943-944.
(ii) read 944-948 (including Example 5)
(iii) Finish Section.
2-27(i)
2-28(ii)
3-3(iii)
(i) 1-5,7
(ii) 17,18, 23-26, 29, 31,36
(iii) 11, 12, 27, 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)
3-6(ii)
3-7(ii)
(i) 1-4, 13, 33
(ii)  7-11 odd, 19,20, 37, 41
(iii) 25-31 odd
 
Exam #1 covers Assigned Material through 3-10
including: 11.1-11.3, 13.1,13.2,13.3,13.5, 14.1-14.4. 15.1-15.6.
15.6 (i) read pp960-963
(ii)  read pp963-968
(iii)p 969-970
3-6(i)
3-7(ii)
3-10(iii)
3-11(iv)
(i)7,8, 3,5, 11 -14
(ii) 21-23,27, 32a
(iii) 34,35,45
(iv) 47,51,57
(iv) 59 
15.7 (i) pp 973-ex.1 p974; p 979
(ii) p274-278 
(iii) Example 7 
(iv) Read notes on Quadratic Functions on line.
3-11(i)
3-13 or14 (ii) 
3-14(iii) 
3-24 (iv)
(i) 5-13 odd (use technology to see extreme/saddle)
(ii) 6,14,15,17 
(iii) 27,29,31
 
15.8 pp 985-989 3-25 1-9 odd,23-31 odd  
13.6 Surfaces 3-28 (i) 9-15 odd, 21-28, 37-39, 41,43 47,49
16.1 (i) pp 1001-1005
(ii) 1006-1008
4-3(i)
4-4(ii)
(i) 3a,5,9 
(ii) 11-13, 17,18
16.2 (i) p1010-1011
(ii)1011-1014
4-4(i)
4-7(ii)
(i)1-11 odd, 4, 8
(ii) 13-15, 18,  25, 29
(ii) 33
13.4 cross products
Notes on Cross Products
4-14(i)
4-15(ii)
(i) 1-9 odd, 13, 15, 23
(ii)29,30, 33, 41,18,42,43 
(Revised 12:20pm 4-14-03)
16.3 (i)pp1015-1020
(ii)pp 1017-1020
4-8(i)
4-10(ii)
4-11(iii)
(i)1-9 odd, 8, 11-15 odd
(ii) 12,19, 33-35
(iii) 39-43 odd, 44, 45
11.4 (i)694-696
(ii) 696-699 
(iii) 699-702
4-17 (i)
4-18(ii) and (iv)
4-21(iii)
(i) 1-3,5,7-11
(ii) 15-17, 31-35, 56
(iii)37-45 odd 
(iv) 57-65 odd
(iii) 71-73,81
 Examination #2 4-23 -03 Self Scheduled
Covers material assigned through 4-21. 
15.5-15.8, 13.6, 16.1-16.3, 13.4 and 11.4
11.5 p707 polar coordinates (Arc length) 4-21 45-49 odd
13.7 Cylindrical and spherical coordinates. 4-28 Read only!
4-29
3-9 odd, 13-19 odd, 31,35,36,9, 40, 49-51
16.4 Integration in polar coordinates. 4-21 Read Only
4-22(i)
4-28(ii)
(i)1-11 odd
(ii) 15-17, 19-23 odd, 27, 33
16.7 Integration in 3 space (rectangular). 4-22 Read only!
4-28(i)
4-29(ii)
(i)1-11 odd, 17
(ii) 25,  37 find mass only, 47
16.8 Integration in 3 space (Cylindrical and polar) 4-29(i)
5-1(ii)
(i)1,2, 5,7 , 15
(ii) 3,17,33,35
16.5 1034-1038 (probability) 23, 25
16.6 Surface area 5-2 1-7 odd
17.1 Vector Fields 5-5 Read only
5-6
1-7 odd, 15-18,21,27,29-32
17.3(i) pp1097 examples 2 -4a, 5. 
(ii)pp 1093-1100
(i)5-6
(ii)5-8
(i)3-9 odd. [NOTE: A vector field is called conservative if it is the gradient vector field for a potential function.]
(ii)13,15,17,21,29-31
17.2 Line Integrals pp 1081-1084, 1086-87;1088-1090. 5-6 READ ONLY!
5-8
7,19, 21, 37