Last updated: 2-6-03
| 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. |
| 4
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 |
| 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. |
| 7 | 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.. |
| 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.!? |
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|
Date Due |
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|
| 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 |
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| 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 |
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| 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 |
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| 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 |
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| 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 |
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| 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 |
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| 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) |
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| 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 |
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| 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 | |
|
Covers material assigned through 4-21. 15.5-15.8, 13.6, 16.1-16.3, 13.4 and 11.4 |
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| 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 |
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| 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 |
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| 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 |
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| 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 |
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| 17.2 Line Integrals pp 1081-1084, 1086-87;1088-1090. | 5-6 READ ONLY!
5-8 |
7,19, 21, 37 | ||