Math
209
Homework
Assignments
From:
Stewart, Multivariable Calculus. 7th Edition.
Instructions:
Once
a homework is assigned (announced in class), it is due on the following class
session – Work all odd problems when a range is given, unless otherwise
specified.
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HW
help: Stewart Multivar 8th edition |
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Book section and
problem numbers: |
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Vectors and the Geometry of Space |
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Integration Techniques Review (HW) 12.1: Three-Dimensional Coordinate System (Exercise pages): 1-17(odds)(hint for #13: find the radius first), 10, 20(use the midpoint formula result of
#19), 21-33(odds),37,41,43. 12.2: Vectors (Exercise pages) 3-29(odds), 35, 40, 41, 45, 47, 51. 12.3: The Dot
Product (Exercise
pages) 3,5,7,9,13(write
components), 14,15,19-43(odds),49,51,52,
54
optional. 12.4: The Cross Product (Exercise pages) 1-7(odds),13,15,19,27,31,33, 37(hint: if 3 vectors are coplanar then
they form a zero volume!), 39,41,43. 12.5: Equations of
Lines and Planes (Exercise pages) 3,5,7,
11-29(odds),30,35,37,39,41,45,48,51-57(odds). 12.6: Cylinders
and quadric surfaces (Exercise pages): 11-19(odds),21-28(all),33,35,48,50. |
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Vector Functions |
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13.1: Vector Functions and Space
Curves (Exercise pages): 1-6(all),7,9,13,14,
17,19 (21-26
in class) 29,30,39,41,42,43,44 48
(hint: “particles collide” means
that r1(t)=r2(t), “paths intersect”
means that there is one or more value of s and t such that r1(t)=r2(s)) 13.2: Derivatives and Integrals of
Vector Functions (Exercise pages): 3,7-15(odds),16,19-27(odds),35-41(odds),49,53. 13.3: Arc Length and Curvature (Exercise pages): 1,3,5,13,15(hint: s(t)=5), 17,21,23,25,29,31,32,
35, 38, 39, 42, 43,47,49,51(parametrize the ellipse then use result 42),63. 13.4: Motion in Space: Velocity and
Acceleration (Exercise pages): 3,9,11,15,19,21,27,37,39. |
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Partial
Derivatives |
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14.1: Functions of Several
Variables (Exercise pages): 2,5,11-21(odds), 23-31 (odds), 32,34,
43,45,51,55,58, 69. (Use CalcPlot3D or Wolfram Alpha or Geogebra3D
to check your results for: 23-31 and 43,45,51,55,58) 14.2: Limits and
Continuity
(Exercise pages): (For some of these, try
limit approaches along x-axis then along y-axis, or along some other line,
example: y=x) 7,9,11,15,17,21,39,41. 14.3: Partial Derivatives (Exercise pages): 5-8(all),15-43(odds),47,49,53,57,65,67,70,71,77,87,95. 14.4: Tangents Planes and Linear
Approximation (Exercise pages) 1,3,5,13,17,35. 14.5: The Chain Rule (Exercise pages): Chain
rule: 1-13(odds),17,19,21,23. Implicit
differentiation and application pbs: 27,31,35,41(the equation relating pressure, volume and temperature is:
PV = 8.31 T),47, 53
try on your own first(answer to 53). 14.6: Directional Derivatives and
the Gradient Vector (Exercise pages): 5-17(odds),23,25,29,33,39,41,45,55,63. 14.7: Maximum and Minimum Values (Exercise pages): 1,5-19(odds),31,39,41,43,49(find the dimensions
of the box in terms of the parameter c),51. |
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Multiple
Integrals |
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15.1: Double Integrals over
Rectangles (Exercise pages): 11,12,13.
15.2: Iterated Integrals (Exercise pages): 3-21
(odds), 25, 29, 31, 35, 37, 38 (in 37 and 38 use even and/or odd properties of
integrands.) 15.3:
Double Integrals over General Regions (Exercise pages): 1,9(odds),14,17-31(odds),43,
47,49, 51, 53. 15.4: Double Integrals in Polar
Coordinates (Exercise pages): 5-13(odds), 19, 21, 25, 27, 29. 15.5: Application - Charge and Mass: (Exercise pages) 1,
3,5,7 (find only the mass). 15.6:
Application - Surface Area (Exercise pages): 7,13,23. 15.7: Triple Integrals (Exercise pages): 3-11(odds),
19, 21, 47a) (mass is density, r, integrated over
volume). 15.8: Cylindrical Coordinates (Exercise pages): 9,
11, 17, 19, 21. 15.9: Spherical Coordinates (Exercise pages): 1, 3, 9, 21, 23. |
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Vector Calculus |
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16.2: Line Integrals (Exercise pages): 1,3,9,11,13,15,19,21. 16.3: The Fundamental Theorem
for Line Integrals
(Exercise pages): 3,5,7,13,15,
and 21(no math!). 16.4:
Green’s Theorem (Exercise pages): 5,
7, 9, 17. 16.5: Curl and Divergence (Exercise pages): 1,3,7,13,15,17.
Check out 38 (if you’re interested in Physics!) |
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