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Fall of 2007 |
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Class Schedule
Problems in green have been graded.
Each graded problem is worth 5 points, unless noted otherwise.
Correctly solved problems are marked with a checkmark; others are given the grade like 3/5, etc.
Unless stated otherwise all problems are due in one week.
Do not hand in problems for which there are solutions or answers in the book, unless told so explicitly here.
I will not remind you to hand in the problems – this is your choice and responsibility.
I will let you know what problems have been graded, if any, after the deadline.
Review I is on this Friday, Dec 13, 2007 Southwick 407
at 10 AM.
I will answer your questions
during this review, like ``What is Jacobian?", or "How to compute the
determinant", or `` What this [--] notation means", etc.
Review III is on Wednesday -- Photos
I will solve a couple of
problems typical for the final.
Office Hours 2:30-3:45 PM (changed from 4 PM) on
Monday and
2:30-4:00 PM
Wednesday
Short guide to the final -- Solutions
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Topics [Smith-Minton] |
Read Sections |
Problems |
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Vectors in the plane, `Vectors in 3-Space, Vectors in n-space. |
10.1, 10.2 |
# 51,52 from 1st section; #23-26, 27, 28,30 from 2nd . |
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Thursday, |
Dot product. Solving problems. |
10.2, 10.3 |
#31, 39, 40 from 10.3 |
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Friday, |
Orientation of space. Cross product. Determinants. Equation of plane. |
10.3, 10.4 |
#42, 44, 60, 62, 66 from 10.3 |
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Monday, |
Cross-products and determinants continued. |
10.3, 10.4 |
#48-58 from 10.4 (corrected – used to be 10.3) Due Wed. Sep. 19 |
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Properties of determinants. Applications of cross-products. Magnus force. |
10.4 |
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Thursday, |
Parametrization of lines and planes. Three ways to define a line. |
10.5 |
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Friday, |
Solving homework problems. Quadratic surfaces. |
10.3 (in regard to problems) 10.6 |
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Monday, |
10.6 |
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10.6 |
42, 44, 48 of 10.6; For a cone described by the equation on page 846 find a section which is a parabola. Hint: 1) find a plane which is parallel to a line contained in the cone. 2) find the equation of the section 3) prove it is a parabola (by a change of variables, if needed) For a higher grade for this problem work with parameters a and b. If this is difficult for you, do the same problem for some chosen values of a and b. |
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Thursday, |
Vector-valued functions. Curves, arcs. Velocity. |
11.1, 11.2 |
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Friday, |
Length of a curve. Velocity. Sep21.jpg |
11.1 |
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Monday, |
Answering questions on practice problems. Motion in space. |
11.3 |
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Midterm |
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Solving midterm problems |
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Firday, |
Curvature, Acceleration. |
11.4 |
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Monday, October 1 |
TNB frame. oct1_r_end oct1_l_end oct1_r_mid oct1_l_mid |
11.5 |
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Wednesday, October 3 |
11.5 |
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Thursday, October 4 |
Review of linear algebra. |
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Firday, October 5 |
11.5 |
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Torsion. Mentioning (without proof) of Derivation of
Kepler’s laws from |
11.5 |
Review Exercises p. 917: 36,38,42,46,48 Solutions: 36_part1 Extra practice (if needed): solve corresponding odd-numbered problems and compare answers with the book. |
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Thursay, October 11 |
Functions of many variables. Visualizing functions of two variables. |
12.1 |
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Friday, October 12 |
Continuity of functions of many variables |
12.2 |
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Monday, October 15 |
Continuity of functions of many variables. Board |
12.2 |
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Wednesday, October 17 |
Partial derivatives. Total differential. |
12.3, 12.4 |
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Thursday, October 18 |
Linear approximation. Tangent plane. Chain rule. Board |
12.5 |
12.5: 7-10, 17-20, 25-27; 12.4: 23-28, 32 (due Oct. 29) Solutions |
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Wednesday, October 24 |
Chain Rule. Implicit function theorem. Board |
12.5, 12.6 |
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Thursday, October 25 |
Implicit Differentiation. Directional derivatives. Gradient. Jacobian (p.973). Board |
12.5, 12.6 |
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Friday, October 26 |
Tangent plane to a surface defined implicitly. Extrema of a function of many variables. Board |
12.6-12.7 |
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Monday, October 29 |
Extrema of a function of many variables. Hessian (p.972, 973). Board |
12.7 |
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Thursday, November 1 |
Second derivatives test (pp. 999-1000). Board |
12.7 |
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Friday, November 2 |
Optimization. Board |
12.7,12.8 |
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Monday, November 5 |
Constrained optimization. Board |
12.8 |
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Wednesday, November 7 |
Solving some text problems. |
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Thursday, November 8 |
Fubini theorem. Computing double integrals by repeated partial integration. |
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Firday, November 9 |
Monter-Carlo integration. Board |
page 1046, web-sources |
Assigned problems: sec 12.7: 65-68 and sec. 12.8: 42,47-50 This set will not be graded, but the solutions will be posted. |
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Wednesday, November 14 |
Monte-Carlo integration. Board |
page 1046, web-sources |
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Thursday, November 15 |
Triple integrals. Computing volumes. Board |
13.2 |
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Friday, November 16 |
Change of variables in double integrals. Jacobian. Board |
13.8, |
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Monday, November 19 |
Using polar coordinates to compute integrals. Board |
13.8, problem #2 from page 1066. |
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Wednesday, November 21 |
Recognizing sphere. Computing the volume of a body with rotational symmetries by switching to spherical coordinates. |
13.8, 13.7 |
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Monday, November 26 |
Computing the volume of a body with rotational symmetries by switching to spherical coordinates. Vector fields. Gradient vector fields. |
13.7, 14.1 |
Homework: sec. 12.8: 40, 44,46 sec. 13.2: 20, 22, 60, 64 sec. 13.7: 54, 46 |
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Wednesday, November 28 |
Vector fields. Conservative vector fields. Potential function. Board |
14.1 |
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Thursday, November 29 |
Integrals along curves. Board |
14.2 |
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Friday, November 30 |
Integrals along curves and surfaces. Mobius strip. Non-orientable surfaces. Board |
14.6 |
Note we do not follow the sections of this chapter in linear order! |
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Thursday, December 6 |
Midterm III |
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Friday, December 7 |
Green's theorem with proof. Board |
14.4 |
Homework: sec. 14.4: 3 (writing), 34, 36 extra credit: 14.4: 31 |
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Monday, December 10 |
Refresher on Green's theorem. Curl of a vector field. Stokes theorem as a generalization of Green's theorem. |
14.5, 14.8 |
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Wednesday, December 12 |
Stokes theorem. Board |
14.8 |
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Thursday, December 13 |
. General form of Stokes theorem. Board |
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© 2000 University of Massachusetts Lowell, Class Connections |
Graphics & Design
by: Thomas Pimental & Michelle Christman |