Evolving Syllabus for Math 234 Lecture 2 (A. Assadi, Spring 2009)

What was the lecture on? Was there any homework?

DayCoveredTopicComments
T Jan 2013.1 vector functions assigned written HW1: §13.3#9,16, §13.4#6,19
p962#34. more challenging HW: p963#3, p964#11,12.
R Jan 2213.1–13.3arc length[be able to do example problems in text]
T Jan 2713.3–13.4curvature and the unit normal [be able to do example problems in text]
R Jan 2913.5 components of acceleration[be able to do example 1 in text]
T Feb 3 14.1–14.2multivariable limits[see suggested problems below]
R Feb 5 14.3–14.5partial and directional derivatives and the chain rule[see suggested problems below]
T Feb 1012.6 quadratic surfaces[see suggested problems below]
R Feb 1214.6 tangent planes and differentials[see suggested problems below]
T Feb 1714.7 extreme values and critical points[see suggested problems below]
R Feb 1914.7 local extrema and 2nd derivative test[see suggested problems below]
T Feb 2414.8 constrained optimization and Lagrange multipliers[see suggested problems below]
R Feb 2614.8 constrained optimization and Lagrange multipliers[see suggested problems below]
T Mar 315.1 double integrals[see suggested problems below]
R Mar 5practice midtermchapters 13–14
T Mar 1015.3, 15.7integration with polar coordinates and variable substitution[see suggested problems below]
R Mar 12midterm 1Chapters 13-14
T Mar 2415.7, 15.6coordinate transformations, cylindrical and spherical coordinates[see suggested problems below]
R Mar 26Ch 15problems: integrating over an ellipsoid[see suggested problems below]
T Mar 31Ch 15problems: integrating over domains with cylindrical and spherical symmetry[see suggested problems below]
R Apr 02Ch 15,16finding areas of surfaces
T Apr 07midterm 2
R Apr 09Ch 16review of midterm, intro to ch 16
T Apr 14Ch 16operations on vector fields: grad, div, and curl
R Apr 1616.1–2line and work integrals, conservative vector fields[see suggested problems below]
T Apr 2116.3–4potential functions and Green's theorem[see suggested problems below]
R Apr 2316.5–6surface integrals[see suggested problems below]
T Apr 2816.4, 16.7–16.8Green's theorem(s) and generalization to three dimensions[see suggested problems below]
R Apr 3016.8Gauss's divergence theorem[see suggested problems below]
T May 0514.10Taylor expansion[see suggested problems below]
R May 07Ch 16flux integrals over parametrized surfaces (review)[see suggested problems below]

What are we going to talk about?

"Week" Topic Dates Comments
I 13.1, 13.3, 13.4 Jan 20–29
II 14.1–14.5 Feb 3–5
III 12.6, 14.6 Feb 10–12
IV 14.7–14.8 Feb 17–19
V 14.9–14.10 Feb 24–26
VI 15.1 and review Mar 3–5
VII Midterm 1 March 12Chapter 13–14 ONLY

spring break March 16-20
VIII Ch 15 March 24–26
IX Ch 15 March 31—April 2
X Midterm 2 April 7Chapter 15 and Lagrange multiplers with two constraints
XI Ch 16.1–2 April 14–16
XII Ch 16.3–6 April 21–23
XIII Ch 16.4–16.8 April 28–30
IV Ch 16 review May 5–7

What does each webwork (and exam) cover?

These dates are subject to change and may not be correct. For official dates consult webwork.
WBOpenDueCovers
WB1Wed 1/27Wed 2/1113.1, 13.3, 13.4.
WB2Thu 2/05Wed 2/1814.1–14.5
(and reviews §12.6, conic sections, and cylindrical and spherical coordinates.)
WB3Sat 2/14Wed 2/2514.4–14.7
WB4Fri 2/20Fri 3/0614.8–14.10
WB5Sat 2/28Wed 3/2515.1.
Midterm 1
3/12 Ch. 13-14 ONLY.
WB6 3/104/01 15.3–15.4, 15.6–15.7.
WB7 3/134/03 reversal of order of integration (15.1) and moments (15.2, 15.5).
WB8 3/204/08 (14.8, 15.2, 15.3).
Midterm 2
4/9 Ch. 15 and Lagrange multipliers with two constraints
WB9 3/204/22 (16.2, 16.3, 16.4).
WB104/034/29(16.2, 16.3, 16.4).
WB114/105/01(15.6, 16.4)
WB124/175/06(16.5, 16.6, 16.7, 16.8)
WB134/245/08(chapters 14-16)
Final Exam
Sun. 5/10 10:05am 60% on Ch16, 20% on Ch15, and 20% on Ch14 (Lagrange Multipliers and
Taylor Expansion of a function with 2 or 3 variables up to 2nd degree)

What do the chapters of the book cover?

chapteranimal topic
13 r(t) curves: shape of motion in space
14 ∇f(r) slopes: differential calculus of surfaces and scalar fields
15 ∫ f(r) volumes: integral calculus of surfaces and scalar fields
16 F(r) vector fields: differentiation, integration, and FTC.

What do the sections of the book cover?

§ topic suggested practice



13 vector-valued functions and motion in space
13.1 vector functions
13.3 arc length and unit tangent vector T
13.4 curvature κ and the unit normal vector N
14 partial derivatives
14.1 multivariable functions 3, 9, 13–18
14.2 limits 1, 9, 13, 17, 21, 27, 29, 31, 33, 35, 37, 51, 57
14.3 partial derivatives 7, 13, 19, 33, 34, 41, 43, 51, 57
14.4 chain rule 1, 5, 9, 13, 15, 25, 27, 29, 30
14.5 directional derivatives and gradient 2, 5, 9, 15, 17, 21, 27, 29, 36
14.6 tangent planes and differentials 1, 3, 9, 18, 22, 37, 38
14.7 extreme values and saddle points 3, 17, 39, 43, 44, 53
14.8 Lagrange multipliers (i.e. constrained optimization) 1, 5, 7, 9, 17, 18, 26
14.9 partial derivatives with constrained variables (i.e. of implicit functions) 1, 3, 7, 11
14.10 Taylor's formula for two variables 1, 5, 9
14 Chapter 14 Practice Exercises 35, 37
15 multiple integrals
15.1 double integrals 1, 5, 7, 11, 15–25(odd), 31, 43, 47, 59
15.2 areas, moments, and centers of mass 3, 11, 16
15.3 double integrals in polar coordinates 3, 5, 7, 21, 29, 40
15.4 triple integrals 7, 8, 21, 23, 25, 43
15.5 masses and moments (3 dimensions) 17
15.6 triple integrals in cylindrical and spherical coordinates 1, 11, 13, 31, 39
15.7 substitution in multiple integrals 1, 9, 21
16 integration in vector fields
16.1 line integrals 1–8, 13, 15, 23, 25
16.2 work, circulation, and flux 11, 12, 13, 21, 23(a), 29(a,b), 33
16.3 path independence, potential functions, and conservative fields 1, 3, 5, 7, 9, 13, 17, 19, 25, 34, 37
16.4 Green's theorem in the plane 3, 5, 7, 15, 17, 22, 29, 35, 39, 40
16.5 surface area and surface integrals 1, 5
16.6 parametrized surfaces 1, 9, 35
16.7 Stokes' theorem 1, 5, 7 or 9, 11, 12, 15, 19
16.8 Divergence theorem 5, 7