Sample Weekly Syllabus for

A Second Course in Vector Calculus

Assigned work in each weekly eSection - open in the .nb document for details, including assigned homework.

Week #1: Review of Partial & Total Derivatives

Mon: Partials and the tangent, don’t forget chain & product rules

Homework#1: Section 3.3, Exercise 1(b), (f), (=Ex.3.3.1(b), (f)),Ex.3.3.2(a), Ex.3.3.5
Exercise 3.8.2

Wed: Implicit functions

HmWk#2: Ex.4.1.6; Ex4.2.4(c); Ex.4.4.1; Ex.4.5.1(b)

Fri:  Contour surfaces & the gradient

HmWk#3Chapter4Lab4
Ex.5.0.1; Ex.5.1.2; Ex.5.2.3

Week #2:  Convexity & Second Derivatives (M-Eigensystem)

Mon (University Holiday)

Wed: Taylor’s Formula & Quadratic functions: a (x^2)+2b x y+c (y^2)

HmWk#4Ex.6.1.1, 2(a), 4; more time for Ex.5.3.2

Fri: More eigenstuff

HmWk#5Ex.6.2.1, 3(a), 4; Ex.6.3.1, 2,

Week #3: MAX-min in several variables (Resonance)

Mon: Interior critical points

HmWk#6: Ex.6.5.2, 3; Ex.7.2.1, 2, 3, 4, 8(a), (c)

Wed: Compact domains

HmWk#7: Ex.7.3.1(F, G), 2(a,b), 3;

Fri: Boundary critical points

HmWk#8: Ex.7.4.3, 7  Project 1 linear oscillators

Week #4: Combined MAX-min (Box Design)

Mon

HmWk#9: Sect 7.5, Ex.7.6.5(b)

Wed

Finish Resonance project (due midnight Thu 18 Sep)

Fri

Project 2 box design (due midnight Thu 25 Sep)
HmWk#10: Ex.7.7.4, 5, 6 (worked in class, due Mon written)

Week #5: Motion along Curves, Vector Fields

Mon

HmWk#11: Ex.10.1.3, 5, 10, 11

Wed

HmWk#12: Ex.11.1.1(a,b,c), 2, 3; Ex.14.1.1, 3

Fri

HmWk#13: Ex.9.4.3; Ex.11.4.4(a, b); 14.2.1

Week #6: Path Integrals and Conservation of Energy

Mon

HmWk#14: Ex.14.3.2; 14.3.6, 7

Wed

HmWk#15: Ex. 14.4.1, 2, 3

Fri

Review

Week #7: Differentiation of Vector Fields

Mon

Exam#1

Wed

HmWk#16: Ex.8.1.1, Ex.8.2.2(b), 5

Fri

HmWk#17: Ex.8.3.2(c, vi CoG), 5

Week #8: Multiple Integration (Moment of Inertia)

Mon

HmWk#18: Section 8.4 Ex.1, 2, 3, 4 (use Mathematica for 1 & 2)

Wed

M-Integration

Fri

Show & tell: Project on CoG, moments of inertia

Week #9:  Parametric Surfaces

Mon

HmWk#19: Ex.15.1.1, 2, 5

Wed

HmWk#20: Ex.15.2.1, 2, 6, 7

Fri

HmWk#21: Ex.15.3.1, 2, 3

Week #10: Surface Area and Flux

Mon

HmWk#22: Ex.15.4.1, 3, 4

Wed

HmWk#23: Ex.15.5.1, 2, 3

Fri

HmWk#24: 17.2.1, 2, 3, 4

Week #11: Coordinate Systems

Mon

HmWk#25: 17.3.2, 3, 4, 5

Wed

HmWk#26: 17.4.3, 4 
Write the integrals on your paper, but you may evaluate them with Mathematica

Fri

Review Coordinates and 19.1 (Review your old HmWk Ex.14.3.2.)

Week #12: Curl & Stokes’ Theorem

Mon

HmWk#27: 19.2, 1, 2, 3

Wed

HmWk#28: 19.3.1, 2, 3

Fri

HmWk#29: 19.4.1, 2 (we’ll finish these Monday, but try...)

Week #13: Divergence & Gauss’ Theorem

Mon

Review

Wed

Review

Fri

Exam#2 in class

Week #14: Heat & Laplace Equations (Heat in a Rod)

Mon

HmWk#30: 20.1.1, 20.2.1

Wed

Project 4 = OneDimensionHeat (in eExercises)

Fri

Project 4 continued

Week #15: Qualitative Behavior of Solutions of PDE

Mon

Maximum Principle

Wed

Project Show & Tell

Fri

Review