**Instructor:** Rodica D. Costin

Will be updated
after each class!

Koch flake
(picture produced by Prof. Ed Overman, with angles a bit
modified, to look nicer)

**Learn
Mathematica!** Here is a first
plot in polar coordinates

Here is the rose with 8 leaves: the
file used (same, but printed as a pdf
file)

Learn to solve equations and to integrate: the file (its pdf print)

**Learn
Maple!** here is a first plot (pdf file)

There rose with 8 leaves: the code printed
as a pdf file

Learn to solve
equations and to integrate (pdf
file)

**Now you try:
**Plot r=2*sin(t). Try each of the intervals
t=0..Pi, t=-Pi..0, t=0..Pi/2

**Solve for practice:**

16.3 1,2,7,13,15,17

16.5: 5,7

17.1: 1, 2, 3

New files to help you learn Mathematica and/or Maple are posted above.

Write up and turn in for grading on T Jan.

15.2: 1a,f; plot the parabolas 3b,e; 9

15.3: 3

15.4: 18, 24a

16.1: 1j,l, 4, 6a 16.2: 5 def, 6 bcd

Write up and turn in for grading on T Jan.

16.3: 2,7,17

16.4: 10, 3ab, 4,12 ALSO: 5

16.5: 2,4,6

17.1: 4, 6, 13

Files to help you learn Mathematica and/or Maple are posted above.

See the Cycloid.
Another cycloid (with Maple
code)

See Hypocycloids: a=3, b=1

a=4, b=1

a=5, b=1

a=5, b=2

a=7, b=3

a=15, b=4

a=Pi, b=2

**Review integration Sec. 10.3,
10.4.**** Learn trig formulas**** by heart.**

**Solve for practice:**

17.2: 1**,**** **** 7, **** 11** you should be able to
solve all problems here

17.3:

**Write up and
turn in for grading on T Jan.**** 31 (date of our first
midterm!):**

17.2: 2**,
**6, 8

17.3: 10 and 4, 6, 8

17.4: 2, 3, 4, 6

**Midterm info: **

You are allowed to use one page with your own notes.

The use of other notes, textbooks, electronic devices etc. is
strictly prohibited on this exam.

**Topics covered:**

Everything up to 17.4 (excluding from 17.4 centripetal force and
arc length parametrization).

**Solve for practice:**
you should be able to solve all
problems there.

17.5:

17.7:

Maple code for graphing evolutes, and their history

17.7

Saturday Feb. 25! Rasor-Bareis-Gordon Math Competition! Fun and cash prizes!

Every year one or two of my students placed high!

See more information here

18.1: 4c, 6cd, 8, 10a, 12, 14a, 16a

18.2: 2, 4b, 6, 8a, 10

Sign up for the RBG competition here!

Y

19.6: 1...16, 19

Comments:

19.3:

18.2: 14, like 13, 15, 17

18:3: 2,3,15, distance from point to line, distance between 2 skew lines (problem 11a)

18.2: 18, 21, 22

18.4: 4, 6, 8, 10a, 14a, 20, 22, 24

19.6: 13a, 15

And:18.4: 16

And: 18.5: 2, 4, 6, 12, 16

18.6: 2, 4, 6, 12, 16, 20, 24 (And solve for practice 1-16, 19-21, 24, 25

18.7:

19.2:

19.2: 19a, 29d

18.7:

19.1: 13, and find and plot the domain in 3,5

19.2: 19, 21b, 29a, 30c

and

You are allowed to use one page with your own notes.

The use of other notes, textbooks, electronic devices etc. is strictly prohibited on this exam.

Everything starting with 17.4 up to 19.6 AND whatever we cover this Friday and Monday, namely 19.10. (We will do 19.7,8,9 after the midterm exam).

Thursday, March 9: You may enjoy this lecture on Neutrinos, Dark Matter and the Nature of the Universe

We covered

19.7:

and

Have a Great Spring Break!

20.2:

19.8:

We did: change of variable in triple integrals

20.4:

Write up and turn in for grading on T

20.7:

and

20.8:

Write up and turn in for grading on T

You need to know about conservative vector fields and simply connected domains in 3d (see here). See also the Informal Discussion here.

Conic sections (be
able to recognize, plot and use)

Polar coordinates (be
able to use when needed)

Parametric equations
for lines, curves, surfaces (be able to parametrize the objects
you need and use in calculations)

Partial derivatives,
the gradient vector, the tangent plane, find normal vectors

Use the chain rule
when needed, use implicit differentiation

Use dot product, find
orthogonal projections of vectors and angles between vectors

Use cross product,
find area of parallelograms, find normal vectors to surfaces

Cylindrical and
spherical coordinates (be able to use them when needed)

Extrema (local,
absolute, Lagrange multipliers)

Multiple integrals (be
able to set up, evaluate, use appropriate coordinates, also
calculate masses, centroids, volumes, area)

Line integrals:
calculation, conservative fields (or not), find potential of F
(or argue it does not exist)

Green's Theorem (be
able to state and use)

Gauss's Theorem (be
able to state and use)

Stokes' Theorem (be
able to state and use)