for MATH 2182H: Honors
Calculus II
call number
19869, MTWThF 11:30
AM-12:25 PM, in 047 University Hall**
Instructor:** Rodica D. Costin

Solve for practice:

**15.2**: 1, 2, 3 and
plot the parabolas in 3, 9

**15.3:** 1, 3, 4

**15.4:** 1,3,5,7, 17, 18, 19, 24a

Check out this
cool web page and this
one.

**16.1: **
1, 5, 9b

**16.2: **1, 2ab, 4 aegh, 5 abcdef, 6abcd

16.3 1,2,7,13,15,17 (I
deleted 20)

**Write up and turn in for grading on T Jan.**** 20:**

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

16.3: 2,7,17
(I deleted 20)

16.4: 2(did in class), 3ab (c did in class), 4, 5, 10, 15, 16

16.5: 2,4,5(did in class),6,7,8

..................................................Solve for practice:

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

**17.1**: from 1 to 11 (did 2 in class), 13

Partial
fraction decomposition

**Write up and turn in for grading on T Jan.**** 27:**

16.4: 4, 5, 12

16.5: 2,4,6

17.1: 4,6,8

.........................................Solve for practice:

17.2: 1, 2, 6, 7, 8, 11

Cycloid
Another cycloid
(with Maple code)

Here are some hypocycloids generated with this Maple code:

a=3,b=1

a=4,b=1

a=5,b=1

a=7,b=3

a=15,b=4

a=Pi,b=2

Hypocycloid
and another Hypocycloid

The
National Curve Bank (with Maple code)

**17.3:** you should be able to solve all problems there

**Write up and turn in for grading on T Feb3****:**

17.2: 2, 6, 8

17.3: 4, 6, 8, 10

...........................................................Solve for practice:

17.4: you should be able to solve all problems there.17.5: 1, 2, 3, 4, 6,7,8,12, 13

How Evolutes were discovered and how to plot them using Maple

17.5: you should be able to solve all problems there.

17.6: you should be able to solve all problems there.

17:7: 1, 2

17.5: 2cd, 8, 13

17.7: 2

...................................................Solve for practice:

18.1: you should be able to solve all problems.

18.2: you should be able to solve all problems.

18.3: you should be able to solve all problems.

18.4: you should be able to solve all problems.

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

18

18

19.1:

19.2: you should be able to solve all problems. Example where mixed derivatives are not equal.

18.7: 6, 8,10,16,18

19.1:

19.2: 10, 16, 20, 22, 27, 30d

19.3: 1...13

19.5: you should be able to solve all problems.

a) (x^2-y^2)/(x^2+y^2)

b) (x^4-y^2)/(x^4+y^2)

x^2 (x^2-y^2)/(x^2+y^2)

19.6: 1...16, 19

19.10: you should be able to solve all problems- except for 11 and 12

19.7: 1...8

You should be able to show that limits exist or not.

You should be able to use knowledge from previous sections as needed!

Just because we are curious: The cubic formula Quartic equations. Abel proved (1823) that here are no formulas in terms of radicals for solving general higher order polynomial equations.

19.6: 8, 10, 14, 16

19.10: 8, 14

19.7: 8, 12

A

20.1: 1, 3-28 (we did 27 in class)

20.2: you should be able to solve all problems

20:4: 1-23, 39

On Fri March 27 we are going over on how to change variables in double integrals, see e.g. these notes. (You need to know!)

20.5: by lecture on Apr 1 be sure you can solve: 1...20 (and/or ask questions in class)

20.5: by lecture on Apr 2 be sure you can solve: 21...27 (and/or ask questions)

20.5: by lecture on Apr 3 be sure you can solve: 28..30 (and/or ask questions)

20.6: 1, 3, 5, 13

20.7: 1, 3, 5, 9, 11, 13 See Bumpy Spheres and calculation of the volume

21.1 you should be able to solve all problems

20.7: 4, 6, 8, 10

21.1: 6, 8, 10, 20, 22

21.2: you should be able to solve all problems

21.3: 1, 3, 5, 7...11, 13...20, 23...28

21.4: 1

References for conservative vector fields in space (which we are discussing in class and you will need to know): here, or here

A spiral surface given parametrically

21.3: 2, 4, 6, 8, 12, 14, 16, 20, 24, 26, 30

21.4:

20.8: 10, 18

F(x,y,z)=y^2z^3

21.4: 1, 3, 5, 7, 9, 11, 12, 14 ....you should be able to solve all problems

21.5: 5, 7, 9, 11, 13, 15 see Klein bottle and Mobius strip

21.4: 2, 4, 6, 8, 10, 18

21.5: 4, 6, 8, 12, 14, 16

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 and

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)