#### Math 1507 A1 Fall 98 Archives

Places and people, and resourses if you are having trouble with the course:

Final Exam Monday 8:00 am
Review Sesion Fri 4:00 pm in the same classroom.

Problems To Look at for the Final

• Page 8: 19,21,23,27,41
• Page 14: 13.15.17.7.9
• page 21: 9,11,13,2,7,27
• page 44: 5,7,9,11
• page 66: 19,31,35,38,55
• page page 168: 25,27,31
• Page 8, Section 0.1: # 20,22,24,26,28,40,41
• Page 14, Section 0.2: # 2,4,8,14,16
• Page 21, Section 0.3: # 2,4,6,20,22, 40,42
• Page 44, Section 0.5, # 4,8,10,12
• page 66, Section 1.2:# 10,12,20,21,23,24
• page 168, Section 2.5: 26,28,32
• Page 94: I,II,..VII, 1,2,3,4,516,17,25
• Page 111: 1,2,3,5,6,7,8
• The derivative of sin(x) is cos(x). Part of section 2.5
• Page 137: 1,2,3,5,6,7,13,15,17,21,22,25,27
• Page 144: 1,2,3,4,5,6,8,9,13,15,17,27,29,35,36
• Page 153 1,3,4,5,6,19,25,26,37,38,39,45,46 and getting a bit ahead --
• Page 160 1,2,3,4,5,,21,22,25,26,27
• Page 267 1.2.3.4.10,11,12,16,17,19,21,22,37,38
• Page 185: # 7,8,10,11,12,19,20,24
• Page 196 3,4,5,7,9,11,16,17,21,23,24
• Page 203 1,2,3,5,7,9,24,25,27
• Page 223: #1,2,3,5,7,9,25,27,30,31,33,35,38,39,40
• Page 238: #5,6,7,8,12,13
• Page 262: # 10,21,22,23.25.26
• page 548 1,3,5,33,34
• page 558 1,3,5,7,27,36
• page 568: 1,3,5,21,22,41,49
• Page 580: 1,2,3,4,519,20,21
• Page 588: 1,3,5,7,9,44,45,46,47,55,57,58,59,75,76
• page A-36: 1,2,3,4,5,6,8,9,16,17,26,27,28,42
• Page 254: 1,2,3,4,5,7,9
Book Calculus, by Stanley I Grossman (Fifth edition)

All quizes will be open book and notes. This means: The calculus book, and any notes that you have written.

Office Skiles 263. TA: Honor Hutton gt2366b@prism.gatech.edu

Class (TM) is at MWF Skiles 270: Time: 8:05-8:55 am

Recitation: (CC): T Th Skiles 270

The grade will be based on
• Appoximately 5 or 6 half hour quizes.
• Group Projects.
• Homework
• Final Exam
The quiz grades will be added together, with one quiz dropped. They count for 55% of the grades. Group Projects 10%, Homework 10%, and Final exam 25%.

All tests and quizes will be open book and notes. Calculators allowed.

Regrading policy: Quizes will be handed back in recitation or lucture. We will go over the quizes the day that they are handed back. If there is any quiestions about the grading, you must write the quiestions on the quiz and return the quiz before you leave the classroom. No exceptions. OK?

Outline of course
Course Outline for Math 1508
Topic Sections Appoximate Days (lecures)
Review of some algebra 0.1-0.5 3
Limites and Derivatives 1.1-1.8 5
More about derivatives 2.1-2.7 6
Applications of the Derivative 3.1-3.7 7
Conic sections and polar coordinates 8.1-8.3, 8.5-8.6 3
Complex Numbers A5 3
Total 27

General comments: I realize that some of you all have have calculus before. This is a good, right and proper thing, and my sister Mary mmorley@ets.org would approve. There will be considerable overlap between AP calculus and this course. But the pupose of this course is not the same as AP calculus:

The purpose of this course is to develop and use calculus
in order to get insight into Mathematics, Science and Engineering

The mechanics of calculation, by hand, calculator, or computer are still important, but not in and of themselves. They are tools.

There is no such thing as a stupid question. Yell them out!

If something confuses you, raise you hand and shout out to the world that the person sitting next to you doesn't understand! :-)

If you have not had Calculus before, that is also OK. Rest assured that this course does not presume any knowledge from AB or BC calculus.

Need to do an integral? Try this. Brought to you by Wolfram Research
Help stamp out meaningless symbolic manipulation
If you are taking MATH 1507, 1508, 1509, 1518, 1709, 1711, 1712, 1713, and 2507, please note that the Math Lab is open on M - Th from 11 to 4 in Skiles 257. It is staffed by teaching assistants. It is free and is open to Georgia Tech students taking the above classes.
Quiz Wed. November 18
Covers Max-Min and Newton's Method. A calculator is suggested, because of the question on Newton's Method.
The Calc I Swiki . An editable web page that is yours. Under construction. Please add whatever you like -- When you get there, just click on "Edit this page". This might be a place to hook up with a partner for the computer projects.

New! Project: Hyperbolae and Loran C. Again a Maple file. Due Wed of dead week. Do in groups of 2 or three. Add lots of english text to expleain what you are doing.

Some problems:

• Page 223: #1,2,3,5,7,9,25,27,30,31,33,35,38,39,40
• Page 238: #5,6,7,8,12,13
• Page 262: # 10,21,22,23.25.26

Some answers to the quiz (November 5) 1. A spherical ball 8" in diameter is coated woth a layer of ice of uniform thinkness. If the ice melts at a rate of 10 cubic inches per minute, how fast is the thinkness of the the ice decreasing with it is 2" think?
```Let x be the thinkness of the ice. The radius of the iron ball is 4, so
that the total volume is:

V = (4/3) pi (x + 4)^3

Differentiating gives:

dV/dt = 4 pi (x + 4)^2  dx/dt

Plugging in numbers:

-10 = 4 pi (2 + 4) ^2  dx/dt

or

-10/(4 pi 36) = dx/dt

```
3. A balloon is 200 ft off the ground and raising vertically at a constant rate of 15 ft/sec.. An automobile passes beneath it traveling at 66 ft/sec. How fast is the distance between them changing 1 second later?
```
Let r be the distance between them, h the height of the balloon, and x
the distance the car travels. Then

r^2 = h^2 + x^2

Differentiating,

2 r dr/dt = 2 h dh/dt + 2 x dx/dt

One second later x = 66, h = 200 + 14 = 215, so r = Sqrt(215^2 + 66^2).
Plugging in numbers gives:

2 Sqrt(215^2 + 66^2) dr/dt = 2 215 15 + 2 66 66 or

dr/dt = (6450 + 8712)/ (2 Sqrt(215^2 + 66^2))

which is about 33.7

```
Next quiz November 5 Related Rates, some curve sketching.

Problems from Related Rates (3.1) and Curve Sketching (3.2,3):

• Page 185: # 7,8,10,11,12,19,20,24
• Page 196 3,4,5,7,9,11,16,17,21,23,24
• Page 203 1,2,3,5,7,9,24,25,27

First Computer Projects:

These are Maple files. If you have enough memory you can set (in preferences) that Maple is the helper app for files with suffix ".mws". Then when you click on the following, Maple will start up with the assignment. Save the file on your own computer, and start....

http://www.math.gatech.edu/~carlen/1507/notes/CalcIMap.mws . (This is an introduction to Maple), and http://www.math.gatech.edu/~cain/calculus/assn3.mws (Although Georgie doen't say this, this project is an adaptation of an original project by A. D. Andrew and T. D. Morley.)

Due November 11. Do in groups of 2 or three. Hand in only one print out per group.

Note due date change -- Nov 11

The Calc I Swiki . An editable web page that is yours. Under construction. Please add whatever you like -- When you get there, just click on "Edit this page". This might be a place to hook up with a partner for the computer projects.

Some solutions to quiz #3:

1. Suppose the f'(x) = f(x), and that f(g(x)) = x. Find g'(x)

```Solution:
Take  f(g(x)) = x, and differentiate useing the chain rule, giving:

f'(g(x)) g'(x) = 1

But f'(junk)  = f(junk), so:

f(g(x)) g'(x) = 1

Using f(g(x)) = x, we get:

x g'(x) = 1

Giving g'(x) = 1/x.
```

3. The radius of a certain sphere is increasing at a rate of 4 inches per minute. If currently the radius is 5 inches, how fast is the volume increasing?

```V = (4/3) pi r^3, so differentiating with respect to t, we get:

dV/dt = 4 pi r^2 dr/dt.

Plugging in r = 5, and dr/dt = 4, we get the answer

dV/dt =  4 pi 5^2 4

= 400 pi

```

4. Find the equation of the norml line to the curve x^2 y^2 + xy = 5 at the point x =1, y =2.

```Differentiating the euqation gives:

2 x y^2 + 2 x^2 y dy/dx + y + x dy/dx = 0.

Solve for dy/dt, giving:

- 2 x y^2 - y
dy/dt =  --------------
2x^2y + x

Plug in x = 1, y = 2 and get:

- 2 1 2^2 - 2
dy/dt =  --------------
2 1^2 2 + 1

=   -10/5  = -2

So slope of the normal is  -1/(-2) = 1/2.

Equation is therefore (y-2) = (1/2) (x-1)

```

Some problems on the chain rule, power rule, trig functions:

• Page 153 1,3,4,5,6,19,25,26,37,38,39,45,46 and getting a bit ahead --
• Page 160 1,2,3,4,5,,21,22,25,26,27
• Page 267 1.2.3.4.10,11,12,16,17,19,21,22,37,38

Solutions to Quiz #2. For compatibility and for ease of loeading, I am attempting to do these in plain text. When I get mathematica working again, I will begin to post solutions to quizes in html + gifs.

Problem 1: (10 points) Calculate the derivative of (3x)^(1/2) by the definition.

```Solution: We compute the limit:

(3(x + h))^(1/2) - (3x)^(1/2)
lim     ---------------------------
h->0              h

Multiply the numerator and denominator by (3(x + h))^(1/2) + (3x)^(1/2):

(3(x + h))^(1/2) - (3x)^(1/2)  (3(x + h))^(1/2) + (3x)^(1/2)
lim     ---------------------------     ---------------------------  =
h->0            h                   (3(x + h))^(1/2) + (3x)^(1/2)

(3(x + h)) - (3x)
lim     ------------------------------  =
h->0  h  (3x + h)^(1/2) + (3x)^(1/2)

3h
lim     ------------------------------  =
h->0  h  (3x + h)^(1/2) + (3x)^(1/2)

3
lim     ------------------------------  =
h->0   (3x + h)^(1/2) + (3x)^(1/2)

3
------------------------  =
(3x)^(1/2) + (3x)^(1/2)

3
-------------  =
2(3x)^(1/2)

```

Problem 2: 5 points each. I'll just give the answers.

```Solutions:
a) 4 x^3 sin(x) + x^4 cos(x)

b) (4 x^3 + 6 x^2 + 4) (3x^2+x^6) - (x^4 + 2 x^3 + 4 x)(6x + 6 x^5)
------------------------------------------------------------------
(3x^2+x^6)^2

c)  (4 x^3 + 6 x^2 + 4)(sin(x) + 42) - x^4 + 2 x^3 + 4 x)(cos(x))
-------------------------------------------------------------
(sin(x) + 42)^2

```

Problem 3: Find the tangent line to the curve sin(x)/6x at the point x = pi/3.

```Solution: Let f(x) = sin(x)/6x, therefore the tangent line goes through
the point x = pi/3, y = f(pi/3) = Sqrt(3)/2.

f'(x) = cos(x) 6 x - 6 sin(x)
---------------------
(6x)^2

So f'(pi/3) =  (1/4 pi) - (3/4) Sqrt(3)/pi^2

So we get

y - Sqrt(3)/2
--------------    = (1/4 pi) - (3/4) Sqrt(3)/pi^2
x  - pi/3

This can be simplified, if you like.

```

Second Quiz: Tomorrow!! Thursday October 15, 1998

WIll cover up through 1.5,1.6,2.5,2.1,2.2

Things to know for the quiz:

• Definition of the derivative and using it.
• Diferentiation rules, up through qutient rule.
• Using the derivative, e.g., rates of change, tangent lines and their slopes, finding where the tangent is horizontal, etc.,etc..

As I said yesterday, I will be arround this afternoon from about 3 to about 4 pm. In my office (Skiles 263) or if I'm not there, check the door of my office. This will say where I am.

Suggested problems for the material covered Wed Oct 7 and Fri Oct 9, Mon 12.

• Page 94: I,II,..VII, 1,2,3,4,516,17,25
• Page 111: 1,2,3,5,6,7,8
• The derivative of sin(x) is cos(x). Part of section 2.5
• Page 137: 1,2,3,5,6,7,13,15,17,21,22,25,27
• Page 144: 1,2,3,4,5,6,8,9,13,15,17,27,29,35,36

First Quiz: Tuesday October 6, 1998

Will cover up through 1.2

Suggested problems for the material covered Chapter 0. and 1.2

• Page 8, Section 0.1: # 20,22,24,26,28,40,41
• Page 14, Section 0.2: # 2,4,8,14,16
• Page 21, Section 0.3: # 2,4,6,20,22, 40,42
• Page 44, Section 0.5, # 4,8,10,12
• page 66, Section 1.2:# 10,12,20,21,23,24
• page 168, Section 2.5: 26,28,32

Sone odd numbered problems to work yourself:

• Page 8: 19,21,23,27,41
• Page 14: 13.15.17.7.9
• page 21: 9,11,13,2,7,27
• page 44: 5,7,9,11
• page 66: 19,31,35,38,55
• page page 168: 25,27,31

Material coverered from Chaprter 1. On September 28, ew did example 4 on page 56, and example 7 (page 58 and page 161).

Book Calculus, by Stanley I Grossman (Fifth edition)

All tests a quizes will be open book and notes

Office Skiles 263.

TA: Honor Hutton gt2366b@prism.gatech.edu

Class (TM) is at MWF Skiles 270: Time: 8:05-8:55 am

Recitation: (CC): T Th Skiles 270

The grade will be based on
• Appoximately 5 or 6 half hour quizes.
• Group Projects.
• Homework
• Final Exam
The quiz grades will be added together, with one quiz dropped. They count for 55% of the grades. Group Projects 10%, Homework 10%, and Final exam 25%.

All tests and quizes will be open book and notes. Calculators allowed.

Regrading policy: Quizes will be handed back in recitation or lucture. We will go over the quizes the day that they are handed back. If there is any quiestions about the grading, you must write the quiestions on the quiz and return the quiz before you leave the classroom. No exceptions. OK?

Outline of course
Course Outline for Math 1508
Topic Sections Appoximate Days (lecures)
Review of some algebra 0.1-0.5 3
Limites and Derivatives 1.1-1.8 5
More about derivatives 2.1-2.7 6
Applications of the Derivative 3.1-3.7 7
Conic sections and polar coordinates 8.1-8.3, 8.5-8.6 3
Complex Numbers A5 3
Total 27

General comments: I realize that some of you all have have calculus before. This is a good, right and proper thing, and my sister Mary mmorley@ets.org would approve. There will be considerable overlap between AP calculus and this course. But the pupose of this course is not the same as AP calculus:

The purpose of this course is to develop and use calculus
in order to get insight into Mathematics, Science and Engineering

The mechanics of calculation, by hand, calculator, or computer are still important, but not in and of themselves. They are tools.

There is no such thing as a stupid question. Yell them out!

If something confuses you, raise you hand and shout out to the world that the person sitting next to you doesn't understand! :-)

If you have not had Calculus before, that is also OK. Rest assured that this course does not presume any knowledge from AB or BC calculus.

Need to do an integral? Try this. Brought to you by Wolfram Research
Help stamp out meaningless symbolic manipulation
If you are taking MATH 1507, 1508, 1509, 1518, 1709, 1711, 1712, 1713, and 2507, please note that the Math Lab is open on M - Th from 11 to 4 in Skiles 257. It is staffed by teaching assistants. It is free and is open to Georgia Tech students taking the above classes.

### To get a hold of me:

Phone: (404) 894-9233, (404) 894-2700, (404) 894-4409 (FAX)

email: morley@math.gatech.edu

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