* MATH 21C (SECTIONS A01-A07), 1100 Social Sciences, 9-9:50 MWF *

* Instructor: Dr. D. A. Kouba *

Text: CALCULUS and ANALYTIC GEOMETRY (5th edition) by Stein and Barcellos

Office: 484 Kerr

Phone: (530) 752-1083

Regular Office Hours: 10:00-11:00 T,Th or by appointment

- ...... MATH21C COURSE GRADES .

KOUBA OFFICE HOURS | FRIDAY, April 22, 2005 | 11-11:30 a.m. and 4-5 p.m. | 484 Kerr | |||

TUESDAY, April 26, 2005 | 10-11 a.m. | 484 Kerr |

Here are Math 21C TA OFFICE HOURS for Spring Quarter 2005. These are subject to periodic and unannounced changes.

EXAM DATES :

- EXAM 1-- Monday, April 18, 2005

- EXAM 2-- Wednesday, May 4, 2005

- EXAM 3-- Monday, May 23, 2005

- FINAL EXAM -- Thursday, June 16, 2005, 8-10 a.m. (7:30-10:15 a.m. ?) in 1100 Social Sciences

The course will likely cover the following sections in our textbook : 14.1-14.6, 14.9, 15.1-15.7, 10.1-10.7, 11.1, 11.2, 11.4-11.7

Here is an OPTIONAL EXTRA CREDIT SURVEY .

SOLUTIONS TO ALL HOMEWORK ASSIGNMENTS AND HOUR EXAMS CAN BE VIEWED ON THE INTERNET at Math 21C Homework and Exam Solutions . In addition, you may look at a copy of solutions during my office hours (or appointment) in 484 Kerr.

Here are copies of the Course Syllabus and Supplementary Class Handouts .

Here is a tentative Schedule of lectures.

Here are copies of Discussion Sheets with some additional optional, challenging discussion sheets.

Here are copies of Basic Derivative Formulas From Math 21A .

Here are copies of Basic Integration Methods from Math 21B

Here are copies of Basic Trig Integrals and Identities from Math 21B

Here are Practice Exam 1 and Solutions .

Here are Practice Exam 2 and Solutions .

Here are Practice Exam 3 and Solutions .

Here is a Practice Final Exam WITHOUT SOLUTIONS.

Here are some TIPS for doing well on my exams.

The following homework assignments are subject to minor changes.- HW #1 ..... p. 784: 1, 4, 6, 7, 12, 16, 17, 19, 21, 22, 26, (You need NOT sketch the surface on these last 5 problems.) 27, 29, 30, 34b (challenging), 35a

- HW #2 ..... p. 794: (Use traces x=0, y=0, and z=0 for problems 2, 3, and 6. Also include traces y=2 and y=-2 for problems 2 and 6.) 2, 3, 6, 10, 16 (Omit traces.), 18, 20, 22 (Use traces x=0, y=0, z=1, and z=-1.), 23 (Use traces x=0, y=0, z=0, z=-1, and z=1.), 25, 28, 32, 47abc

- HW #3 ..... p. 802: 2, 6, 10, 12, 14, 16, 22 ..... and ... Worksheet 1

- HW #4 ..... p. 807: 1-8, 9a, 12a, 14a, 21 (optional), 24

- HW #5 ..... p. 814: 2, 4, 6, 7, 10, 12, 13, 15, 17, 18, 20, 22, 24, 26, 27, 30, 31, 32, 35, 37, (See 36.), 40ab

- HW #6 ..... p. 828: 1, 2, 4a, 5a, 7, 10, 12, 14a, 16, 17a, 21 (challenging), 22, 23, 26

- HW #7 ..... p. 855: 2, 4, 9, 10, 12, 14, 15, 20, 22, (You need not verify that your critical point is a maximum or minimum on problems 26, 28, and 31.) 26, 28 (closed rectangular box), 31, 32, (Find absolute maximum and minimum values for problems 36 and 37.) 36, 37, 39ac (You want to use x = cos t and y = sin t to represent the circle.), 48

TYPES OF QUESTIONS FOR EXAM 1 2005 (THIS IS SUBJECT TO UNANNOUNCED CHANGES.).

- 1 -- graphing surfaces, intersections, and projections
- 1 -- sphere
- 1 -- finding equation for surface of revolution
- 2 -- limits
- 1 -- determine domain (and sketch domain) and range
- 1 -- partial derivatives
- 1 -- find and classify critical points
- 1 -- chain rule
- 1 -- OPTIONAL EXTRA CREDIT

HERE ARE SOME RULES FOR EXAM 1.

- 1.) No notes, books, or classmates may be used as resources for this exam. YOU MAY USE A CALCULATOR ON THIS EXAM.
- 2.) You will be graded on proper use of limit notation.
- 3.) You will be graded on proper use of derivative and integral notation.
- 4.) Put units on answers where units are appropriate.
- 5.) Read directions to each problem carefully. Show all work for full credit. In most cases, a correct answer with no supporting work will NOT receive full credit. What you write down and how you write it are the most important means of your getting a good score on this exam. Neatness and organization are also important.

SOLUTIONS TO EXAM 1 ARE POSTED ON THIS WEBPAGE.

THE GRADING SCALE FOR 2005 EXAM 1 IS :

A+ ...... 100-112

A ...... 90-99

A-/B+ ...... 88-89

B ...... 74-87

C ...... 55-73

D ...... 45-54

F ...... 0-44

- HW #8 ..... p. 887: 3, 4, 7, 9, 11, 12, 13 (challenging)

- HW #9 ..... p. 895: 1, 2, 5, 8, 10, 12, 14, 17, 20, 24abc, 26abc, 28, 29, (DO NOT evaluate integrals for problems 31, 32, 34.), 31, 32, 34, (Evaluate the remining problems.) 35, 36, 38

- HW #10 ..... p. 901: (SET UP BUT DO NOT evaluate integrals for this entire homework set.) 4, 5, 7, 8, 9, 12, 13, 14, 17, 18

- HW #11 ..... p. 907: 2, 3, 5, 6, 7, 8, 13, (SET UP BUT DO NOT evaluate integrals in polar coordinates for the remainder of this homework set, except for problems 22, 25, and 28. Evaluate the integrals for problems 22, 25, and 28.) 16, 18, 20 (Assume that the density at point P=(x,y) is xy.), 21, 22, 25, 29b, 34, 35, 39 (challenging), 44

- HW #12 ..... p. 916: 10, 11, 14, 15, 18, 19, 20, (SET UP BUT DO NOT evaluate triple integrals in rectangular coordinates for the remainder of this homework set.) 23, 24, 26, 28, 32 (Add the surface z=0 as one of the boundaries.), 33

- HW #13 ..... p. 921: 1, 2, 3, 4, 5, 6, 12, 14, 16, 18, 20, 21, 24, 25, (SET UP BUT DO NOT evaluate triple integrals in cylindrical coordinates for the remainder of this homework set.) 27, 29, 30 31, 35

- HW #14 ..... p. 929 : 3, 4, 5, 11, 12, 13, 14, 16, 18, 19, 24, 26 (challenging), 28 (SET UP only.), 31abc, 32 (SET UP only.), 36 (SET UP only.), 43 (optional)

TYPES OF QUESTIONS FOR EXAM 2 2005 (THIS IS SUBJECT TO UNANNOUNCED CHANGES.).

- 1 -- describe flat region in plane using vertical cross sections, horizontal cross sections, and polar coordinates
- 1 -- describe solid region in space using rectangular, cylindrical, or spherical coordinates
- 2 -- evaluate a double integral; know how to switch the order of integration if one order is difficult or impossible and know how to convert between rectangular and polar coordinates
- 1 -- set up and evaluate a triple integral
- 3 -- set up but do not evaluate applications of double or triple integrals in various coordinate systems
- 1 -- optional extra credit

HERE ARE SOME RULES FOR EXAM 2.

- 1.) No notes, books, or classmates may be used as resources for this exam. YOU MAY USE A CALCULATOR ON THIS EXAM.
- 2.) You will be graded on proper use of derivative and integral notation.
- 3.) Put units on answers where units are appropriate.
- 4.) Read directions to each problem carefully. Show all work for full credit. In most cases, a correct answer with no supporting work will NOT receive full credit. What you write down and how you write it are the most important means of your getting a good score on this exam. Neatness and organization are also important.

SOLUTIONS TO EXAM 2 ARE POSTED ON THIS WEBPAGE.

THE GRADING SCALE FOR 2005 EXAM 2 IS :

A+ ...... 100-112

A ...... 90-99

A-/B+ ...... 87-89

B ...... 74-86

C ...... 55-73

D ...... 45-54

F ...... 0-44

- HW #16 ..... p. 590: 1, 2, 3, 6, 7, 10, 11, 12, 13, 14, 15, 16, 18, 19, 20, 22, (For the next two problems, write the answers as a mixed fractions.) 23, 25, 28, 29, 31 (challenging), 33ab, 34b (optional)

- HW #17 ..... p. 596: 1, 3, 4, 5, 6, 7, 10, 12, 13ab (On part b Use equation (*) from handout in class and let n go to infinity.), 14 (Use cases on p. Let 0 < p < 1, p=1, p=0, and p<0.), 16, 18, 20, 21, 26 (HINT: Consider the graph of f(x)=1/sqrt(x) for x>or=1 and use equation (*) from handout in class.), (Use equation (*) from handout in class.) 27, 28b, 30 (optional)

- HW #18 ..... p. 601: 1-8, 10, 11, 13, 15-18, 20, 21, 23-34, 36 (challenging), 39a, 41 (optional), 43, 44

- HW #19 ..... p. 605: 1-8, 13, 14, (Use equation (*) on problems 16, 20, 22, and 23.) 16, 20, 22, 23, 26.

- HW #20 ..... p. 615: 1-10, 28, 30, 31, 39

- HW #21 ..... p. 615: 11-25

TYPES OF QUESTIONS FOR EXAM 3 2005 (THIS IS SUBJECT TO UNANNOUNCED CHANGES.).

- 8 -- determine if given series converges or diverges
- 1 -- estimating partial sum (equation (*)) or estimating error (equation (*)(*))
- 1 -- question about alternating series
- 1 -- other
- 1 -- OPTIONAL EXTRA CREDIT

HERE ARE SOME RULES FOR EXAM 3.

- 1.) No notes, books, or classmates may be used as resources for this exam. YOU MAY USE A CALCULATOR ON THIS EXAM.
- 2.) You will be graded on proper use of derivative and integral notation.
- 3.) Put units on answers where units are appropriate.
- 4.) Read directions to each problem carefully. Show all work for full credit. In most cases, a correct answer with no supporting work will NOT receive full credit. What you write down and how you write it are the most important means of your getting a good score on this exam. Neatness and organization are also important.

SOLUTIONS TO EXAM 3 ARE POSTED ON THIS WEBPAGE.

THE GRADING SCALE FOR 2005 EXAM 3 IS :

A+ ...... 100-112

A ...... 88-99

A-/B+ ...... 84-87

B ...... 70-83

C ...... 51-69

D ...... 41-50

F ...... 0-40

- HW #22 ..... p. 648: 1, 2, 3, 4, 7, 10, 11, 12, 14, 15, 16, 18, 19, 22, 24, 26, 33, 34

- HW #23 ..... p. 628: (Find 1st four nonzero terms and general formula for the Maclaurin series on the next 4 problems.) 13, 15, 17, 18, 2 (Start by finding the 1st four nonzero terms and general formula for the Taylor series centered at x=1 for f(x)= 1/(1+x).), 3 (Use problem 13.), 6 (Start by finding the 1st four nonzero terms and general formula for the Taylor series centered at x=2 for f(x)=e^x.), 10 (Use class notes.), 22, 27ab (Start by finding the 1st four nonzero terms and general formula for the Taylor series centered at x=0 for f(x)=sqrt(1+x). On part b use interval [-2, 2].), 34 (Let n=4)

- HW # 24 ..... p. 635: (Use the Lagrange form of the Taylor remainder on problems 1 and 2.) 1, 2, 7 (Use the absolute error |Rn| for an alternating series and use an error of at most 0.0005.), {{{ Problem A: Use the Maclaurin series for f(x)=cos(x) (See problem 15 on page 628.) to estimate the value of cos(1) with absolute error at most 0.0001., Problem B: If we use the Maclaurin series for f(x)=ln(1+x) (See problem 13 on page 628.), how many terms should be used to estimate the value of a.) ln(2) with absolute error at most 0.001 ? b.) ln(1.5) with absolute error at most 0.001 ? }}}, 8 (Use the Lagrange form of the Taylor remainder and make it at most 0.0005.), 14 (Use the Maclaurin series for cos(x), the absolute error |Rn| for an alternating series, and use an error of at most 0.0005.)

- HW # 25 ..... p. 655: 3 (On d. use an absolute error of at most 0.0005.), 6, 7, 8, 9, 11, 14, 15 (On b. use an absolute error of at most 0.00005.), 25 ..... and ..... p. 674: 18 (Use the Lagrange form of the remainder.), 19 (Use the absolute error |Rn| for an alternating series.), 33ad (Use the absolute error |Rn| for an alternating series.), 49 (You need not use L'Hopital's Rule.), 51 (First write the power series as an ordinary function, then differentiate.)

- HW # 26 ..... p. 664: 1ad, 2ad, 3ab, 5, 6, 7abcd, 11, 12, 13, 14, 19degh, 20d, 23, 36, 21, 10.... Here are Class Notes for this section (Section 11.6).

- HW # 27 ..... p. 670: 1, 6, 9, 17, 18, 23, 25, 26.... Here are Class Notes for this section (Section 11.7).
The FINAL EXAM is Thursday, June 16, 2005,

8 a.m.-10 a.m. (7:30-10:15 a.m. ?)

in 1100 Social Sciences

BRING A PICTURE ID TO THE EXAM

AND BE PREPARED TO SHOW IT TO KOUBA OR THE TEACHING ASSISTANTS !!The final exam will cover handouts, lecture notes, and examples from class, homework assignments 1 through 25 (Homework assignments 26 and 27 are optional), and material from sections 14.1-14.6, 14.9, 15.1-15.7, 10.1-10.7, 11.1, 11.2, 11.4, 11.5 (11.6 and 11.7 are a source of problems for the extra credit problems on the final exam), and discusssion sheets 1-11.

TYPES OF QUESTIONS FOR THE FINAL EXAM 2005 (THIS LIST IS TENTATIVE AND IS SUBJECT TO UNANNOUNCED CHANGES.).

- 2 -- limits for functions f(x,y)
- 1 -- interval of convergence
- 1 -- three dimensional graphing
- 1 -- triple integral
- 1 -- partial derivatives
- 1 -- using (*) or (**)
- 2 -- find Maclaurin series using shortcuts
- 1 -- conditionally convergent, absolutely convergent, divergent
- 1 -- find Taylor series using f^(n)(a)/n!
- 1 -- find Taylor polynomial of degree n
- 1 -- find and classify critical points for z=f(x,y)
- 1 -- use Lagrange form of Taylor error, Rn(x;a)
- 2 -- others
- 3 -- OPTIONAL EXTRA CREDIT (ON ANY TOPIC)

HERE ARE SOME RULES FOR THE FINAL EXAM.

- 2.) You will be graded on proper use of limit notation.
- 3.) You will be graded on proper use of derivative and integral notation.
- 4.) Put units on answers where units are appropriate.
- 5.) Read directions to each problem carefully. Show all work for full credit. In most cases, a correct answer with no supporting work will NOT receive full credit. What you write down and how you write it are the most important means of your getting a good score on this exam. Neatness and organization are also important.

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