Math 21C (Thomas) Website

MATH 21C (SECTIONS C01-C04), 1322 Storer, 4:10-5 MWF

Instructor: Dr. D. A. Kouba

Last Updated: June 6, 2006

Text: Thomas' Calculus: Early Transcendentals (11th edition) by Weir, Hass, Giordano

Office: 3135 MSB

Phone: (530) 752-1083

Regular Office Hours: 9:15-10 am MWF or by appointment

...... MATH21C COURSE GRADES will be posted by ..... 2006 (listed by the last five digits of your student ID number)

TA OFFICE HOURS	James Matthews	2204 MSB	5-7 p.m.	TUESDAY
	Carlos Barrera-Rodriquez	2202 MSB	12-1 p.m.	MONDAY
	Carlos Barrera-Rodriquez	2202 MSB	1-2 p.m.	WEDNESDAY

EXAM DATES :

EXAM 1-- MONDAY, April 17, 2006
EXAM 2-- WEDNESDAY, May 10, 2006
EXAM 3-- FRIDAY, June 2, 2006
FINAL EXAM -- MONDAY, June 12, 2006, 8-10 a.m. (7:50-10:10 a.m.) in 198 Young

The course will likely cover the following sections in our textbook : 11.1-11.10, 12.1-12.5, and 14.1-14.8.

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 3135 MSB.

Here is a copy of the Course Syllabus .

Here is a copy of the Schedule of Lectures .

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

Here are copies of Supplementary Class Handouts .

Here are copies of Discussion Sheets .

Click here for additional optional PRACTICE PROBLEMS with SOLUTIONS found at

THE CALCULUS PAGE .

Here are some TIPS for doing well on my exams.

The following homework assignments are subject to minor changes.

HW #1 ... (Section 11.1) ... p. 741: 2, 3, 4, 8, 11, 12, 13, 16, 18, 22 (Hint: Use greatest integer function.), 24 (Use Sandwich Theorem.), 28, 29, 31, 35 (Use Sandwich Theorem.), 36, 38, 39, 42 (Use Sandwich Theorem.), 44, 45, 48, 50, 56, 59 (Use Sandwich Theorem.), 70, 74, 75, 81, 85, 94 (Assume the case where x>1.) ... and ... Worksheet 1
HW #2 ... (Sections 11.2) ... p. 753: 7, 8, 12, 14, 16, 19, 24, 25, 26, 28, 30, 34, 36, 37, 39, 52, 53, 66, 70, 73, 75
HW #3 ... (Section 11.3) ... p. 759: 3, 5, 6, 7, 9, 12, 14, 16, 20, 22, 23, 25, 28, 33ab, 42 ... and ... Problems Using Star and Double Star from the Integral Test Handout. Here are the Solutions .
HW #4 ... (Sections 11.4) ... p. 765: 2, 3, 6, 8, 9, 11, 14, 15, 19, 20, 22, 23, 25, 28, 29, 34, 36, 38, 40
HW #5 ... (Section 11.5) ... (Use Ratio or Root Test) p. 770: 1, 4, 5, 12, 14, 18, 19, 21, 22, 28, 29, 37, 40, 43 ... and ... (Use Any Test) p. 770: 6, 7, 8, 10, 11, 13, 15, 23
HW #6 ... (Section 11.6) ... p. 776: 1, 3, 4 (optional), 5, 6, 9, 10, 12, 13, 15, 16, 18, 21, 23, 26, 27, 29, 34, 38, 39, 46, 50, 54, 58

EXAM 1 is Monday, April 17, 2006. It will cover handouts, lecture notes, and examples from class, homework assignments 1 through 6, discussion sheets 1, 2, and 3 (except problem 3) and material from sections 11.1-11.6 in the book which was presented in lecture notes through Friday, April 14, 2006. MOST of the exam questions will be like examples from lecture notes, homework problems, or discussion sheets.

TYPES OF QUESTIONS FOR EXAM 1 FOR WINTER 2006 (THIS IS SUBJECT TO UNANNOUNCED CHANGES.)

8 -- Determine convergence or divergence of series using various series tests
1 -- Alternating series
1 -- (*) or (*)(*) problem ... Here is the problem .
1 -- Other
1 -- OPTIONAL EXTRA CREDIT

HERE ARE SOME RULES FOR EXAM 1.

0.) IT IS A VIOLATION OF THE UNIVERSITY HONOR CODE TO, IN ANY WAY, ASSIST ANOTHER PERSON IN THE COMPLETION OF THIS EXAM. PLEASE KEEP YOUR OWN WORK COVERED UP AS MUCH AS POSSIBLE DURING THE EXAM SO THAT OTHERS WILL NOT BE TEMPTED OR DISTRACTED. THANK YOU FOR YOUR COOPERATION.
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 SPRING 2006 EXAM 1 IS :

A+ ...... 100-110

A ...... 88-99

A-/B+ ...... 83-87

B ...... 70-82

C ...... 53-69

D ...... 42-52

F ...... 0-41

HW #7 ... (Section 11.7) ... p. 788: 1a, 4a, 6a, 7a, 10a, 12a, 17a, 22a, 23a, 25a, 27a, 34, 36, 46
HW #8 ... (Section 11.8) ... p. 794: 1, 4, 6, 8, 9 (Use Maclaurin series for e^x.), 10 (Use Maclaurin series for e^x.), 11 (Use Maclaurin series for 1/(1-x).), 13 (Use Maclaurin series for sin x.), 23, 25, 26 (Use Maclaurin series for 1/(1-x).), 27, 33, 35
HW #9 ... (Section 11.9) ... p. 803: 1, 6, 8, 12, 13 (Do 2 ways : i. trig identity 1st, ii. series multiplication), 15, 16, 17 (Do 2 ways: i. differentiation, ii. multiplication of series), 18, 19, 22 (Begin by finding the first 4 nonzero terms and the general formula for the Maclaurin Series for f(x)= sqrt(1+x).), 23, 31, 32, 36, 42
HW #10 ... (Section 11.10) ... p. 815:2, 7, 33, 35, 38, 43, 46, (For 47, 50, and 52 also use L'Hopital's Rule to evaluate limits.) 47, 50, 52, 63a, 66
HW #11 ... (Section 12.1) ... p. 836: 1, 3, 6, 8, 12-14, 16ac, 17b, 18, 20-22, 24-26, 28, 30-33, 36, 37, 41, 46, 49, 52-54
HW #12 ... (Section 12.2) ... p. 844: 1, 4, 6, 7, 9-13, 16, 18, 21, 23, 25, 28, 29, 31, 33, 35, 38, 40, 41, 43, 46
HW #13 ... (Section 12.3) ... p. 854: 1, 4, 7, 10, 12, 13, 16, 18, 19, 21 (See properties of Dot Product on page 850.), 26-28, 29, 31, 45, (Do not use results from problems 33 and 34 to do problem 51. Simply use basic facts about vectors and lines.) 51
HW #14 ... (Section 12.4) ... p. 862: 2, 3, 7, 9, 10, 14, 16, 19, 20, 23, (See definition of torque at the bottom of page 860.) 25, 27-29, 31, 33, 36, 40
HW #15 ... (Section 12.5) ... p. 871: 1, 4, 6-8, 10, 21, 22, 24, 25, 28, 31, 34, 43, 45, 47, 55, 59, 67

EXAM 2 is Wednesday, May 10, 2006. It will cover handouts, lecture notes, and examples from class, homework assignments 7 through 15, discussion sheets 3 (Problem 3 only), 4, 5, and 6, and material from sections 11.7-11.10 and 12.1-12.5 in the book which was presented in lecture notes through Monday, May 8, 2006. MOST of the exam questions will be like examples from lecture notes, homework problems, or discussion sheets.

TYPES OF QUESTIONS FOR EXAM 2 FOR SPRING 2006 (THIS IS SUBJECT TO UNANNOUNCED CHANGES.)

1 -- Find interval of convergence for power series
2 -- Find 1st 3 nonzero terms of Taylor Series centered at x=a
1 -- Lagrange form of the Taylor remainder. Here is the problem.
1 -- Use Taylor Polynomial to compute an estimate
5 -- Problems involving, lines, planes, angles, normal vectors, parallel vectors, points of intersection, etc. Here is one of the problems.
2 -- Others
1 -- OPTIONAL EXTRA CREDIT

HERE ARE SOME RULES FOR EXAM 2.

0.) IT IS A VIOLATION OF THE UNIVERSITY HONOR CODE TO, IN ANY WAY, ASSIST ANOTHER PERSON IN THE COMPLETION OF THIS EXAM. PLEASE KEEP YOUR OWN WORK COVERED UP AS MUCH AS POSSIBLE DURING THE EXAM SO THAT OTHERS WILL NOT BE TEMPTED OR DISTRACTED. THANK YOU FOR YOUR COOPERATION.
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 ARE POSTED ON THIS WEBPAGE.

THE GRADING SCALE FOR SPRING 2006 EXAM 2 IS :

A+ ...... 100 - 110

A ...... 89 - 99

A-/B+ ...... 85 - 88

B ...... 71 - 84

C ...... 52 - 70

D ...... 40 - 51

F ...... 0 - 39

HW #16 ... (Sections 12.6 and 14.1) ... p. 881: (For first 3 problems sketch graph in 2 dimensions, then 3 dimensions.) 13, 14, 16, (Foe next 5 problems use intercepts, traces, and the indicated values of z's for level curves to create a topographical map for the surface.) 22 (Use z=-4, -2, 0, 2, 4), 27 (Use z=8, 7, 4, -1, -8), 31 (Use z=-2, -1, 0, 1, 2), 35 (Use z= -sqrt{8}, -sqrt{3}, 0, sqrt{3}, sqrt{8}) ... and ... p. 957: (Determine and sketch domain) 2ab, 3ab, 7ab, 8ab, 9ab
HW #17 ... (Section 14.2) ... p. 966: 1, 4, 9, 12, 14, 16, 20, 35-38, 41 ... and ... p. 1044: 12, 16
HW #18 ... (Section 14.3) ... p. 978: 2, 7, 10, 13, 16, 21,43, 45, 46, 54, 57, 65, 66, 69, 72
HW #19 ... (Section 14.4) ... p. 987: 1 (Change the function to w=x^2+2y.), 6, 8, 9, 14, 15, 20, 22, 24, 26, 28, 40, 41, 42a ... and .... these second-order chain rule problems
HW #20 ... (Section 14.5) ... p. 997: 2, 3, 5, 8, 10, 13, 14, 17, 20, 27, 31, 32a
HW #21 ... (Section 14.6) ... p. 1008: 1, 4, 9, 12, 14, 15, 20, 21
HW #22 ... (Section 14.7) ... p. 1018: 1, 5, 19, 23, 25, 28

EXAM 3 is Friday, June 2, 2006. It will cover handouts, lecture notes, and examples from class, homework assignments 16 through 22, discussion sheets 7, 8, and 9, and material from sections 14.1-14.7 in the book which was presented in lecture notes through Wednesday, May 31, 2006. MOST of the exam questions will be like examples from lecture notes, homework problems, or discussion sheets.

TYPES OF QUESTIONS FOR EXAM 3 FOR SPRING 2006 (THIS IS SUBJECT TO UNANNOUNCED CHANGES.)

1 -- 3D Graphing (intercepts, traces, level curves)
1 -- Domain and Range
2 -- Limits. Here they are .
1 -- Compute various partial derivatives
1 -- Chain Rule
1 -- Directional Derivative
1 -- Tangent Plane
1 -- Second Derivative Test
2 -- Others
1 -- OPTIONAL EXTRA CREDIT

HERE ARE SOME RULES FOR EXAM 3.

0.) IT IS A VIOLATION OF THE UNIVERSITY HONOR CODE TO, IN ANY WAY, ASSIST ANOTHER PERSON IN THE COMPLETION OF THIS EXAM. PLEASE KEEP YOUR OWN WORK COVERED UP AS MUCH AS POSSIBLE DURING THE EXAM SO THAT OTHERS WILL NOT BE TEMPTED OR DISTRACTED. THANK YOU FOR YOUR COOPERATION.
00.) IT IS A VIOLATION OF THE UNIVERSITY HONOR CODE TO COPY ANSWERS FROM ANOTHER STUDENT's EXAM.
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.) Do not use any shortcuts from the book when using the method of integration by parts.
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 3 ARE POSTED ON THIS WEBPAGE.

THE GRADING SCALE FOR SPRING 2006 EXAM 3 IS :

A+ ...... 100-110

A ...... 89-99

A-/B+ ...... 86-88

B ...... 74-85

C ...... 60-73

D ...... 50-59

F ...... 0-49

HW #23 ... (Section 14.7) ... p. 1018: 31 (REWRITE PROBLEM: Use the triangle formed by the graphs of x=0, y=3, and y=x.), 34, 41 (For the remaining two problems you need only find the critical points and extreme values. You need NOT verify that each corresponds to a maximum or minimum.) ... and ...
I.) The material for the top and bottom of a rectangular box costs 3 cents per square foot, and that for the sides costs 2 cents per square foot. What are the cost and dimensions of the least expensive box that has a volume of 1 cubic foot ?
II.) Determine the dimensions and volume of the closed rectangular box of largest volume if the total surface area is to be 12 square meters.
HW #24 ... (Section 14.8) ... p. 1031: 1, 3, (Minimize distance squared.) 8, 14, (Minimize distance squared.) 21, 27, 30, 33, (Minimize distance squared.) 35

The FINAL EXAM is Monday, June 12, 2006,

8-10 a.m. (7:50-10:10 a.m.)

in 198 Young

BRING A PICTURE ID TO THE EXAM
AND BE PREPARED TO SHOW IT TO KOUBA OR THE TEACHING ASSISTANT !!

The final exam will cover handouts, lecture notes, and examples from class, homework assignments 1 through 24, and material from sections 11.1-11.10, 12.1-12.5, 14.1-14.8, and discusssion sheets 1-10.

TYPES OF QUESTIONS FOR THE SPRING 2006 FINAL EXAM (THIS IS SUBJECT TO UNANNOUNCED CHANGES.). The following topics will NOT BE COVERED on this final exam -- Lagrange form of the Taylor error (remainder), 3D-graphing, limits, and chain rule.
HERE ARE SOME RULES FOR THE FINAL EXAM.

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MATH 21C (SECTIONS C01-C04), 1322 Storer, 4:10-5 MWF

Instructor: Dr. D. A. Kouba

THE CALCULUS PAGE .

Here are some TIPS for doing well on my exams.

Your comments, questions, or suggestions can be sent via e-mail to Kouba by clicking on the following address : kouba@math.ucdavis.edu .

Your comments, questions, or suggestions can be sent via e-mail to Kouba by clicking on the following address :
kouba@math.ucdavis.edu .