Here is a link showing the days and times for the Math 21ABCD Calculus Room , where TA's are available to answer your questions.
TA OFFICE HOURS 

Monday 
2:103:10 p.m. 

Drew Gallatin 
3217 MSB 


Thursday 
34 p.m. 

Ji Chen 
3131 MSB 


Friday 
11:30 a.m.  12:30 p.m. 

Joe Corliss 
2139 MSB 


Friday 
23 p.m. 

Jianping Pan 
2232 MSB 
EXAM DATES :
 EXAM 1 FRIDAY, January 27, 2017
 EXAM 2 FRIDAY, February 17, 2017
 EXAM 3 FRIDAY, March 10, 2017
 FINAL EXAM  FRIDAY, March 24, 2017, 68 p.m. in 198 Young
The course will likely cover the following sections in our textbook : 4.8, 5.15.6, 6.16.6, 7.1, 7.2, 8.18.5, 8.7, 8.8, and 11.111.4
SOLUTIONS TO ALL HOMEWORK ASSIGNMENTS AND HOUR EXAMS CAN BE VIEWED ON THE INTERNET at
Math 21B 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 .
Here are Practice Exam 1 and Solutions .
Here are Practice Exam 2 and Solutions .
Here are Practice Exam 3 and Solutions .
Click here for additional optional PRACTICE PROBLEMS with SOLUTIONS found at
THE CALCULUS PAGE .
Here are some
TIPS for doing well on my exams.
Here is an OPTIONAL EXTRA CREDIT Survey .
The following homework assignments are subject to minor changes.
SCANNED PROBLEMS for Sections 4.8, 5.15.6
 HW #1 ... (Section 4.8) ... p. 287: 2, 5, 8, 11, 15, 20, 21, 23, 26, 34, 36, 39, 46, 50, 51, 60, 62, 66, 69, 7880, 82, 83bc, 86bc, 90, 96, 98, 101, 103, 105, 108, 109, 113, 117, 120 (... and how high will the rocket be after 1 minute ?), 122, 125
 HW #2 ... (Sections 5.1 and 5.2) ... p. 307: 1bd, 3bd, 6, 10, 12, 19 ... and ... Here are formulas and rules for finite Summation ...
p. 315: 25, 7, 8, 11, 12, 16, 17, 20, 23, 25, 28, 29, 30, 33
 HW #3 ... Here are notes on the limit definition of the Definite Integral together with some Pictures , and here is a detailed Example ... These are Properties of the definite integral ... (Section 5.3) ... p. 324: 10, 11, 13, 16, 1820, 22, 24, 53, 73, 75, 76, 79 ... and ... Worksheet 1
 HW #4 ... (Sections 5.3 and 5.4) ... Here are brief notes on the Fundamental Theorems of Calculus ... Here you can find information about the Average Value of a Function and Even and Odd Functions ... p. 326: 55, 58, 61 ... and ... p. 336: 1, 7, 9, 12, 13, 16, 20, 22, 26, 29, 32 (Change 1/sqrt{3} to 1/2), 3436, 39, 43, 45, 47, 48, 50, 52, 56, 58, 60, 61, 64, 7578, 80, 81, 83, 84
 HW #5 ... (Section 5.5) ... p. 345: 3, 57, 1012, 14, 15, 17, 2225, 28, 29, 3133, 36, 38, 4044, 46, 47, 51, 54, 55, 58, 59, 65, 6971, 78, 80
 HW #6 ... (Section 5.6) ... Here are brief notes on finding area between curves using Vertical CrossSections and area between curves using Horizontal CrossSections ... (Use usubstition when appropriate in the following problems.) p. 353: 2a, 4b, 7b, 12a, 16, 22, 24, 31, 35, 37, 3941, 43, 45, 47, 5355, 58, 63, 66, 68, 73, 74, 80, 85, 95, 99, 102, 106 (Set up integrals but do not evaluate.), 112, 113, 115, 116
EXAM 1 is Friday, January 27, 2017. It will cover handouts, lecture notes, and examples from class, homework assignments 1 through 6, discussion sheets 1, 2, and 3, and material from sections 4.8 and 5.15.6 in the book which was presented in lecture notes through Wednesday, January 25, 2017. MOST of the exam questions will be homeworktype, discussion sheettype, practice examtype questions.
TYPES OF QUESTIONS FOR EXAM 1 FOR WINTER 2017 (THIS IS SUBJECT TO UNANNOUNCED CHANGES.)
 5  Indefinite Integrals
 1  Even/Odd Function
 1  Properties of Definite Integral
 1  Limit Definition of the Definite Integral
 2  Area Using Definite Integrals
 1  Average Value of a Function
 2  Derivatives Using FTC1
 1 or 2  Others
 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. IT IS A VIOLATION OF THE UNIVERSITY HONOR CODE TO COPY ANSWERS FROM ANOTHER STUDENT'S EXAM. IT IS A VIOLATION OF THE UNIVERSITY HONOR CODE TO HAVE ANOTHER PERSON TAKE AN EXAM FOR YOU. 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 WINTER 2017 EXAM 1 IS :
A+ ...... 100  108
A ...... 90  99
A/B+ ...... 87  89
B ...... 70  86
C ...... 55  69
D ...... 44  54
F ...... 0  43
SCANNED PROBLEMS for Sections 6.16.6
 HW #7 ... (Section 6.1) ... Here are brief notes on finding the volume of a static solid using CrossSectional Area ... Here are brief notes on finding the volume of a Solid of Revolution using the Disc Method ... (SET UP BUT DO NOT EVALUATE INTEGRALS.) ... p. 373: 1, 2, 6b, 7, 10, 11, 14 (Evaluate the volume integral.), 15, 16, 2022, 25, 30, 32, 35, 40, 41, 43, 46, 47, 5053, 56 (Evaluate the volume integral.), 60 (Evaluate the volume integral.), 62ab (SET UP volume V as a function of c and stop.).
 HW #8 ... (Section 6.2) ... Here are brief notes on finding the volume of a Solid of Revolution using the Shell Method ... (SET UP BUT DO NOT EVALUATE INTEGRALS.) ... p. 381: 24, 6, 8, 10 (right half of region), 12, 13 (Evaluate this integral.), 15, 18, 22, 27, 29, 30, 32 (Set up the Disc Method and Shell Method for each part.), 33, 36, 38, 42 (Evaluate this integral.), 43, 46, 47 (Evaluate this integral.)
 HW #9 ... (Section 6.3) ... Here are brief notes on finding the Arc Length of a graph ... Here is a worked out Example of arc length ... p. 388: 14, 8, 10, 11, 23a, 24a, 25, 26, 28, 35
 HW #10 ... (Section 6.4) ... Here are brief notes on finding the Area of a Surface of Revolution ... Here is a worked out Example of surface area ... p. 393: 9, 13, 14, 17, 20, 21, 24a, 25, 29, 32
 HW #11 ... (Section 6.5) ... p. 400: 1, 2, 4, 7, 8, 9, 11 (Include the weight of the bucket when computing work.), 13a, 14a, 17, 19, (Use the result from problem 23.) 21 (SET UP integral only.), 2426
 HW #12 ... (Section 6.5) ... p. 403: 34, 36, 37a, 38, 40, 41, 43a, 44, 48
 HW #13 ... (Section 6.6) ... Here are brief notes on finding Centroids for flate plates of constant density ... This explains an ALTERNATE FORMULA for the ycoordinate of the Centroid, Y bar ... Here are formulas for Mass and Center of Mass for a plate with Variable Density ... Read about how Centroids can be used to solve crimes ... p. 413: (For these problems, unless otherwise noted, you need only SET UP integrals.) 1, 2 (Change y=25x^2 to y=sqrt{25x^2}.), 3, 6, 9, 12, 15, 16, 21 (Use points (0,0), (1,0), and (1,1) and the formulas from class. Evaluate the integrals.), 25 (Also find moment about the yaxis, SET UP ONLY), 26 (Evaluate integrals.), 27 (Evaluate integrals.), 29, 31, 35, 37 (Also find surface area.), 39, 42, 45
EXAM 2 is Friday, February 17, 2017. It will cover handouts, lecture notes, and examples from class, homework assignments 7 through 13, discussion sheets 4, 5, and 6, and material from sections 6.16.6 in the book which was presented in lecture notes through Wednesday, February 15, 2017.
TYPES OF QUESTIONS FOR EXAM 2 FOR Winter 2017 (THIS IS SUBJECT TO UNANNOUNCED CHANGES.)
 1  Volume by CrossSectional Area, A(x) (SET UP ONLY.)
 4  Volume by Disc Method/Shell Method (SET UP ONLY.)
 1  Arc Length (Evaluate integral.)
 1  Area of Surface of Revolution (Evaluate integral.)
 1  Moment, Mass, Centroid, or Center of Mass (SET UP ONLY.)
 1  Work (SET UP ONLY.)
 1  Force of Fluid Pressure (SET UP ONLY.)
 1  Other
 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. IT IS A VIOLATION OF THE UNIVERSITY HONOR CODE TO COPY ANSWERS FROM ANOTHER STUDENT'S EXAM. IT IS A VIOLATION OF THE UNIVERSITY HONOR CODE TO HAVE ANOTHER PERSON TAKE AN EXAM FOR YOU. 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 WINTER 2017 EXAM 2 IS :
A+ ...... 100  108
A ...... 90  99
A/B+ ...... 85  89
B ...... 68  84
C ...... 49  67
D ...... 38  48
F ...... 0  37
SCANNED PROBLEMS for Sections 7.1, 7.2, 8.18.5, 8.7
 HW #14 ... (Section 7.1) ... p. 428: 2, 3, 59, 12, 13, 15, 20, 22, 2426, 28, 32, 33, 36, 39, 42, 45, 46 (Change log_8 x to log_10 x.), 49, 51, 53, 55, 67, 68, 70b
 HW #15 ... (Section 7.2) ... Here are brief notes and a worked out example of exponential decay using the halflife of radioactive Carbon 14 in a process called Carbon Dating ... Here is an example of a naturally occurring exponential function in the field of music ... After reading the following newspaper article, estimate the age of the corpse of Kwaday Dan Sinchi ... p. 437: 13, 7, 1013, 16, 17, 19, 20, 22, 26, 27, 30, 35, 37, 38, 41 (See Newton's Law of Cooling formula on pages 435, 436. Assume that the cooling constant k is the same for both parts a and b.), 43, 45, 47, 48 ... and discrete and continuous interest problems on Handout 1 (with solutions)
 HW #16 ... (Section 8.1) ... p. 460: 110, 13, 14, 16, 18, 19, 21, 23, 25, 26, 29, 34, 3840, 43, 4749
 HW #17 ... (Section 8.2) ... p. 467: 1, 4, 5, 8, 9, 1113, 15, 23, 26, 27, 29, 30, 31 (Change x sec(x^2) to x sec^2(x^2), 3335, 3739, 41, 4447, 49, 50, 55, 58a, 6466, 6972, 74
 HW #18 ... (Section 8.3) ... Here is a list of Trig Identities and Trig Integrals ... p. 474: 13, 57, 10, 11, 14, 15, 17, 19, 20, 22, 24, 25, 27, 28, 33, 35, 36, 39, 34 (little bit challenging), 41, 44, 46, 47, 51 (Use integration by parts), 54, 55 (Use integration by parts), 57 (Use integration by parts), (Do problems 51, 55, and 62 using trig identies on page 473) 51, 55, 62, (For the following five problems, see examples of how to use and derive Recursion (Reduction) Formulas . ) 6367, 69, 71, 73 (SET UP integrals only.) , 74 (Evaluate integrals.)
 HW #19 ... (Section 8.4) ... p. 479: 1, 4, 5, 8, 11, 13, 17, 18, 20, 28, 29, 32, 35, 37, 38, 45, 47, 52, 5658
 HW #20 ... (Section 8.5) ... p. 487: 9, 12, 13, 16, 19, 20, 21, 23, 26, 28, 29, 34, 37, 39, 42, 45, 4749, 50, 55
 HW #21 ... (Section 8.7) ... Here are brief notes showing estimate formulas and absolute error formulas for the Trapezoidal Rule and Simpson's Rule ... Here are worked out examples computing Absolute Error for Simpson's Rule ... This link briefly explains the Plausibility of Simpson's Rule ... Here is a detailed development and derivation of the Trapezoidal Rule Error Formula ... p. 501: 4 (parts a and b only), 7 (parts a and b only), 15, 17, 20 (CHANGE 1/sqrt{x+1} TO sqrt{x+1}.), 2426, 32, 38
EXAM 3 is Friday, March 10, 2017. It will cover handouts, lecture notes, and examples from class, homework assignments 14 through 21, discussion sheets 7, 8, and 9 (problems 15 only), and material from sections 7.1, 7.2, 8.18.5, and 8.7 in the book which was presented in lecture notes through Wednesday, March 8, 2017.
Bring it ...
TYPES OF QUESTIONS FOR EXAM 3 FOR WINTER 2017 (THIS IS SUBJECT TO UNANNOUNCED CHANGES.)
 1  Exponential Growth/Decay
 1  Trapezoidal or Simpson's Rule
 7 or 8  Various Integrals
 1 or 2  Other
 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. IT IS A VIOLATION OF THE UNIVERSITY HONOR CODE TO COPY ANSWERS FROM ANOTHER STUDENT'S EXAM. IT IS A VIOLATION OF THE UNIVERSITY HONOR CODE TO HAVE ANOTHER PERSON TAKE AN EXAM FOR YOU. 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.) 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 WINTER 2017 EXAM 3 IS :
A+ ...... 100  108
A ...... 9099
A/B+ ...... 86  89
B ...... 69  85
C ...... 45  68
D ...... 35  44
F ...... 0  34
SCANNED PROBLEMS for Sections 8.8, 11.111.4
 HW #22 ... (Section 8.8) ... Here are brief notes and examples illustrating the Comparison Tests for Convergence/Divergence for improper intergrals ... p. 513: 1, 4, 6, 9, 14, 15, 20, 21, 25, 30, 34, 37, 41, 42, 51, 53, 59, 67, 69, 70, 75b (Show that this integral converges.)
 HW #23 ... (Sections 11.1) ... Here are examples of Parametric Equations ... This is an example of Arc Length using parametric equations ... p. 659: 1, 46, 8, 1012, 14, 16, 19, 22 (It's misnumbered as 21 in the solutions.), 24, 27, 28, 31, 3335, 39
 HW #24 ... (Section 11.2) ... p. 669: 1, 5, 6, 9, 11, 1315, 1820, 22 (Change e^(t) to t^3.), 23, 24a, 2527, 29, 31, 32, 34, (CHALLENGING) 38a (Find CENTROID of the curve.) 38b (Find CENTROID of region enclosed by the graph and the yaxis and SET UP ONLY.), 43 (On part c. change (4/3)pi to (7/6)pi.), 44, 45, 48 (SET UP but do NOT evaluate the integral.)
 HW #25 ... (Sections 11.3) ... p. 674: 1, 6dfh, 7, 8bd, 9ac, 11, 17, 27, 32, 36, 38, 40, 42, 44 (First find the function's largest yvaule.), 47, 49, 5257, 6163, 66 ... The following problems are from Edition 11, which you can find HERE ... 31, 3335, 45, 47ac
 HW #26 ... (Section 11.4) ... p. 678: 1, 6, 7, 10, 18, 19, 21b, 22a, 23b, 24a, 2628 (For fun on your graphing calculator, graph the following.) 31, 32, 34acd
The FINAL EXAM is Friday, March 24, 2017
68 p.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 (Homework assignments 25 and 26 will NOT be covered on the Final Exam.), material from sections 4.8, 5.15.6, 6.16.6, 7.1, 7.2, 8.18.5, 8.7, 8.8, and 11.111.2 (Sections 11.3 and 11.4 will NOT be covered on the Final Exam.) and discusssion sheets 110.
TYPES OF QUESTIONS FOR THE FINAL EXAM FOR WINTER 2017 (THIS IS SUBJECT TO UNANNOUNCED CHANGES.). This exam will NOT HAVE PROBLEMS on Work, Surface Area of Solid of Revolution, and Limit Definition of Definite Integral.
 5  Integrals Using Any Method
 2  Improper Integrals
 1  Trapezoid or Simpson's Rule
 1  Exponential Growth/Decay
 2  Volume
 1  Centroid
 3 or 4  Parametric Equations  Parametrize, Graphing, Slope, Concavity, Area, Arc Length, etc.
 1  Force of Water Pressure
 1  Arc Length
 1 or 2  Others
 1  OPTIONAL EXTRA CREDIT
HERE ARE SOME RULES FOR THE FINAL EXAM.
 0.) IT IS A VIOLATION OF THE UNIVERSITY HONOR CODE TO, IN ANY WAY, ASSIST ANOTHER PERSON IN THE COMPLETION OF THIS EXAM. IT IS A VIOLATION OF THE UNIVERSITY HONOR CODE TO COPY ANSWERS FROM ANOTHER STUDENT'S EXAM. IT IS A VIOLATION OF THE UNIVERSITY HONOR CODE TO HAVE ANOTHER PERSON TAKE AN EXAM FOR YOU. 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.
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Your comments, questions, or suggestions can be sent via email to Kouba by
clicking on the following address :
kouba@math.ucdavis.edu .