EXAM DATES :

• EXAM 1-- MONDAY, October 16, 2017
  
  
• EXAM 2-- WEDNESDAY, November 8, 2017
  
  
• EXAM 3-- MONDAY, December 4, 2017
  
  
• FINAL EXAM -- MONDAY, December 11, 2017, 8-10 a.m. in 212 Viehmeyer

This is an OPTIONAL EXTRA CREDIT survey

THE CALCULUS PAGE .

Here are some TIPS for doing well on my exams.

SCANNED PROBLEMS for Chapter 10 (Sections 10.1-10.6)


• HW #1 ... (Section 10.1) ... p. 581: 2, 3, 4, 8, 11, 12, 13, 16, 18, 19, 21, 23-25, 26 (Hint: Use greatest integer function.), 28 (Use Sandwich Theorem.), 32, 33, 35, 39 (Use Sandwich Theorem.), 40, 42, 43, 46 (Use Sandwich Theorem.), 48, 49, 52, 54, 56, 57, 59, 60, 63 (Use Sandwich Theorem.), 64, 66-69, 74, 78-81, 83, 86, 87, 89, 92, 93, 96-99, 108 (Assume the case where x>1.), 116, 118, 119, 121, 123, 124 ... and ... Worksheet 1 ... Here is a link showing why the number e is a limit ... Here are some notes on the Formal Definition of the Limit of a Sequence and here is an example of a Factorial Sequence .
  
  
• HW #2 ... (Sections 10.2) ... p. 591: 3, 5, 7, 8, 12, 14, 16-18, 20, 21, 28, 30-35, 39, 40, 42, 45, 50-52, 54, 59, 60, 62, 64, 65, 67, 83-88, 89a, 90, 91, 92 ... Here are some notes on the Sequence of Partial Sums Test and the Geometric Series Test .
  
  
• HW #3 ... (Section 10.3) ... p. 598: 1, 3, 4, 6, 7, 13-17, 19, 22, 24, 28, 30, 32, 33, 35, 38, 41, 43, (Use (*)(*) from the Integral Test Handout for the following two problems) 49, 52, 58 ... and ... Problems Using Star and Double Star from the Integral Test Handout. Here are the Solutions ... Here are some notes on Equations (*) and (**), the Integral Test, and the P-Series Test .
  
  
• HW #4 ... (Sections 10.4) ... p. 603: 1, 2, 4, 5-9, 11-23, 26-31, 33-41, 43-45, 47, 48, 51, 52, 54, 56-58, 60, 61 (optional), 66 (optional) ... Here are some notes on Comparison Tests and Limit Comparison Tests .
  
  
• HW #5 ... (Section 10.5) ... p. 609: 1, 3-9, 11, 13-15, 17, 20-24, 26-31, 35, 37, 38, 39 (Change -n to n.), 43, 46-48, 51, 52, 54, 55, 57, 58, 60, 61, 66 ... Here are some notes on the Ratio Test and the Root Test .
  
  
• HW #6 ... (Section 10.6) ... p. 615: 2-7, 9-11, 13, 14, 16, 19, 20, 22, 25, 27, 28, 31, 33, 36, 40, 41, 42, 44, 47, 48, 50, 53, 54, 56, 58, 62, 63, 66-68 ... Here are handouts on the Alternating Series Test and the Absolute Convergence Test .
  
  
• Here is a Summary of tests for infinite series and this is a list of Subtle Facts about infinite series.

TYPES OF QUESTIONS FOR EXAM 1 FOR FALL 2017 (THIS IS SUBJECT TO UNANNOUNCED CHANGES.)

• 6-8 -- Determine convergence or divergence of series using various series tests
• 1 -- Alternating series
• 1 -- Epsilon,N Proof
• 1 or 2 -- (*) or (*)(*) problem
• 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. 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 FALL 2017 EXAM 1 IS :

A+ ...... 100-108

A ...... 88-99

A-/B+ ...... 85-87

B ...... 66-84

C ...... 43-65

D ...... 33-42

F ...... 0-32

SCANNED PROBLEMS for Chapter 10 (Sections 10.7-10.10)


• HW #7 ... (Section 10.7) ... p. 624: 1a, 4a, 6a, 7a, 10a, 12a, 17a, 24a, 25a, 27a, 29a, 33-36, 38-42, 44, 46, 50a, 53, 54, 60
  
  
• HW #8 ... (Section 10.8) ... p. 630: 1-4, 6, 8, 10, 11 (Use Maclaurin series for e^x.), 12 (Use Maclaurin series for e^x.), 13 (Use Maclaurin series for 1/(1-x).), 14 (Use Maclaurin series for 1/(1-x).), 15 (Use Maclaurin series for sin x.), 17 (CHANGE THE FUNCTION TO: x^2 cos(x^3) and use Maclaurin series for cos x.), 21, 22 (Change x^2/(x+1) to x^2/(x^3+1) and use Maclaurin series for 1/(1-x).), 25, 27, 29, 33 (Use Maclaurin series for 1/(1-x) and for cos x.), 34 (Use Maclaurin series for e^x.), 36 (Use Maclaurin series for sin x.), 41b, 42b, 43b ... Here are some notes on Taylor Series and Taylor Remainder (Error) .
  
  
• HW #9 ... (Section 10.9) ... p. 637: 1, 4, 5, 6 (Change the function from cos(1/sqrt{2}*x^(2/3)) to cos( 1/sqrt{2}*x^(3/2)), 7, 9-12, 16, 17 (Do 2 ways : i. trig identity 1st, ii. series multiplication), 19, 20, 21 (Do 2 ways : i. differentiation 1st, ii. series multiplication), 22, 24 (Do 2 ways : i. trig identity 1st, ii. series multiplication), 25 (Change e^x + 1/(1+x) to (e^x)(1/(1+x))., 29, 31, 33, 37, 40 (Begin by finding the first 4 nonzero terms and the general formula for the Maclaurin Series for f(x)= sqrt(1+x).) 41, 43, 48 ... Here is a list of well-known Maclaurin Series .
  
  
• HW #10 ... (Section 10.10) ... p. 645: 1, 2, 6, 7, 10, 12, 15, 17, 20, 22, 25, 28, (For 29, 32, 34, 38, and 39 also use L'Hopital's Rule to evaluate limits.) 29, 32, 34, 38, 39, 41-53, 61, 62, 65
  
  SCANNED PROBLEMS for Chapter 12 (Sections 12.1-12.5)
  
  
• HW #11 ... (Section 12.1) ... p. 707: 1, 3, 6, 8, 12, 13, 16, 17ab, 18abc, 20ac, 21b, 22ab, 26-28, 30-32, 34,36-39, 42, 43, 47, 52, 55, 58-60, 62-66 ... Here are some notes on points and graphs in Three-Dimensional Space .
  
  
• HW #12 ... (Section 12.2) ... p. 716: 1, 4, 6, 7, 9-13, 16, 18, 21, 23, 25, 28, 29, 31, 33, 35, 38, 40, 41, 43, 45-48, 49, 52 (See problem 51 first.) ... Here are some detailed notes on Vectors in 2D-space and 3D-space ... Here are two worked out Examples using vectors; one is a hanging weight and the other is a plane flying into a headwind.
  
  
• HW #13 ... (Section 12.3) ... p. 724: 1, 4, 7, 10, 12, 13, 16-18, 22-25, 27, 41, 43, 44, 49 (Do not use results from problems 31 and 32 to do problem 49. Simply use basic facts about vectors and lines.) ... Here are brief handouts on Properties of Dot Product , the (Orthogonal) Projection , and an Alternate form of the dot product.
  
  
• HW #14 ... (Section 12.4) ... p. 730: 2, 3, 7, 9, 10, 14, 16, 19, 20, 23, 25 (See definition of torque on page 729.), 27-29, 31, 33, 36, 39, 42, 45, 46 (Use points (0,0,0), (-2,3,0) and (3,1,0).), 48, 50 ... Here is a brief explanation of the Right-Hand Rule for cross products ... Here are notes on the Triple Scalar Product .
  
  
• HW #15 ... (Section 12.5) ... p. 738: 1, 4, 6-8, 10, 21, 22, 24, 25, 28,30 (and find point of intersection), 31, 34, 37, 40, 43, 45, 47, 51, 55, 59, 65, 67, 69

TYPES OF QUESTIONS FOR EXAM 2 FOR FALL 2017 (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.
• 1 -- Use Taylor Polynomial to compute an estimate
• 5 -- Problems involving lines, planes, angles, normal vectors, parallel vectors, points of intersection, etc.
• 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. 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 2 ARE POSTED ON THIS WEBPAGE.

THE GRADING SCALE FOR FALL 2017 EXAM 2 IS :

A+ ...... 100 - 108

A ...... 90 - 99

A-/B+ ...... 82 - 89

B ...... 64 - 81

C ...... 41 - 63

D ...... 31 - 40

F ...... 0 - 30

SCANNED PROBLEMS for Chapter 12 (Sections 12.6)


• HW #16 ... (Sections 12.6) ... p. 744: 1, 4, 6, 7, 13, 15, (Foe next 5 problems use intercepts, traces, and/or the indicated values of z's for level curves to create a topographical map for the surface.) 18 (Use z=-4, -2, 0, 2, 4), 22 (Use z=8, 7, 4, -1, -8), 25 (Use z=-2, -1, 0, 1, 2), 27 (Use z= -sqrt{8}, -sqrt{3}, 0, sqrt{3}, sqrt{8}), 29, 31, 39 ... Here is a 3D graphing example using Level Curves ... Here is an example where we create an equation for a Surface of Revolution .
  
  SCANNED PROBLEMS for Chapter 14 (Sections 14.1-14.6)
  
  
• HW # 16.5 ... (Section 14.1) ... p. 799: 1d, 4c, 5, 7, 10, 11, (Determine and sketch domain for the following functions.) 18ab, 19ab, 23ab, 24ab, 25ab, and f(x,y)=ln(4-x^2-y^2)
  
  
• HW #17 ... (Section 14.2) ... p. 807: 1, 4, 9, 12, 14, 16, 20-24, 41-50, ... and ... p. 876: 12, 16 ... and ... Worksheet 2 (with solutions ) ... Here is the statement for the Precise Limit of a Function of Two Variables and a worked out Example .
  
  
• HW #18 ... (Section 14.3) ... p. 819: 2, 4, 5, 7, 10, 12, 13, 15 (Change ln(x+y) to ln(3x+y^2).), 16, 19-21, 41-46, 48, 51-54, 58, 60 (Change x^2+y^2 to x^2+y^4.), 62, 65, 75-77, 81, 84, 85
  
  
• HW #19 ... (Section 14.4) ... p. 828: 1 (Change the function to w=x^2+2y.), 3, 5, 6, 8, 9, 14, 15, 20, 24, 26, 28, 30, 32, 39, 40, 42, 43-45, 47, 48, 49a, 51, 52 ... and .... these second-order chain rule problems ... Here is a handout on Exact Change, the Differential, and the Chain Rule for z=f(x,y) ... Here is an explanation for finding the Second Partial Derivative using the Chain Rule.
  
  
• HW #20 ... (Section 14.5) ... p. 838: 2, 3, 6, 7, 10, 12, 13, 15, 16, 17, 19, 22, 29, 32-35, 36a ... Here are notes on the Directional Derivatives and Gradient Vectors for a function of two variables ... Here is an alternate form of the Differential for z=f(x,y) using a Directional Derivative ... Here is a handout discussing why Gradient Vectors are Normal to Level Curves.
  
  
• HW #21 ... (Section 14.6) ... p. 845: 1, 4, 9, 12, 14, 15, 20, 21, 23, 26b, 28a, 30b, 52, 56

TYPES OF QUESTIONS FOR EXAM 3 FOR FALL 2017 (THIS IS SUBJECT TO UNANNOUNCED CHANGES.)

• 1 -- 3D Graphing (intercepts, traces, level curves)
• 1 -- Domain and Range
• 2 or 3 -- Limits
• 1 -- Compute various partial derivatives
• 1 or 2 -- Chain Rule
• 1 or 2 -- Directional Derivative
• 1 -- Epsilon,Delta Proof
• 1 -- 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. 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 FALL 2017 EXAM 3 IS :

A+ ...... 100-110

A ...... 90-99

A-/B+ ...... 83-89

B ...... 68-82

C ...... 45-67

D ...... 34-44

F ...... 0-33

SCANNED PROBLEMS for Chapter 14 (Sections 14.7. 14.8)


• HW #22 ... (Section 14.7) ... p. 855: 1, 5, 15, 16, 19, 22, 26, 28-30 ... Here is a statement of the Second Derivative Test for partial derivatives to find and classify critical points for a function of two variables ... For those interested, here is a Proof of the Second Derivative Test.
  
  
• HW #23 ... (Section 14.7) ... p. 855: 31 (REWRITE PROBLEM: Use the triangle formed by the graphs of x=0, y=3, and y=x.), 34, 41 (For the remaining problems you need only find the critical points and extreme values. You need NOT verify that each corresponds to a maximum or minimum.) 50 (HINT: Start with a point (x,y,z) on the paraboloid. Use a projection vector to find the distance from (x,y,z) to the plane. Then find the critical point for the distance function.), 51 (First find the distance from point (x,y,z) on the plane to the point (0,0,0).), 53-55, 57-59 ... and ... the two problems below ...
  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. 864: 1, 3, (Minimize distance squared.) 8, 14, (Minimize distance squared.) 21, 27, 30, 37, (Minimize distance squared.) 39
  
  
  
  

  The FINAL EXAM is Monday, December 11, 2017
  
  

  8-10 a.m.
  
  
  

  in 212 Viehmeyer
  
  
  
  

  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 23 (Omit problems 31, 34, and 41 and omit HW #24.), and material from sections 10.1-10.10, 12.1-12.5, 14.1-14.7 (Omit Section 14.8.), and discusssion sheets 1-10.
  
  

  TYPES OF QUESTIONS FOR THE FALL 2017 FINAL EXAM (THIS IS SUBJECT TO UNANNOUNCED CHANGES.). The following topics will NOT BE COVERED on this final exam -- Taylor Error (Remainder), 3D-graphing, epsilon/delta proofs, epsilon/N proofs, and 3D-limits.
  
  

  • 1 -- Domain, Range
  • 2 -- Taylor Series
  • 1 -- Taylor Polynomial
  • 1 -- (*) or (*)(*)
  • 1 -- Chain Rule
  • 1 -- Absolute and Conditional Convergence
  • 1 -- Interval of Convergence
  • 2 -- Directional Derivatives
  • 1 -- Differential
  • 1 -- Find and Classify Critical Points
  • 3 or 4 -- Others
  • 1 or 2 -- 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. 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 e-mail to Kouba by clicking on the following address :

kouba@math.ucdavis.edu .