• EXAM 1-- MONDAY, April 24, 2017
  
  
• EXAM 2-- WEDNESDAY, May 17, 2017
  
  
• EXAM 3-- MONDAY, June 5, 2017
  
  
• FINAL EXAM -- TUESDAY, June 13, 2017, 1-3 p.m., in 6 Wellman

Sheet 1 , Sheet 2 , Sheet 3 , Sheet 4 , Sheet 5 , Sheet 6 , Sheet 7 , Sheet 8 , Sheet 9 , Sheet 10

Here are Math 17B ... HOMEWORK SOLUTIONS . . . and . . . EXAM SOLUTIONS .

Here are Supplementary Class Handouts .

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 .

SCANNED PROBLEMS for Chapter 5, Section 8


• HW #1 ... (Section 5.8) ... p. 272: 1, 8, 10, 17, 19, 20, 22, 24, 25, 28, 31, 33, 35, 39, 41, 42 (HINT:Use the trig identity cos 2z=1-2 sin^2 z.), 43-46, 49, 50, 54, 60, 66, 70, 72, 73, 75 (Assume that the height of the object at time t seconds is s(t) feet and that the acceleration of the object at time t seconds is s''(t)= -32 ft/sec.^2.), 76, 77 (CORRECTIONS: V(t) is mass in grams NOT volume in grams. Evaporation rate is proportional to t(24-t). dV/dt is the net rate of change of H20 in the plant.)
  
  SCANNED PROBLEMS for Chapter 6
  
  
• HW #2 ... (Section 6.1) ... Here is a list of Finite Summation Rules ... p. 291: 6, 7, 8, 10, 11, 14, 16, 18, 22, 23, 25, 27, 28, 30
  
  
• HW #3 ... (Section 6.1) ... p. 291: 35, 36, 61, 62, 64, 67, 75, 77, 83 ... and ... Worksheet 1 ... Here is a brief summary of how to use the Limit Definition of Definite Integral
  
  
• HW #4 ... (Section 6.2) ... Here are statements of and explanations for the Fundamental Theorems of Calculus ... p. 305: 5, 7, 12, 15, 16, 20, 24, 27, 32, 33, 36 (Remove restriction that x>0.), 40, 44, 45, 50, 51, 55, 57, 62, 65, 67, 73, 80, 82, 88, 89, 92, 93, 95, 97, 99, 105, 108, 114, 115, 116, 119, 123, 126
  
  
• HW #5 ... (Section 6.3) ... Here are explanations and formulas for the Average Value of a Function ... Even and Odd Functions ... Average Value of a Function ... Volume of a Solid ... Arc Length and an Example of Arc Length ... p. 321: 1-3, 7, 11, 14, 17, 20, 22 (w: pounds, x: months), 24 (N: people, t: years), 25-27, 29, 31, 33 (Replace "Find" with "Use a solid of revolution to derive the formula for".), 34 (Replace "Find" with "Use a solid of revolution to derive the formula for".), 36, 38, 41, 43, 47, 51, 52, 53b, 55 (Assume that y>= 0.), 57
  
  SCANNED PROBLEMS for Chapter 7
  
  
• HW #6 ... (Section 7.1) ... Why does u-substitution work ? ... Here is an explanation of the derivative and integrals using Arctangents with examples ... Here is a comprehensive list of Integration Formulas ... Here are some trig Rules and Identities with some Explanations ... p. 333: 1, 4, 6, 8, 9, 12-14, 16, 18, 20, 21, 24, 26-28, 31-33, 35, 36-43, 45, 48, 50, 52, 54, 55, 57
  
  
• HW #7 ... (Section 7.2) ... Here is a brief explanation of Integration by Parts with an example ... p. 342: 1, 6, 7, 10, 12, 15, 19, 23, 25, 29, 40, 43, 45, 48-57, 59, 60, 63, 68
  
  
• HW #8 ... (Section 7.3) ... Here are some notes for Partial Fractions ... p. 350: 1, 4, 5, 9, 11, 13, 27, 29-32, 34, 35, 38, 43, 45, 46, 51
  
  EXAM 1 is Monday, April 24, 2017. It will cover handouts, lecture notes, and examples from class, homework assignments 1 through 8, discussion sheets 1,2, and 3 and material from sections 5.8, 6.1-6.3 and 7.1-7.3 in the book which was presented in lecture notes through Friday, April 21, 2017. Most of the exam questions will be similar to problems presented in class, homework problems, or discussion sheet problems. There will be an OPTIONAL EXTRA CREDIT problem on the exam.
  
  

  TYPES OF QUESTIONS FOR EXAM 1 FOR SPRING 2017 (subject to unannounced change)

  • 5-- Indefinite Integrals Using Any Method
  • 1 or 2-- Volume (SET UP ONLY.)
  • 1-- Area (SET UP ONLY.)
  • 1-- Limit Definition of Definite Integral
  • 1-- Average Value of a Function
  • 1-- Arc Length
  • 1-- Even/Odd Function
  • 1-- FTC1
  • 1 or 2-- Others
  • 1 -- OPTIONAL EXTRA CREDIT
  
  
  

  HERE ARE SOME RULES FOR EXAM 1.

  • 1.) 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 STUDENT TAKE YOUR 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.
  • 2.) No notes, books, or classmates may be used as resources for this exam. YOU MAY USE A CALCULATOR ON THIS EXAM.
  • 3.) You will be graded on proper use of limit notation.
  • 4.) You will be graded on proper use of integral and derivative notation.
  • 5.) Put units on answers where units are appropriate.
  • 6.) Read directions to each problem carefully. Show all work for full credit. In most cases, a correct answer with no supporting work will receive little or no 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.
  
  
  

  THE GRADING SCALE FOR EXAM 1 FOR SPRING 2017 IS :
  
  

  A+ ...... 100-108
  

  A ...... 87-99
  

  A-/B+ ...... 84-86
  

  B ...... 64-83
  

  C ...... 43-63
  

  D ...... 33-42
  

  F ...... 0-32
  
  
  

• HW #9 ... (Section 7.4) ... p. 362: 1-5, 8, 9, 11, 14, 17, 18, 20, 25, 28, 29 (Integrate from 0 to infinity, not negative infinity to infinity.), 31, 32
  
  
• HW #10 ... (Section 7.5) ... Here are brief explanations of the Midpoint Rule and Trapezoidal Rule ... p. 370: 2, 4, 7, 10, 15, 16, 18, 20, 23
  
  
• HW #11 ... (Section 7.6) ... p. 381: 1-3, 5-7, 11, 15, 16, 19, 22, 27, 28, 30
  
  SCANNED PROBLEMS for Chapter 8
  
  
• HW #12 ... (Section 8.1) ... p. 403: 1, 2, 4, 7, 9, 10, 12, 13, 17, 19 (Solve for N.), 20 (Solve for W.), 22 (Solve for L.), 28, 32, 36, 37 (Solve for N.), 44, 45, 47, 48, 53 ... and ... Here is a short list of Logarithm Properties ... and ... Problem A (and Solution) ... and ... Problem B (and Solution) ... You can find a site to download copies of your own semi-log graph paper (numbered) HERE .
  
  
• HW # 13 ... What is a First-Order Linear Differential Equation and how do you solve one ? ... Here is a First-Order Linear Differential Equations Worksheet ... and ... Here are brief Notes Explaining the Set-Up of mixture problems ... Here are two Mixture Problems and their Solutions ... Do Worksheet 2
  
  
• HW #14 ... (Section 8.2) ... Here are some notes on Direction Fields ... Here are some links on Warder Allee , the Allee Effect , and the California Condor ... p. 417: 2, 3, 4, 6a(Use graphing calculator.)bc, 8a, 9, 10, 14, 21, 24, 25
  
  EXAM 2 is Wednesday, May 17, 2017. It will cover handouts, lecture notes, and examples from class, homework assignments 9 through 14, discussion sheets 4, 5, and 6 and material from sections 7.4, 7.5, 7.7, 8.1, and 8.2, which was presented in lecture notes through Monday, May 15, 2017. Most of the exam questions will be similar to problems presented in class, homework problems, or discussion sheet problems.
  
  

  TYPES OF QUESTIONS FOR EXAM 2 FOR SPRING 2017 (subject to unannounced change)

  • 1 -- Using Semi-Log Paper to Find Growth Equation N and its Growth rate dN/dt in Autonomous Form
  • 1 or 2 -- Taylor Polynomial/Taylor Error (I will provide Taylor Error formula.)
  • 1 -- Mixture Problem (Rate In Minus Rate Out); SET UP Differential Equation Only (Not solve it)
  • 1 -- Determining (Two Ways) Stable and Unstable Equilibria for Autonomous Differential Equation
  • 3 -- Solving Differential Equations (Separable, First-Order Linear)
  • 2 -- Improper Integrals
  • 2 -- Midpoint Rule/Error or Trapezoidal Rule/Error (I will provide Error formulas.)
  • 1 -- OPTIONAL EXTRA CREDIT
  
  
  

  HERE ARE SOME RULES FOR EXAM 2.

  • 1.) 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 STUDENT TAKE YOUR 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.
  • 2.) No notes, books, or classmates may be used as resources for this exam. YOU MAY USE A CALCULATOR ON THIS EXAM.
  • 3.) You will be graded on proper use of 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.
  
  
  
  

  THE GRADING SCALE FOR EXAM 2 FOR SPRING 2017 IS :
  
  

  A+ ...... 100 - 108
  

  A ...... 90 - 99
  

  A-/B+ ...... 85 - 89
  

  B ...... 68 - 84
  

  C ...... 46 - 67
  

  D ...... 36 - 45
  

  F ...... 0 - 35

SCANNED PROBLEMS for Chapter 9


• HW #15 ... Here are some notes on Linear Systems of Equations and some rules for Matrix Row Reduction ... (Section 9.1) ... p. 443: 1, 3, 4, 17, 18ab and add c. Assume now that the mice require nutrients in the ration 5:6., 21, 23, 25, 27, 28, 35
  
  
• HW #16 ... (Section 9.2) ... p. 465: 1, 7, 15, 21ab, 24, 26, 27, 29, 34, 35, 37, 39, 42, 43, 45, 51, 53, 55, 63, 65, 67, 69, 71, 73, 75, 77
  
  
• HW #17 ... ... (Section 9.3) ... Here are some brief notes on the algebra and geometry of Vectors ... Here are some brief notes on the properties of eigenvalues and stable age distribution (eigenvector) of a Leslie Matrix ... Here are some properties of a matrix multiplication shortcut using eigenvalues and eigenvectors; and an example finding and "explaining" the stable age distribution (eigenvector) of a Leslie Matrix ...p. 486: 1-4, 6, 8, 9, 12, 14, 15, 17, 19, 22-24, 31, 34, 37, 39, 42, 45, ... (Find eigenvalues and eigenvectors only for the next 3 problems.) ... 49, 53, 55, (Problems 63 and 65 can be skipped. They will be referred to later in Math 17C.) 63, 65, 71, 72, 75, 79
  
  EXAM 3 is Monday, June 5, 2017. It will cover handouts, lecture notes, and examples from class, homework assignments 15 through 17, discussion sheets 7, 8, and 9 and material from sections 9.1-9.3, which was presented in lecture notes through Friday, June 2, 2017. Most of the exam questions will be similar to problems presented in class, homework problems, or discussion sheet problems.
  
  

  TYPES OF QUESTIONS FOR EXAM 3 FOR SPRING 2017 (subject to unannounced change)

  • 2 or 3 -- Solve System of Equations Using Matrix Reduction Rules or using the Inverse Matrix A^{-1}
  • 1 -- Find Eigenvalues, Eigenvectors
  • 2 -- Read Leslie Matrix, or Leslie Matrix Set-Up, or Find Specific Age Distribution, or Find Eigenvalues, Growth Parameter (Increasing or Decreasing in Size), and Stable Age Distribution
  • 2 -- Find Inverse of Matrix
  • 1 -- Rotation Matrix
  • 2 or 3 -- Others
  • 1 -- OPTIONAL EXTRA CREDIT
  
  
  
  

  THE GRADING SCALE FOR EXAM 3 FOR SPRING 2017 IS :
  
  

  A+ ...... 100 - 108
  

  A ...... 90 - 99
  

  A-/B+ ...... 84 - 89
  

  B ...... 65 - 83
  

  C ...... 46 - 64
  

  D ...... 33 - 45
  

  F ...... 0 - 32
  
  
  

  
  
  
  • HW #18 ... (Section 9.4) ... Here is an Alternate Formula for dot product using the angle theta between the vectors ... Here are some brief notes on Lines in two- and three-dimensional space... Here are some brief notes on Planes in three-dimensional space ... p. 500: 2, 4, 5, 7, 10, 12, 16, 17, 23, 26, 27, 30, 31, 35, 39, 42, 43, 47, 53, 55, 58, 59, 62, 63, 65, 66
    
    
  
  
  

• FINAL EXAM -- TUESDAY, June 13, 2017, 1-3 p.m., in 6 Wellman
  
  

  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 18, discussion sheets 1-11, and material from sections 5.8, 6.1-6.3, 7.1-7.6, 8.1, 8.2, and 9.1-9.4. Use your three hour exams, 18 homework assignments, and discussion sheets as a guide to your preparing for the final exam.
  
  

  THE FOLLOWING TOPICS WILL NOT BE COVERED ON THE SPRING 2017 FINAL EXAM -- limit definition of definite integral, semi-log graphing problems, stability of equilibria, midpoint and trapezoidal rules, find inverse of matrices
  
  

  TYPES OF QUESTIONS FOR THE FINAL EXAM FOR Spring 2017 (subject to change)

  • 2 -- Leslie Matrix Problems
  • 1 -- Taylor Polynomial or Taylor Error
  • 1 -- Mixture Problem
  • 1 -- Eigenvalue, Eigenvector Problem
  • 3 -- Differential Equations
  • 4 -- Indefinite Integrals
  • 3 -- Lines or Planes in 3D Space
  • 3 -- Applications of Definite Integral-- Area, Volume, Arc Length, or Average Value
  • 1 -- OPTIONAL EXTRA CREDIT
  
  
  

  HERE ARE SOME RULES FOR THE FINAL EXAM.

  • 1.) 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 STUDENT TAKE YOUR 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.
  • 2.) No notes, books, or classmates may be used as resources for this exam. YOU MAY USE A CALCULATOR ON THIS EXAM.
  • 3.) You may NOT use shortcuts from the textbook for finding limits to infinity.
  • 4.) You need NOT MEMORIZE trigonometry identities. A short list of identities will be provided on the front cover of the exam.
  • 5.) Using only a calculator to determine the value of limits will receive little or no credit.
  • 6.) You will be graded on proper use of limit notation.
  • 7.) Put units on answers where units are appropriate.
  • 8.) 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 .