• EXAM 1-- FRIDAY, April 19, 2019
  
  
• EXAM 2-- FRIDAY, May 10, 2019
  
  
• EXAM 3-- FRIDAY, May 31, 2019
  
  
  • FINAL EXAM for the 9 a.m. Class -- MONDAY, June 10, 2019, 8-10 a.m., in 6 Wellman
    
    
  • FINAL EXAM for the 12:10 p.m. Class -- FRIDAY, June 7, 2019, 8-10 a.m., in 1001 Giedt

Here are Math 16C . . . . . HOMEWORK Solutions . . . . . and . . . . . EXAM Solutions

Here are copies of Worksheets .

Here are Supplementary Class Handouts .

Here are Trigonometry Review Sheets including graphs, exact values, and identities.

Here are Properties of Logarithms and Exponents .

Here are Differentiation Rules from Math 16A and Math 16B.

Here are Trig Integration Formulas from Math 16B.

Here are Methods of Integration from Math 16B .

Here are Practice Exam 1 and Solutions .

Here are Practice Exam 2 and Solutions .

Here are Practice Exam 3 and Solutions ... and another (Ignore problem 7 and Extra Credit problem 2 for this exam.) Practice Exam 3 and Solutions .

Here are Practice Final Exam and Solutions .

These are the OPTIONAL EXTRA CREDIT survey and short paper .

Here is some ADVICE about how to generally approach this Math 16C class.

Here are some TIPS for doing well on my exams.

Click here for additional optional PRACTICE PROBLEMS with SOLUTIONS found at THE CALCULUS PAGE .

SCANNED PROBLEMS for Sections C1-C4, 7.1, and 7.2


• HW #1 ... (Section C.1) ... p. A24: 3, 6, 8, 10-12, 16, 17, 20, 26-29, 32-34, 39, 40, 42-44, 47, 53, 54, 56, 57, 59-61, 63, 66
  
  
• HW #2 ... (Section C.2) ... Here is an example of an Applied Differential Equation , which we will solve in class and here are Two Practice Applied Differential Equation Problems with Solutions , ... p. A32: 1, 4, 6, 7, 10, 12, 14, 15, 17, 18, 20, 23, 25-28, 30, 33, 34, 37, 39, 40 (Solve for V), 42
  
  
• HW #3 ... (Section C.3) ... p. A37: 1-19, 22, 28, 31, 34, 35, and 44
  
  
• HW #4 ... (Section C.4) ... Here are Mixture Problem 1 and Mixture Problem 2 , both of which we will solve in class ... Here are two Solved Examples of Applied Differential Equations ... p. A44: 1, 6, 7, 15, 20, 28-33, ... and ... Q3 (from Mixture Problem handout from class) ... and ... Worksheet 1
  
  
• HW #5 ... (Section 7.1) ... Here are some concepts in 3D-Space and here are Practice Problems finding Equations of surfaces in 3D-Space using the Distance Formula ... Here is a derivation of the Distance Formula in 3D-Space ... p. 462: 1, 6, 8, 9, 12, 13, 15, 17, 18, 21, 24, 26, 27, 29, 32, 34, 36, 39, 41, 43, 46, 47 ... and ... Worksheet 2
  
  ***** .... Here is a free online 3D Graphing Calculator sponsored by GeoGebra. Here is a free online 2D Graphing Calculator sponsored by Desmos....****
  
  
• HW #6 ... (Section 7.2) ... What are Traces and Level Curves ? ... Here is a Detailed Example using Intercepts, Traces, and Level Curves to graph in 3D-Space ... Here are other examples graphing surfaces in 3D-Space using Traces and Level Curves ... p. 472: 2, 4, 8, 10, (On the following problems use intercepts, traces, and level curves to sketch the 3D surfaces.), 31, 33, 38, 48, 51, 54, 56 ... and ... Worksheet 3

TYPES OF QUESTIONS FOR EXAM 1 FOR SPRING 2019 (subject to unannounced changes)

• 4 or 5 -- Solve Differential Equations using any method (integrate once, integrate twice or more, separable, or first-order linear)
• 1 -- Use implicit differentiation to show equation solves D.E.
• 1 -- Sphere problem
• 1 -- Sketch surface in 3D-Space using intercepts, traces, or level curves.
• 1 -- Mixture problem (SET UP the D.E. with Initial Conditions and/or find an Integrating Factor, but do NOT SOLVE the D.E.)
• 1 -- Create an Equation in 3D-Space
• 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 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.
• 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 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.

THE GRADING SCALE FOR EXAM 1 FOR SPRING 2019 IS :

A+ ...... 100-110

A ...... 90-99

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

B ...... 70-84

C ...... 50-69

D ...... 40-49

F ...... 0-39

SCANNED PROBLEMS for Sections 7.3-7.6, 7.8, and 7.9


• HW #7 ... (Section 7.3) ... p. 480: 2, 3, 6, 11, 15-18, (Also find range for the next 7 problems.) 20, 22-24, 26-28, 46
  
  
• HW #8 ... (Section 7.4) ... p. 491: 1-16, 20, 21, 24, 26, 27, 29, 31, 38, 39, 41-43, 49, 52, 55, 59 (Simplify answers.), 62, 72-74
  
  Here is 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 #9 ... (Section 7.5) ... p. 501: 2, 3, 5, 7, 9, 10, 14, 18, 20 ... and ... Worksheet 4
  
  
• HW #10 ... (Section 7.5) ... p. 501: 33-35, 37, 42(optional), 43, 46 ... and ... Worksheet 5 ... Here is a challenging example and solution to an Applied Max/Min Problem
  
  
• HW #11 ... (Section 7.6) ... p. 511: 2, 4, 5, 7, 10, 13, 14, 16 ... and ... Systems of Equations with Solutions
  
  
• HW #12 ... (Section 7.6) ... p. 511: 18, 22, 24, 28, 33 ... and ... Worksheet 6 ... Here is an "average" example and solution to a Lagrange Multiplier Problem with Two Constraints ... Here is a challenging example and solution (Assume that T is the temperature in degrees F at point (x,y,z) on the ellipse, which is the intersection of the paraboloid and the plane in 3D-Space.) to a Lagrange Multiplier Problem with Two Constraints
  
  
• HW #13 ... (Section 7.8) ... p. 530: 1, 2, 3, 7, 9-11, 14-16, 20, 26, 30 (NOTE TYPO IN BOOK-- dx dy should be dy dx in problem 30.), 31, 32, 35, 40, 41, 44, 45
  
  
• HW #14 ... (Section 7.8 and 7.9) ... p. 530: 33, 34 ... and ... p. 538: 5, 6, 11, 12, 17, 20, 22, 27, 30, 35, 36 ... and ... Worksheet 7
  
  
• HW #15 ... (These are challenging Optional Practice Problems.) ... Worksheet 7 1/2 (and solutions) ... and ... Worksheet 8

Bring it ...

TYPES OF QUESTIONS FOR EXAM 2 FOR SPRING 2019 (subject to unannounced changes)

• 1 -- Derive various partial derivatives
• 2 -- Evaulate double integrals; switch order of integration if necessary
• 2 or 3 -- Volume and/or Determine average value of function z=f(x,y), y=f(x), or w=g(y)
• 1 -- Find and classify critical points for z=f(x,y)
• 1 or 2 -- Use Lagrange multipliers with either one constraint or two constraints to determine critical point for maximum or minimum
• 1 -- Determine domain and range for functions z=f(x,y)
• 1 or 2 -- Others
• 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 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.
• 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 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 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 2 FOR SPRING 2019 IS :

A+ ...... 100-113

A ...... 90-99

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

B ...... 68-83

C ...... 45-67

D ...... 34-44

F ...... 0-33

SCANNED PROBLEMS for Sections 10.1-10.4


• HW #16 ... (Section 10.1) ... p. 658: 2-5, 7, 31, 34, 36, 38, 40-42, 44, 50 (Find nth term.), 51 (Find nth term.), 66, 68a ... and ... Worksheet 9 ... and ... Here are extra practice problems finding Formulas for sequences with Answers
  
  
• HW #17 ... (Section 10.1) ... p. 658: 9-28 ... and ... (Section 10.2) ... p. 670: 13-16, 18, 19, 24, 26, 47, 51, 52
  
  
• HW #18 ... (Section 10.2) ... p. 670: 6-9, 12, 31-40, 45, 49, 50, 53 ... and ... Here is information about the P-Series Test ... (Section 10.3) ... p. 679: 7-16, 32, 33
  
  
• HW #19 ... Here is information about the Ratio Test ... (Section 10.3) ... p. 679: 17-26, 28-30, 41, 42, 44, 46, 47, 50-56
  
  
• HW #20 ... (Section 10.4) ... p. 689: 1, 3, 9-12, 14-16, 20, 22, 23, 39
  
  
• HW #21 ... (Section 10.4) ... (Find the 1st four nonzero terms in the Taylor Series. Try to find formula for Taylor Series and the resulting interval of convergence, even though this is very difficult for some of the problems.) p. 689: 26, 28, 29, 32, 34, 36, 41, 43, 45 (Start with the Taylor series for 1/(1-x).), 46, 48 (yes, before 47), 47 .. and ... I.) Find the Taylor Series centered at c=1 for f(x)=lnx, and find the radius of convergence R.... Here is an Applied Problem involving Coffee , Probability Density Functions, and Taylor Polynomials.
  
  
• HW #22 ... Worksheet 10

TYPES OF QUESTIONS FOR EXAM 3 FOR SPRING 2019 (subject to unannounced changes)

• 2 or 3-- Find nth term of sequence
• 3 or 4-- Use series tests to determine convergence or divergence of series
• 1-- Sequence applied to problem
• 1-- Interval and radius of convergence
• 1-- Using error formula for p-series
• 1-- Find Taylor Series Using Taylor's Theorem, Where a{n}= f^{n}(c)/n!
• 1 or 2-- Find Taylor Series Using Shortcuts
• 1 or 2-- Others
• 1-- OPTIONAL EXTRA CREDIT

HERE ARE SOME RULES FOR EXAM 3.

• 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 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.
• 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 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.

THE GRADING SCALE FOR EXAM 3 FOR SPRING 2019 IS :

A+ ...... 100-108

A ...... 90-99

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

B ...... 65-84

C ...... 46-64

D ...... 35-45

F ...... 0-34

SCANNED PROBLEMS for Sections 10.5 and 10.6


• HW #23 ... (Section 10.5) ... (Use shortcuts to get Taylor polynomials.) p. 698: 1, 2, 3 (Use formula on p. 687.), 4, 5, 9, 10, 17, 18
  
  
• HW #24 ... (Section 10.5) ... (Use shortcuts to get Taylor polynomials.) p. 698: 21, 22, 23 (Use formula on p. 687.), 25-28 ... and ... Worksheet 11
  
  
• HW #25 ... (Section 10.6) ... P. 705: 4, 9, 14, 16, 31, 36, 39, 44
  
  
  
  

  The FINAL EXAM for Math 16C at 9 a.m. is Monday, June 10, 2019,
  

  8-10 a.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 for Math 16C at 12:10 p.m. is Friday, June 7, 2019,
  

  8-10 a.m.
  

  in 1001 Giedt
  
  

  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 24, and material from sections C.1-C.4, 7.1-7.6, 7.8, 7.9, and 10.1-10.5. Use your three hour exams, 24 homework assignments, and the practice exams as a guide to your preparing for the final exam.

  
  Let's do it ...
  

  
  
  

  TYPES OF QUESTIONS FOR THE FINAL EXAM FOR SPRING 2019 (subject to unannounced changes). There will be NO MIXTURE PROBLEM on the Final Exam.

  • 2 -- Solve differential equations
  • 1 -- Show solution equation solves differential equation
  • 1 -- Domain and range
  • 1 -- Lagrange multiplier
  • 1 -- Find and classify critical points
  • 2 -- Double Integrals (Switch order of integration, if necessary.)
  • 1 -- Sequence problem
  • 1 -- Interval and radius of convergence
  • 2 -- Find Taylor Series (One using shortcuts and formulas, which will be given, or using Taylor's Theorem)
  • 1 -- Taylor polynomial
  • 1 -- Taylor error (I will provide the Absolute Taylor Error Formula.)
  • 2 or 3 -- Others
  • 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 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.
  • 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 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 .