Course: MAT 112A (Fall 2021) - Calculus I and Modeling | Davidson College

  • General

    • Neidinger's Office Hour Zoom link TuTh 10:50 -- 11:50 URL

      Expected Tues & Thurs 10:50 -- 11:50 a.m.  Email Neidinger (rineidinger) if not working or to arrange any other time.

    • Neidinger in-person Office hour:  in Chambers 3043 after class MWF 10:40 -- 11:40.

    • Embedded Tutor Basel Elzatahry Zoom Link (if and when arranged by email) URL

    • Basel Elzatahry in-person help sessions:  In Chambers 2130 (starting 9/7/21) on 
      Sundays 3-5p;
      Tuesdays 8-10p,
      Thursdays 8-10p.

    • Math & Science Center URL

      The linked page will post tutor schedules for drop-in assistance, as well as links to schedule an appointment with a tutor. Located in the Center for Teaching & Learning (CTL) on the first floor of the College Library, the MSC’s drop-in hours are Sunday through Thursday, 8-11 PM, beginning Sunday, August 29. Prior to visiting for drop-in help, be sure to look at the tutor schedules to determine when an appropriate tutor for Calculus will be present. 

    • Announcements (Broadcast to students) Forum
    • Question Forum

      Students can ask any questions about the course here.

    • Coronavirus in the US (and elsewhere) -- meaningful graphs that are up-to-date URL

  • Open all

    Close all

  • Instructions: Clicking on the section name will show / hide the section.

    • #1 Due Wed. Assignment

      Look through Section R.6 (p. R-21-24) and Section 2.1 p. 73-74 and Examples 6 and 7 at end.  We will do interest later.
      Do Exercises:
      R.6; 15, 25(single term means one fraction), 46.
      2.1; all in range 3 - 11 matching (Calculator graphing is not required.)   Hint: rewrite algebra expression as a multiple and/or shift of 3x or 3-x.
      2.1; 38, 45.  
      Hint on 38(d):  64 = 2^6.
      Hints on 45: (b) explain means physically, in terms of cortisone.  (c) Show rough sketch of graph WITH SCALE whenever used to answer a question -- throughout the course.  Set Window to an appropriate xmin and xmax and may use ZoomFit.

    • #2 click for assignment handout

      Discrete Models I Homework

    • Discrete I in-class worksheet File
    • Discrete Growth Lecture Slides File
    • #3 Due Mon Assignment

      Read rest of 2.1 and review everything in section 2.2.
      2.1; 36, 51abde+(f)daily, 53, 58c(compounded continuously) (I'm replacing a and b with this new part.)
      2.2; 12, 19, 36, 39, 50, 54, 56, 63, 67, 88.
      Answer to 2.2; 36 is 2c+2.

    • CompoundingLimit File

    • On Monday, Aug. 30, bring your laptop or device with Excel or very comparable spreadsheet program.

    • BRING A LAPTOP COMPUTER on Monday Aug. 30 for our "Lab" work using an Excel spreadsheet.  So in-Lab will mean in-class with laptop.

    • Discrete Models II In-Lab File
    • Discrete II In-Lab Solutions File
    • IbuprofenGraph File
    • #4 Assignment

      Discrete Models II Homework

    • DiscreteIIHmwkSoln File
    • Cobweb Diagram in-class handout File

      Textbook section 14.2 covers Cobweb Diagrams!
      I made handouts for technique and problems, but the textbook is a consistent source.


    • #5 Assignment

      Discrete Models III Homework

    • Cobweb applet URL
    • Alternative Cobweb App URL
    • #6 Due Mon Assignment

      Read 2.3 and 2.4 (at least through p. 110).
      Unless instructed otherwise, you may use a calculator in any way that is helpful to solve any "word problem" throughout the rest of the course.  However, if you use it in some way other than simple numerical calculation, then you must show and/or explain what command (like Solve or Graph intersection) you used.
      2.3; 7, 16, 21, 25.
      Hint 7:  Trophozorites are single-cell organisms, so when they "divide" it doubles the population.
      Hint 16:  The "1 in n" chance is the number 1/n.
      2.4; 1, 55, 61, 91, A and B below:
      Prob A:  Derive (show steps where it comes from) the trigonometric identity for 1 + cot2 x  by using only identities on page 105.  First change to sin and cos, simplify to get one function.
      Prob B:  In the triangle right triangle with length 1 on the x-axis, positive angle theta, and opposite side length x. , find sin \(\theta\) in terms of x (with no trig function in answer).


    • Forensic example URL
    • 3.1 Limit Reasoning File
    • #7 Assignment

      Read 3.1; Formality of the page 134 rules will not be emphasized, but the conceptual introduction in previous pages is helpful, and you still need to understand all examples.
      3.1; 9, 10, 11, 12, 21, 22.  (On 21 & 22 and throughout Calculus, you must use Radians.)
      On all that follow, use good notation to show steps or explain reasoning; just an answer will not suffice.
      3.1; 38, 41, 45, 61, 79, 95, 96(Do you need to know constants are positive?).

    • #8 Assignment

      Read 3.2.
      3.1; 50, 54, 55 on all three, show algebra steps as in class and/or explain reasoning in a sentence; just an answer will not suffice.
      3.2; 2, 3, 6,
      3.2; 8, 9, 11, 14, 16, 
      Hint on  8 through 16:  You should be able to tell where it is discontinuous by just thinking about the formula domain.  However, you may graph the function to decide the limit as you approach a discontinuous point.
      3.2; 24, 38.
      True or False:  The function modeling Circadian Testosterone, on p. 122; 114, is continuous everywhere.  If false, where is it discontinuous?

    • #9 Assignment

      Read 3.3. (Also, do the 3.4 problems listed at the bottom.)  Remember units in applications.
      3.3; 6, 20, 25, 33, 34, 44.  You are required to follow the instructions below:
      On 20, use limit with algebra.
      On 25, use a table of values as on p. 158.
      On 34c, graph the function and get derivative from a graph tool (On TI89 graph, F5 Math, Derivative; On Desmos, can ask for f '(a)).
      3.4; 8, 9, 10.  (Since tangent line is drawn in, just take two convenient points, fairly far apart, to find slope of line.)

    • In class handout on definition of derivative File
    • #10 Assignment

      Read 3.4

      • Prob A.  If f(x)=x, prove f '(x)=1 by definition of derivative.

      • Prob B.  If f(x)=x4, prove f '(x)=4x3 by definition of derivative (expand (x+h)4).
      3.4; 1, 15+, 17+, 38, 39, 55.
      On 15 and 17, in addition to everything instructed, after you prove the derivative formula, use it to find the equation of the tangent line to the curve at x=3.

    • Differentiabul song URL
    • Example: Derivative Definition with Square Root File
    • #11 Assignment

      Read 3.5 and 4.1.
      3.5; 6, 7, 8, 9, 10, 12.
      4.1; 3, 12, 17, 20, 32.
      On 20:  Rewrite as powers of x; don't use quotient rule.

    • #12 Assignment

      Read 4.2.
      Prob A:  If f(x) = c u(x), prove f '(x) = c u'(x) by definition of derivative.
      4.1; 43, 57, 58abcd, 62, 71.  (Hints below; remember to include units in 62 and 71)
      4.2; 7, 19, 22, 29, 30, 33.   (Instructions specify use product or quotient rule, so you must!)
      Hint for 4.1 probs:  Easier not to use quotient rule, instead pull constants out front and/or use negative exponents.
      Hint on 56d: Units of BMI are just that, units of BMI. Describe the derivative as how much something changes for every what?
      Optional star (hand in separately within a week): do the pair of problems *(4.1;65 and 4.2;37 ).

    • #13 Due Wed 9/22, after class click this "quiz" to report self-grade

      Read 4.3.
      4.2; 43, 45.  (I don't like the 45a answer in back; a simpler form with only one H is better and makes 45b easier.)
      4.3; 11, 12, 22, 27, 33, 34, 38, 44, 51, 52.
      On 51 "explain the discrepancy" by showing that one answer can be algebraically converted into the other.

    • CrowWhelk File

    • Review #1 Friday 9/24 in class plus take home due by Monday at start of class.
      Covering material on assignments #1 through #13 (including chain rule).

      Usually three or four pages with space to work on the test.
      Notation and showing your work is important, not just answers.
      Similar to the variety of problems from the homework.
      Graphing calculator (bring one) use is unrestricted BUT:

      • Mark how calculator is used beyond simple number crunching; in particular, mark if you use calculator graph (sketch), solve or algebra (enter an algebraic expression to get simplification).
      • Limits and Derivatives must show "hand" steps and reasoning.
      • You must follow instructions, e.g. a particular problem may say:
        • use definition of the derivative (so answer or derivative rule are worthless), or
        • use quotient rule, or
        • use logarithms to solve.
      If you have extended-time accommodations or other reason why you cannot take this test in-class, contact Neidinger this week by Thursday to arrange pick-up and return.

      While in-class part is closed book, the TAKE HOME part is OPEN BOOK:  You are allowed to use of your text book and your notebook of materials of all kinds (including e-files) that you have gathered. Use of spreadsheet software will probably be necessary and you may use Desmos or other online calculator (tell me if you do).  You MAY NOT get assistance from anyone else or use the internet to research how to do a problem.  You may not reference other materials, not gathered in your personal collection before picking up the test.
    • Practice Test from a previous year File
    • Practice Test Solutions File
    • Review 1 take home F21 File
    • Review #1 -- submit Excel file here Assignment
    • Review #1 solutions File
    • ExponentialLimit File
    • #14 Assignment

      Read 6.4 Example 2 only (for now).
      Read 4.4.
      I suggest the following unusual order of sections and problems.
      4.3; 56, 58, 62ab.
      6.4; 15, 18, 19, 13.  (13 is trickier than the other three.)
      4.4; 3, 8, 15, 21, 27.

    • #15 Assignment

      Read 4.5.
      4.4; 41, 48, 60 as below, 67.
      4.5; 7, 14, 16, 23, 37, 57.
      Hints on 4.4; 48:  You may use calculator graph (y1(x) for V(t)) or Desmos to answer a,c,e.  On c, may find intersection with y=0.5.  On e, get value from graph (V'(240) in Desmos) but try symbolic derivative for practice (evaluation optional).
      On 4.4; 60: Just find I' for r=4,n=3, but leave the rest of the constants as letters; you don't have to do parts a and b.  This prepares you for the evaluations of parts a and b, but these are OPTIONAL and most easily done by typing the formula into some computing (TI-89 or Desmos) where you can specify constants (b=8) and evaluate at points.

    • FALL BREAK:  No office hours or help sessions on Thursday or Friday.  Enjoy the time off!

    • #16 Assignment

      Read 4.6
      On 40 may get derivative from graph, on all other problems you must show finding the derivative formula.
      4.6; 3, 7, 10, 18, 21, 33, 35, 38, 40.  
      p. 312; 76.
      On 76: Plot over 0 to 2 sec.  Measurements are positive going counterclockwise and negative going clockwise (as is usual in math).  So in d, positive acceleration corresponds to counterclockwise force.

    • #17 Assignment

      Read 5.1 & 5.2.
      5.1; 17+, 26+, 29+, 32+, 41, 44, 53, 56.
      The + means to also find (d) where a relative maximum is at x or relative minimum is at x.
      Hint on 17-32:  simplify y' by common denominator or factoring.
      Hint on 53 & 56:  The quadratic formula (p. R-13) can help find where derivative = 0.

    • Actual alcohol incr/decr URL
    • blood vessels photo URL
    • Poiseuille's equation for fluid flow resistance in tube URL
    • some blood vessel branching video URL
    • #18 Assignment

      You must find maximums or minimums by using the derivative.
      5.2; 15, 42ab, 46, 50, 53 as specified below.
      Hint on 42b:  Include both + and - when you take a 6th root or ^(1/6).
      On 46b, do find the time but actual maximum value is optional.
      On 53:  On (b-i), I require you to use csc functions instead of sin as in back of book.  On (j-m), change to sin and factor out sin functions.  On m, consider at or near endpoints 0 and pi/2.  Throughout, try to avoid looking at the back of book unless necessary; it's fine if you "get ahead" of what they are asking on each step.


    • Exercise 5.2; 42 plots File
    • 5.3Example File
    • #19 Assignment

      Read 5.3.
      5.3; 28, 33, 43, 48, 68, 69, 80, 92ab, 96, 103+find the maximum slope of R.
      Hint on 80:  sketch how c(t) could look and conclude signs for each of the three functions, and incr or decr for c and c'.
      On 92, all letters other than T are treated as positive constants.

    • Skin polygons as in 6.1; 49. URL
    • 6.1; 49 solve File
    • myelin sheath URL
    • #20 Assignment

      When finding max and/or min for the remainder of the course, you should show solving derivative = 0, not "maximum" from graph.  (In a very technically detailed or complicated function, may use Wolfram Alpha, TI-89, or equivalent, to solve an equation, or even d( ) to differentiate, if you LABEL that is what you did.)  Of course, assignments and problems may occasionally instruct otherwise.
      Read 6.1.
      6.1; 1, 7, 28, 47, 50+use 2nd deriv test, assuming all constants are positive,
      On 47: Graph only M, not derivatives. Hint: You can use quadratic formula to find the solution.
      6.1; 51&52&53 done together.
      6.2; 9.

    • CircleSquare (Wolfram Mathematica Notebook requires campus license) File
    • Do Dogs Know Calculus? article URL
    • Video of Elvis and Dr. Pennings URL

    • The 6.2 outline of steps for Solving an Applied Extrema Problem is pretty good -- I emphasized step 3 in class.  I would combine steps 4 and 6 into the following advice:
      Alternative ways to decide if a critical number c is a max or min:

      • First Derivative Test  (sign of f' on sides)
      • Second Derivative Test  (f''(c) sign)
      • With domain endpoints, compare f values (at all critical points and endpoints)
      • By graph (showing approximate extrema location that match your exact c)
      • Say "physical reasoning" when only one critical number and physically it must be max (or must be a min).
      Pick any one of these but remember to check one.  (See the CAUTION after the book outline.)

    • #21 Assignment

      Read 6.2
      6.2; 4(non-negative x and y is important; why?), 13, 20, 30, 32, 40, 42.
      Hint on 13: think of energy "cost" by using relative cost/mile where cost/mile on land is 1.

      *Optional Star:  Do two more problems: 6.2; 44 and the following Problem A: 
      Not only dogs know calculus but light does too!  When light hits water it bends because it moves faster in air than in water.  The angle is given by Snell's Law shown on p. 116.  Derive this law by minimizing the total time for light to go from start to finish.  From upper left point to lower right, label constants for the vertical distances through Medium 1 and Medium 2 and the total horizontal distance.  The variable is the horizontal distance x in Medium 1.  Take derivative of total time and set it equal to zero.  Do not solve for x but, instead, interpret the ratios as trigonometric functions and rewrite as Snell's Law.

    • #21 6.2 Optimization Word Problems Solutions File
    • #22 Assignment

      Read 6.3
      6.3; 3, 14, 17, 19, 38, 48.
      6.4; 3, 8, 16.

    • #23 Assignment

      Read 6.4; geometry formulas are on page A-10 (Appendix D).
      6.4; 21, 22, 23, 24, 25, 27, 28.

    • #23 Solutions 6.4 Related Rates File
    • Rotation related rates example File
    • #24 due Monday and "quiz" link for after class

      Read 6.5 but replace p. 352 with the following:  The linear approximation of f(x) for x near a is
      f(x) ≈ f(a) + f '(a)(x-a). This should approximate any f with a line, as in the point slope form f(x) ≈  y1 + m (x-x1).

      6.4; 30, 36.
      6.5; 1, 25, 29, 32, 35:  do all these problems using differentials.
      Exercises:  For each of the following, write down the linear approximation f(x) ≈ f(a) + f '(a)(x-a) for x near a; then, if requested, test it by using it to approximate the specific value(s).  (An example answer looks like: x^5 ≈ 1+5(x-1) for x near 1; test (1.003)^5 ≈ 1+5(.003)=1.015  (actual 1.01509...).)
      A.  f(x) = sin(x) for x near 0; test sin(.03); test sin(-.12)
      B.  f(x) = x^(1/2) for x near 25.
      C.  f(x) = ln(x) for x near 1; test ln(.996). 
      D.  f(x) = (1+x)^n  for x near 0; test 1.001^37.

      The "Quiz" is a way to record your grade out of 10 from in-class corrections.
      For Monday:  You may bring past assignment and problem numbers that you want to go over.

    • Review 2 practice test File
    • Review 2 practice test solutions File

    • Review #2 Wednesday 10/27 in class, then take home.
      Covering material on assignments #14 through #24.
      If needed in-class, I'll give (at start of test or in problem):

      • formulas for SPHERE and CONE on p. A-10 but know other formulas on that page.
      • D(ax) = (ln a)ax   and  D(loga x) = 1/[(ln a)x].  Memorize all other derivative rules that we have used.

      In-class is probably three pages with space to work on the test.
      Pick up TAKE HOME part due Friday.

      Notation and showing your work is important, not just answers.
      Similar to the variety of problems from the homework.
      Graphing calculator (bring one) use is unrestricted BUT:

      • Limits and Derivatives must show "hand" steps and reasoning; Maximums or minimums must be found by derivative (unless specifically told that you may get it from graph).
      • Mark how calculator is used beyond simple number crunching; in particular, mark if you use graphing or symbolic calculator to do something other than number calculation.
      • Problem instructions may specify "hand" steps or a specific technique (eg. second derivative test).
      While in-class part is closed book, the TAKE HOME part is OPEN BOOK:  You are allowed to use of your text book and your notebook of materials of all kinds (including e-files) that you have gathered.  You may use Desmos or other online calculator (tell me if you do), though same bullet requirements as above.  You MAY NOT get assistance from anyone else or use the internet to research how to do a problem.  You may not reference other materials, not gathered in your personal collection before picking up the test.
    • Review #2 solutions File
    • #25 Due Mon. Assignment

      Read 7.1
      7.1; 7, 16, 27, 31, 36, 38, 39, 43, 47, 48, 51, 59, 62.

    • 7.1 Antideriv Examples File
    • #26 Assignment

      Read 7.2
      Must show u and du on all problems except 37.
      7.2; 3, 8, 9, 12, 15, 18, 29, 31, 37, 40, 43, 46, 47, 49, 55, 60.
      On 60, show how the two answers are essentially equal.

    • 7.2TrigIntWorksheetSoln File
    • SpeedometerToOdometerGraph File
    • #27 Assignment

      Read 7.3
      7.3; 3, 4, 15, 36, 38, 41.  p. 420; 53.  Problem A below.
      On 4b, you may want to sketch y=f(x) and the rectangles to understand the integral; these are left endpoints, so it is not obvious.
      On 36, further instructions are in the paragraph above.
      p. 420 (Chapter Review): 53.
      Problem A:  Estimate the integral of sin(x^2) from 0 to 2 using
      (a): n=4 intervals and right endpoints; by hand except for simple decimal calculations.  (Three decimal places will suffice.)
      (b): integral approximation website below with Midpoints and n=10, 20, and 100.  Report six decimal places.

    • Integral Approximation Calculator URL
    • SpeedometerToOdometerGraph with A(x) File
    • #28 Assignment

      Read 7.4  Good notation is required.
      7.4; 3, 14, 21, 35, 40, 51, 53, 54, 60, 64, 65, 77.
      Hint on 60: use symmetry of graph.

    • Bring your calculator to class on Monday Nov. 8.

    • TrapRuleFormula File
    • #29 Assignment

      Read 8.1 and Extended Application p. 461-3.

      7.4; 84 version:  a. Just describe V(t) from t=0 to t=T.  b. Evaluate the given formula by first finding the integral value by calculator (say what command you use, fnInt is suggested).  (May ignore book's hint.)
      8.1; 9(show calculation steps using rule formulas), 15, 16, 17-20(see below), 37(just report your calculator's approximation of the integral).
      p. 463; 2 (Typo: the integral should be from 0 to 24, not 0 to t.)
      On 17 & 19, To compute all requested values, may use online app, record all digits, in a table (could use a spreadsheet): summarize results in a table of " n,  Trap,  Err,  Err*np " & corresponding for "Simp" in 19.  Hint: in finding p, you may assume that Simpson has a higher p than Trapezoidal and "approximately a constant" means just agreeing in a couple of digits.

      Optional Star: 7.4; *61+on (c) repeat for h=.0001 and also use calculator/computing to graph antiderivative f(x) on [0,1], write what you do and what you input.

    • Laminar flow in tubes (blood vessels) -- old video that shows it well URL
    • Laminar flow in tube (Poiseuilles eq) File
    • #30 Assignment

      Read 8.3
      On every problem that asks for a volume, also sketch the region to be rotated and sketch the solid of revolution.
      8.3; 12, 17, 24, 25, 31, 34, 36, 42.

    • #31 Assignment

      Do problems on handout (also linked here).

    • Homework31InverseTrigSoln File
    • #32 Assignment

      Read 11.1
      On all problems, solve for y if possible.
      11.1; 1, 9, 12, 15, 19, 23, 34, 52, optional star: pair *(39ab and 41)
      Problem A:  Find the general solution (solved for y) of dy/dx = 1 + y2

    • Folder with recording of 11/17/21 Lecture (for #33) URL

      Click on file zoom_0.mp4 in the folder.
      Sorry about Gallery View so lecture is only the right half of the screen.

    • DE software -- slopefield and numerical solutions (use RKF45) URL
    • #33 with handout for the day Assignment

      Do homework on back of in-class handout (also attached).

    • Zoom Recording of 11/19 (for #34) lecture URL
    • #34 "quiz" link after Mon. class

      Read 11.6 especially Example 2.
      Instructions for the following problems are changed to Moodle instructions below.  When using online slope field on this homework, you may simply answer the question (say from online graph or table) and/or hand-copy the solution curve if you clearly label the axes ranges.
      11.6; 3 Replace the "and 400 are infected 10 days later" with "and at the beginning of the epidemic (when y=100) the infection rate (y') is 14 people per day."  For (a) write a differential equation with initial condition (not the solution as in the back).  Then find equilibrium values and make a qualitative sketch of the solution curve for this initial condition.  (b) Use online slope field to estimate the answer to b.
      11.6; 10, 11, 12, 13.  The first sentence should be prefaced with the word "Initially," since the physical tank might hold at least twice as much over time.  On each of these problems, replace all instructions with:  (a) Write a differential equation with initial condition for y(t), the lbs of salt in the tank at minute t.  (b) If the DE is autonomous (10 & 13), find equilibrium values and make a qualitative sketch of the solution curve for this initial condition.  If not autonomous (11 & 12), use online slope field to make an accurate sketch over 100 minutes.  (c) Does the trend make physical sense?
      11.6; 14, 16.  As intended in the text; write and solve the separable DEs.
      The "Quiz" is a way to record your grade out of 10 from in-class corrections.


    • Zoom recording of 11/22 class (grade #34 on Moodle and review for test) URL

    • OFFICE HOURS BY APPOINTMENT this week.
      I will be happy to meet with you to go over questions or studying.  Just send an email to propose a time you want to meet.
      Avoid Tuesday morning until say 11:30.  Let's avoid Thanksgiving day and preferably not Sunday.

    • Practice Test File

      Ignore last part (d) of last question.  We are not covering the section on Euler's Method.  Instead, we covered the qualitative sketches of autonomous DEs.  Also, we have covered arctan and arcsin derivatives and corresponding antiderivatives, which are not on this practice test.

    • Practice Test Solutions File

    • Review #3  Monday 11/29 in class.
      Covering material on assignments #25 through #34.

      Expect 3 pages with space to work on the test and a take home page due Wed.
      Similar to the variety of problems from the homework.
      Notation and showing your work is important, not just answers.  In particular:

      Show u and du (with change of limits) whenever it is not exactly an antiderivative rule.  Exception: a linear u=kx+c, may simply produce a 1/k in the antiderivative, without showing u.

      Bring a calculator, especially for numerical evaluation of integrals (by calculator approximation, "hand" trapezoidal rule and/or simpson's rule).  Be able to use a online slope field output to draw in solution curve for a given initial condition. Calculator use unrestricted BUT:

      • Limits and Derivatives and Antiderivates must show "hand" steps and reasoning.
      • Mark how calculator is used beyond simple number crunching; in particular, mark if you use calculator to graph, solve, or algebra.
      • Problem instructions may specify "hand" steps or a specific technique or formula.
      While in-class part is closed book, the TAKE HOME part is OPEN BOOK:  You are allowed to use of your text book and your notebook of materials of all kinds (including e-files) that you have gathered.  You may be asked to use class online Apps and may use Desmos or other online calculator (tell me if you do), though same bullet requirements as above.  You MAY NOT get assistance from anyone else or use the internet to research how to do a problem.  You may not reference other materials, not gathered in your personal collection before picking up the test.
    • Rev3F21b Take Home File
    • Rev3F21 Solutions File
    • To follow Dec 1 class remotely, use #35 link to print sheet with one side being in-class worksheet (and the other side is homework).
    • Zoom recording for 12/1 class (for #35) URL
    • DiscreteLogisticCobweb File
    • DiscreteSimple (for use in homework if desired) File
    • Cobweb applet URL
    • #35 Assignment

      Hand in self-scheduled exam envelope with name on envelope and cards.  Don't enclose anything.
      Do Discrete Models IV Homework handout (also attached).

    • Zoom recording of 12/3 class URL
    • #35 solutions File


    • Zoom recording of 12/6 class reviewing for final URL

    • To complete course feedback surveys, students should go to http://moodle.davidson.edu and login. Students will be able to login to Moodle and access the survey even if you have not used Moodle for your course. Once logged in, they should see an “EvaluationKit” box on either the right side of the page or at the very bottom of the page (it is at the very bottom of the page on a mobile device). Some users need to use an incognito browser window in Chrome or a private browser window in Firefox in order to see the box. Please note that this box appears on the Moodle homepage, and not the page for your individual course. From there, they should click on the link that says, “Click here to complete your course feedback surveys” and then select the appropriate course (if any student is enrolled in more than one of your courses, they should pay careful attention to the course title). They should click on your course to begin the survey. Once they submit the survey for a particular course, the link for that course will disappear. Students who are unable to attend your class during the normal time will be able to access the survey on their own until December 7.

      Current Known Issue: Some users cannot see the EvaluationKit box on their Moodle homepages or the box appears without a link. This issue is typically resolved when using an Incognito or Private browser window in Chrome or Firefox.

    • Final Exam -- Self-scheduled exam system.

      The final exam is comprehensive and will cover a selection of problems from throughout the course.  Expect similar to the variety of problems from the homeworks and tests.  Problems might include ideas from multiple sections.  Be able to do the last homework; the last follow-up lecture is optional, though you should know the name "chaos" (for when an iteration bounces almost randomly around within a range of values).

      Expect nine or ten pages with space to work on the test.  If you use any scratch paper, you must enclose it in your exam envelope.  This is designed for about 3 times a 50 minute test (2.5 hr), but you have up to 3.5 hours max in an exam session.

      Bring a calculator, though derivatives and antiderivatives should be found by hand unless otherwise instructed.  Otherwise calculator use is unrestricted but write how calculator is used for anything beyond simple number arithmetic.  Some problems will specify things to show by hand, but I always want to see all steps you take using good notation.

    • Everyone will be required to take the exam in 3.5 hours during one of these periods.  I suggest you plan on the full 3.5 hours and if you finish early, great.  (Those with accommodations may extend the time as arranged; if the system is closed, return to slot in Registrar's Office door, writing time returned on the envelope card.)  

      Wednesday, Dec. 8th

      8:40am – 12:15

      1:40 – 5:15pm

      Thursday, Dec. 9th

      8:40 – 12:15

      1:40 – 5:15

      Friday, Dec. 10th

      8:40 – 12:15

      1:40 – 5:15

    • Monday office (Cham 3043) hour after class.
      Tuesday office hour by Zoom 10:50 - 11:50.

      OFFICE HOURS BY APPOINTMENT other times and during finals.
      Dr. Neidinger will be around most of the time, but send an email proposing a time you want to meet.