Week 13 of m171
(§ 3, Mr. Lane)
24–28 April 2017

Math Learning Center (in Math 011) has tutors:
9am–4pm on Monday–Thursday and 9am–1pm on Friday

math@Mansfield (Library) has tutors: 6:30pm – 9:00pm on Sunday–Thursday

math@Mansfield (Library) has tutors: 6:30pm – 9:00pm on Sunday–Thursday

- Monday [d42] (24 Apr 2017)
WeBWorK:
RQ-6-1 closes at noon
- Study section 6.1
(
*Antiderivatives Graphically and Numerically*).- Examples 1–3 omit formulas and detailed computations in favor of emphasizing relations between graph of a continuous function and graphs for some of its antiderivatives.
- Notice how Example 4 does a
**connected sequence**of definite integral calculations. - Revisit Example 1 (page 320). Figure 6.1 shows a graph which
can be described with a piecewise expression.
You can find an explicit (but piecewise) expression for an
antiderivative of the function graphed in that figure.
- Find an antiderivative for the first piece: derivative of this answer must be the correct constant.
- Find an antiderivative for the second piece: derivative of this answer must match the decreasing linear part of Figure 6.1
- Adjust your second partial answer, if necessary, so that
it beomes continuous with your first partial answer
**at**the single point where they need to match. - Compare a graph of your result
(
*a piecewise antiderivative*) with the curves in Figure 6.2.

- Work on these items at end of §6.1: 3, 5; 12, 13, 15, 17, 23; 31, 33, 34, 35

- Study section 6.1
(
- Tuesday [d43]
WeBWorK:
RQ-6-2 closes at noon,
day-41 closes at 11 pm
- Study section 6.2
(
*Constructing Antiderivatives Analytically*). - Work on these items at end of §6.2: 9, 15, 23, 35, 39, 59; 64, 71, 73, 79, 81; 85, 90, 91, 95

- Study section 6.2
(
- Wednesday [d44]
WeBWorK:
RQ-6-3a closes at noon,
day-42 closes at 11 pm
- Study section 6.3 (
*Differential Equations and Motion*) through Example 3 (pages 335–6). - Work on these items at end of §6.3: 1, 5, 9, 12; 13, 15, 16, 21, 22, 25; 41, 43, 45, 47, 49, 51

- Study section 6.3 (
- Friday [d45]
WeBWorK:
RQ-6-3b closes at noon,
day-43 closes Saturday at 11 pm
- Write-up solutions of these three problems —
show your work and interpret your results. Hand-in your written
homework at the
**start**of Friday's class.**section**5.4 6.1 6.2 **problems**34 16 62 - Read
**History of the Equations of Motion**on page 336. (Relevant discussion, with interactive demos, is online at www.pbs.org/wgbh/nova/pisa/galileo.html) - Work on these items at end of §6.3:
**2**; 29, 31, 33,**35**, 37, 39; 40, 48, 52, 53, 54 - Study first three paragraphs of the
**Slope Field**discussion on page 351 at the end of chapter six (but skip parts a,b,c).- Sketch a slope field for
**dy/dx = 1 / (1 + x**, then sketch the solution thru point (0,2)^{2}) - Sketch a slope field for
**dy/dx = (−1/4) y**, then sketch the solution thru point (0,2) - After working on problem 6.3:2, consider how a slope field could help visualizing other solutions to that differential equation.

- Sketch a slope field for
- Maple (a Computer Algebra System available to all UM students) has
procedures to display a slope field and to sketch one or more solution
curves. This will be demonstrated during class on Friday.
Differential equation
**dy/dx = −2 y**is an important example; problem 6.3:2 is also interesting.

- Write-up solutions of these three problems —
show your work and interpret your results. Hand-in your written
homework at the

© Richard B Lane
Last modified: 21 April 2017, Friday 09:50