Date |
Topic |
Reading |
Homework Problems Due |
| Aug 22 |
Introductions and Course Overview
PowerPoint Course Overview (pdf file)
TI-89 Tutorial (see Algebra, Trig, Calculus menu for Solve and Factor commands) |
|
|
| Aug 24 |
Populations and Drugs
|
2.1 |
(show work, check with TI-89)
1.1: #22, 26
1.3: #64, 68
1.4: #42
1.5 #44 |
| Aug 26
|
Logarithmic functions |
2.2 |
2.1: #20, 24, 28, 32, 37, 38 |
| Aug 29 |
Additional exponential models; Newton's Law of Cooling |
2.3 |
2.2: #12, 20, 36, 40, 50, 56 |
| Aug 31 |
Discrete models with Excel
Meet in Chambers 3146. Half of the class will meet at a time to be determined by this poll. |
14.1
Excel tutorial (pp. 1-10) |
2.2 #68, 82
2.3 #6, 10, 14, 20, 24, 25, 28, 30 |
| Sept 2
|
Equilibria, Stability and Chaos
Cobweb diagrams animated gif
Cobweb for logistic in Mathematica (download CDF player) |
14.2 |
14.1 #2, 4, 6, 10, 12, 14*, 18*, 20*
*do the last three problems with Excel, find the population for the next 12 years (not 4, as instructions say), graph the resulting population as a function of time, turn in a printout showing the numbers and the graph) |
| Sept 5
|
Discrete Population and Logistic Models, cont.
ibuprofen example spreadsheet |
|
14.2 #13, 14, plus:
Discrete Models HW #2 (print and turn in hard copy with solutions)
|
| Sept 7 |
Limits |
3.1 |
Discrete Models HW #3
|
| Sept 9 |
Continuity |
3.2 |
3.1: #12, 26, 28, 30, 36, 44, 46, 50, 52, 81, 82, 83 (show your work by hand and check with the TI-89 limit function) |
| Sept 12 |
Average and Instantaneous Rates of Change
Mathematica demo |
3.3 |
Worksheet
3.2 #8, 14, 20, 24 |
| Sept 14 |
Definition of the Derivative
Graphical Differentiation |
3.4 and 3.5 |
3.3 #6, 14, 24, 31, 33 |
| Sept 16 |
Class cancelled - turn in HW on my office door by 5 p.m. |
|
3.4 #3, 8, 18, 20, 34, 36, 46
3.5 #7-14 |
| Sept 19 |
Review I Preparation
Everyone can do math! |
|
|
| Sept 21 |
REVIEW I |
| Sept 23 |
Optimization: Blood Vessel Branching
Circulatory system: Why do blood vessels branch the way they do?
Angiogenesis
Chick embryo
Poiseuille's equation and blood flow
- Relative extrema (section 5.2)
- Techniques for finding derivatives (section 4.1)
- Chain rule (section 4.3)
|
4.1, 4.2, 4.3, 5.1, 5.2 |
REVIEW I Takehome problems |
| Sept 26 |
Optimization: Nerve Sheath |
4.5, 5.1 |
Show all derivative rules by hand; check with calculator:
4.1 #2, 14, 20
4.2 #26, 28, 30
4.3 #8, 12, 24
5.2 #4, 6, 8 |
| Sept 28 |
Optimization: Do Dogs Know Calculus?
Optimal pursuit of frisbees, baseballs, mates and prey |
6.1, 6.2 |
4.2 #33
4.3 #36, 44, 58
4.5 #12, 36, 47, 48
5.1 #14, 22
5.2 #12, 18, 22 |
| Sept 30 |
Nerve sheath and Elvis, continued
The crow and whelk model |
|
4.2 #22, 38, 40
4.3 #54, 60
6.1 #20, 24, 44
|
| Oct 3 |
Applications of the Derivative:
Biomechanics and Enzyme Kinetics
|
4.4, 4.6 |
5.2 #26, 38
5.3
#30, 42, 52, 54, 58, 62 |
| Oct 5 |
Linear Approximation |
6.5 |
4.4 #20, 30, 34
4.6 #18, 22, 40
6.2 #4, 6, 15
|
| Oct 7 |
Related Rates |
6.3, 6.4 |
Linear approximations homework
|
| Oct 10 |
FALL BREAK |
| Oct 12 |
Related Rates, cont.
Strain-gauge plethysmography: method, equipment, application |
6.3, 6.4 |
6.3 #16, 30, 35
6.4 #20, 22
|
| Oct 14 |
Related Rates, cont.
Asteroid with Spirograph [use settings of 60, -15, 15]
|
|
6.4 #10, 14, 24, 25, 28 |
| Oct 17 |
REVIEW II |
| Oct 19 |
Integration: Antiderivatives |
7.1-7.2, 7.5 |
|
| Oct 21 |
NO CLASS |
|
|
| Oct 24 |
Area and Definite Integrals |
7.3 |
7.1 #45, 46, 47, and Worksheet |
| Oct 26 |
Integration: Pollution and Thermodilution
|
7.1-7.3, 7.5 |
7.3 #4, 10, 14, 16, 18 |
| Oct 28 |
Integration: Fundamental Theorem of Calculus |
7.4 |
7.2 #37, 38
7.3 #24, 25, 26, 32 |
| Oct 31 |
Integration: Volume and Average Value
|
8.3 |
7.4 #36, 42, 44, 56, 58, 60 |
| Nov 2 |
Integration: Numerical Integration |
8.1 |
8.3 #12, 14, 25, 34, 36 |
| Nov 4 |
NO CLASS |
|
|
| Nov 7 |
Differential Equations Models |
11.1, 11.6 |
8.1 #15-21 (17, 19, and 21 with Excel; print each problem on a separate sheet)
|
| Nov 9 |
Qualitative Solutions: Slope Fields
Mathematica file
DField Applet
Slope Field Applet |
N/A |
11.1 #8, 16, 20, 32
|
| Nov 11 |
Differential Equations Models, cont.
Group Project Assignment Guidelines |
11.1, 11.2, 11.6 |
Slope field HW |
| Nov 14 |
Differential Equations Models, cont.
|
11.1, 11.2, 11.6 |
11.2 #26, 32
11.6 #10, 11, 12, 13 (solve by separation of variables, if possible, or by drawing slope field if not separable)
|
| Nov 16 |
Euler's Method
Applet
|
11.3 |
11.6 #3, 4, 14, 15 (solve by separation of variables, if possible, or by drawing slope field if not separable)
Group Project Topic Due
|
| Nov 18 |
Prepare for Review III |
|
11.3 #8, 31 (Do Euler's Method by hand) and #18, 20 (Euler's Method with Excel). Finally, use Euler's Method in Excel to solve the equation in #18 and 20 with a small enough h to achieve error < 0.0001.
|
| Nov 21 |
|
| Nov 23 |
THANKSGIVING BREAK |
| Nov 25 |
| Nov 28 |
Case Study: Can We Save This Child? |
Handout |
Work on project |
| Nov 30 |
Case Study: Can We Save This Child? |
Handout |
Work on project (Sample layout for PPT) |
| Dec 2 |
Group Project Presentations |
|
Project Due; Presented in class |
| Dec 5 |
Group Project Presentations, cont.
|
|
Project Due; Presented in class |
| Dec 7 |
Prepare for Final
Course evaluations |
Formula Sheet |
|
| Dec 9-15
|
Final Exam Period (self scheduled exam) |
