## Martin Flashman's Courses - Math 105 Spring, '98

Last updated:4/22/98

TEXT:  Calculus in Context by Callahan, Hoffman, et al.

Assignments (subject to change)
due Wed.
1 Modelling the spread of a disease M.L.King Day
1/21 1.1
Discussion of model
2 Analyzing the model 1/26
1.1 First analysis of model
read 1.2 1.1:15, 16, 17, 18, 19 1/28 Backgrounds
1.2 Graphing, Technology,
Linear functions,etc
1.2:8,10,12, 11,14

Using a computer program,
Approximations
2/2 Finish review. 1.3 Using tech. for SIR model.
1.3:1-6
1.3
Appendix A as appropriate for 1.3 (SIR)
1.2:16,17,18, 21, 19, 23, 24, 25, 27 2/4 Breath, then Begin Better Approximations for SIR. read 1.4
1.4: 6, 7
4 Euler's method 2/9Euler's method
SIR estimates
dt->0, h-> infinity
1.4: 1-4
P'=.00005P
P(0)=500,000
Est. P(3)  with n=3, 30
2/11Begin Rates:
Also Logistic Model discussed with Euler
3.1:1-6
5 The Derivative 2/16 Rates and the derivative. Finding and estimating rates for functions. Read 3.2
3.1:7
3.3: 2(a,c),6,14,17
2/18 More on the derivative: the microscope equation (local linearity),the global view of f', qualitative graphing of f' from the graph of f. read 3.3
3.3: 9a,10(a,c),13
3.5: 1, 5
6 2/23 The derivative of xp, with p = 2,3,-1 3.3 3.3: 6(a,b,e,g), 8(a,b,d),9 2/25 More derivatives, velocity, Leibniz notation. 3.5 3.5:10,17,18,19
7 3/2 The Chain Rule 3.6 3.6:1(a,e),2(a-d),4,8,10 3/4 Product and Quotient Rules  5.1 5.1: 1(a-i), 2(a-j)
3/9 Exponential functions. Differential equations. 4.2(thru p181)
4.3(thru p204)
4.2: 1(a,b),2, 4(a,b),5, 8
4.3: 3(a-e), 8
3/11 Logarithmic functions.  4.4(thru p221) 4.4:3, 4
9 3/16 No class-
spring break
3/18 No class-
spring break
10  3/23 More on logs and exp, solving de's y'=f(t) 4.4 (p 223-4)
4.5
4.4: 5, 7, 9,15, 16
4.5: 1-3
3/25 Slope fields Antiderivatives
(linearity rules)
11.1(p 608-9,617bottom-8) 4.5: 4, 5
11.1:10( 1st 6),14
11 3/30 Graphing features. Continuity,first derivative analysis, begin extrema 5.3,5.4 5.3: 1,2, 3(a-c),4,5,7 4/1More on extremes 5.4 5.3: 9-11,14
5.4: 2,3,5
12 4/6 Newton's method 5.5 6.1  5.5: 2,5,6
6.1:1-3,6-8
4/8 More examples of extrema and Newton's Method
13 [Exam II?] 4/13Euler and reimann sums and the integral 6.2 (p 308-314)
6.3
6.2:2,16-20 4/15The Fundamental Theorem 6.4
14 4/20 More on the Fundamental Theorem and the Definite Integral.  4/22 Substitution.
Applications of the definite integral
Average value.
Begin Darts
6.3:p328-333,335-339,
346-48, 351
6.4
11.1: p608-9,614-620
11.2:626-630
6.3:1,2,19,20
6.4:1,3,7, 10(a,d,e,f,h), 11(a,c,d,e,f), 12(a-c),13a
11.1:21(a,b),24,25,26
11.2: 1(a,c,d,n)
15 4/27 More applications of the integral: Separation of variables 11.4 11.2: 2(a-c,e)
11.4: 2(a-c)
4/29 logistic growth.
Estimates of Integrals,Trapezoid.
Volume, probability.
6.3  p339-346
11.6 Trapezoid rule
p324-326 on Volume.
p307 on work
6.2:13
6.3:9
16 5/4 review application: implicit and logarithmic differentiation, related rates. 5/6 Breath!