| We ek |
Date | Lec- ture |
Contents |
| 1 | 0905 |
Labour Day | |
| 0907 | L01 |
outline and overview, §1.1 power functions |
|
| 0909 | L02 | §1.1 an example §1.2 cell size, §1.2.3 even and odd funcitons |
|
| 2 | 0912 | L03 | §1.2.3 examples §1.4 sketching of combined power functions |
| 0914 | L04 | §1.5 Michaelis-Menten Kinetics and Hill functions §2.3 average rate of change, slope of secant line |
|
| 0916 | L05 | §2.4 average velocity and instantaneous velocity §2.5 + Appendix D: limit |
|
| 3 | 0919 | L06 | §2.5 definition of derivative §3.1 geometric view of derivative, slope of tangent vector, sketching df/dx for given gragh of f(x) §3.2 definition of continuity |
| 0921 | L07 | §3.2 examples of removable/nonremovable
discontinuity,
definition of derivative revisited with examples,
limit of (sin t)/t as t goes to 0 §3.3 computation/approximation of derivative using finite difference |
|
| 0923 | L08 | §3.3 example: computation by spreadsheet,
spreadsheet example
§4.1 Rules for differentiation: power rule, linearity quiz 1 and quiz 1 solution |
|
| 4 | 0926 | L09 | §4.1 product Rule, quotient Rule, chain Rule |
| 0928 | L10 | §4.2 antiderivative of power functions, application to
position, velocity and acceleration §4.3 sketch antiderivative y(t) from the graph of f(t)=dy/dt §5.1 tangent line and its x-intercept, introduction to Newton's method |
|
| 0930 |
L11 | §5.3 linear approximation §5.4 Newton's method, spreadsheet example §5.5 tangent line from an outside point |
|
| 5 | 1003 |
L12 | §5.5 continued §6.1 increasing and decreasing, the sign of df/dx |
| 1005 |
L13 |
§6.1 -§6.2: examples, concave up/down and the sign of
d^2f/dx^2 | |
| 1007 |
L14 | §6.2 Example 5 §6.3 Sketching the graph of f(x) using the signs of f' and f'' quiz 2 and quiz 2 solution |
|
| 6 | 1010 |
Thanksgiving Day |
|
| 1012 |
L15 |
§6.2.3 Types of critical points, first and second
derivative tests §6.3.1 Absolute maximum and mimimum |
|
| 1014 |
L16 | §7.1 Some biological optimizations, Examples 7.1 and
7.2 §7.2 Optimization under constraint, Example 7.3 |
|
| 7 | 1017 |
L17 |
§7.2 Example 7.4 §7.3 Example 7.5 absolute maximum may occur at end point §7.4 optimal foraging |
| 1018 | Midterm Exam: Tuesday October 18 evening | ||
| 1019 |
L18 |
§7.4 continued supplement: least square |
|
| 1021 |
L19 | least square continued Chapter 8. Chain rule and its application to optimization |
|
| 8 | 1024 |
L20 | optimal attention,
spread
sheet example
§9.1 Related rate, Examples 1 and 2 |
| 1026 |
L21 | §9.1 Examples 3 and 4 §9.2 Implicit differentiation, Example 1 (pic) and Example 2 (pic) |
|
| 1028 |
L22 | §10.1-10.2 Exponential functions and their derivatives |
|
| 9 | 1031 |
L23 | §10.3-10.4 Inverse functions and logarithmic functions |
| 1102 |
L24 | §11.1-11.2 Differential equations (DE) for exponential
growth and decay |
|
| 1104 |
L25 | §11.3 exponential decay §13.1 nonlinear DE, qualitative study |
|
| 10 | 1107 |
L26 | §13.2 slope field, solution curve, and phase line analysis,
Examples
1-4 |
| 1109 |
L27 |
§13.2 Example 5 §12.3 Linear differential equation y'=a-by, terminal velocity, Newton's law of cooling, Examples 1-3 |
|
| 1111 |
Remembrance Day |
||
| 11 | 1114 |
L28 | §12.3 phase line analysis for Newton's law of cooling and general linear DE,
meaning of b, solution formula, characteristic time |
| 1116 |
L29 | §12.3 example of characteristic time, snow melting DE §12.4 Euler's method, introduction |
|
| 1118 |
L30 | §12.4 Euler's method, example 1,
spreadsheet
example 1,
1b
quiz 3 and quiz 3 solution |
|
| 12 | 1121 |
L31 | §12.4 Example 2, Euler's method applied to logistic equation,
spreadsheets
example
2
§13.3 finding inflection points for solutions of the logistic equation, the DE system for a model of spreading of disease |
| 1123 |
L32 | §13.3 study of the DE system for a model of spreading
of disease §14.1 trigonometric functions, angle-sum identities |
|
| 1125 |
L33 |
§14.1 double angle formulas and other trig functions §14.2 periodic functions §14.3 inverse tan function arctan |
|
| 13 |
1128 |
L34 |
§15.1 derivative of trig functions §15.2 changing angles and related rates |
| 1130 |
L35 |
§15.2 continued §15.3 Zebra danio's escape responses |
|
| 1202 |
L36 |
conclusion and review |
|
| 1212 |
Final Exam: Monday December 12 8:30am-11am at MATH 100. | ||