## MATH 102 Section 103 Sep-Dec 2016 Lecture Summary

 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, linearityquiz 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 continuedChapter 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.