## MATH 100 Section 102 Sep-Dec 2017 Lecture Summary

 We ek Date Contents 1 0905 Imagine UBC: First-day orientation 0907 outline: homepage, grading, quiz, Webwork, textbook, piazza, MLC, office hours §1.1-1.2 tangent and instantaneous velocity, Ex 1 (briefly as motivation) §1.3 definition of limit, Ex 1 2 0912 §1.3 Ex 2, 3, jump, one sided limits, Ex 4, oscillation, Ex 5, 5', blow up, Ex 6 §1.4 limit laws, Ex 1-3 0914 §1.4 cancellation of factors going to zero in a quotient, Ex 4-6, squeeze theorem, Ex 7-8 §1.5 definition of limit at ∞, Ex 1-5 3 0919 §1.5 nonexistence of limit at ∞, Ex 6, squeeze theorem at ∞, Ex 7 §1.6 continuity and one-sided continuity, Ex 1-4, arithmetic of continuous functions, Ex 5, composition of continuous functions, Ex 6-7 0921 §1.6 intermediate value theorem, Ex 8-10, bisection method, Ex 11 §2.1-2.3 definition of derivative, Ex 1 Quiz 1 4 0926 §2.1-2.3 more definitions, Ex 2-5, tangent, Ex 6, a differentiable function must be continuous, Ex 7-11 §2.4 linearity rule, Ex 1, product rule 0928 §2.4 and 2.6, Ex 2-3, Extensions of product rule, Ex 4-7, quotient rule, Ex 8-9 (we skip §2.5) §2.7 exponential functions, logarithmic functions, derivative of a^x 5 1003 §2.7 example for derivative of exponential functions §2.8 trigonometric functions, sin x < x < tan x, derivatives of sin, cos and tan, examples, trig functions on unit circle, formula for sin(x+y) §2.9 chain rule, Ex 1 1005 §2.9 alternative form and heuristic of chain rule, Ex 2-7 Quiz 2 6 1010 §0.6 inverse functions§2.10 the natural logarithm 1012 §2,10 continued§2.11 implicit differentiation notes for 0.6, 2.10 and 2.11 7 1017 §2.12 inverse trig functions and their derivatives §3.1 velocity and acceleration 1019 §3.1 Ex 2 continued §3.3 differential equations, exponential decay and growth, carbon dating, Newton's rule of cooling Quiz 3 8 1024 §3.3.3 population growth §3.2 related rates 1026 §3.4 constant, linear and quadratic approximations, coefficient formula for Taylor polynomials 9 1031 §3.4 Taylor polynomials for e^x, ln x, cos x and sin x. Remainder formula for R_0(x) using Mean Value Theorem (MVT), error bound and over/under estimate for R_0. (We skip percentage error of §3.4.7 and derivation of remainder formula of §3.4.9) 1102 §3.4 remainder formula for R_n(x), error bound and over/under estimate for R_n. §3.5.1 local and global maximum and minimum. Quiz 4 10 1107 §3.5.1-3.5.2 first and second derivative tests for local max/min, critical and singular points, finding global maximum and minimum. 1109 §3.5.2 one more example on global extrema §2.13 Rolle's theorem, Mean value theorem 11 1114 §3.6.1-3.6.3 sketching the graph of y=f(x) using info of f, f' and f'' 1116 3.6.3-3.6.6 graphs of odd/even and periodic functions, examples of global max/min Quiz 5 12 1121 3.6.6 one more example on graphing3.5.3 word problems for optimization, global max/min on open intervals, Ex 1-3 1123 3.7 l'Hôpital's rule, examples 13 1128 Two examples on 3.7, one example on 3.5.3 4.1 antiderivative 1130 4.1 examples comments on final exam, review 2016 final exam, teaching evaluation