Math 125: II - Dr. Loveless Essential Course Info My Course Website: math.washington.edu/~aloveles/ Homework Log-In (use UWNetID): webassign.net/washington/login.html Directions for Webassign code purchase: math.washington.edu/webassign Math Department 125 Course Page: math.washington.edu/~m125/

First week to do list 1. Read 4.9, 5.1, 5.2, and 5.3 of the book. Start attempting HW.

2. Print off the “worksheets” and bring them to quiz sections.

Today 1st HW assignments  Syllabus/Intro Closing time is always 11pm.  Section 4.9 - HW1A,1B,1C close Oct 4 - (Wed) (covers 4.9, 5.1, and 5.2) Expect 6-8 hrs of work, start today!

What we will do in this course: 4. Ch. 8-9 – More Applications We learn the basic tools of - , Center of Mass calculus which provide the essential - Differential Equations language for engineering, science and economics. Specifically, 5. Practicing , Trig and Precalc Students often say: The hardest part 1. Ch. 5 – Defining the Integral of calculus is you have to know all - Definition and basic techniques your precalculus, and they are right.

2. Ch. 6 – Basic Integral Applications Improving your algebra, trig and - Areas, Volumes precalculus skills will be one of the - Average Value best benefits you will gain from this - Measuring Work course (arguably as valuable as the course content itself). You will use 3. Ch. 7 – Integration Techniques these skills often in your other - by parts, trig, trig sub, partial courses at UW. frac

Entry Task: Differentiate 7 1. 퐹(푥) = − 5√푥3 + 4ln (푥) 푥10 6푥 2. 퐺(푥) = 푒 + 5 tan(푥) + 휋 3. 퐻(푥) = 2 tan−1(푥) − 3 + 푒

4. 퐽(푥) = 푥3 cos(4푥) + ln (2)

4.9 Antiderivatives Example: Goal: Before we jump into defining Give an of 푔(푥) = 푥2. (ch. 5), we need to remember some (in reverse).

Def’n: If g(x) = f’(x), then we say

g(x) = “the of f(x)”, and

f(x) = “an antiderivative of g(x)”

Examples (you do): Find the general antiderivative of 1. 푓(푥) = 푥6 1 1 2. 푔(푥) = cos(푥) + + 푒푥 + 푥 1+푥2 5 3 3. ℎ(푥) = + √푥2 √푥 푥−3푥2 4. 푟(푥) = 푥3

Initial Conditions Example: 푓′′(푥) = 15√푥, and There is no way to know what “C” is 푓(1) = 0, 푓(4) = 1 unless we are given additional Find 푓(푥). information about the antiderivative. Such information is called an initial condition.

Example: 푓’(푥) = 푒푥 + 4푥 and 푓(0) = 5 Find 푓(푥).

Motivational: You know the acceleration or velocity for some object. What is the original function for the position of the object?

Example: Ron steps off the 10 meter high dive at his local pool. Find a formula for his height above the water. (Assume his acceleration is a constant 9.8 m/s2 downward)