110.109 CALCULUS II
Week 7 Lecture Notes: March 14 - March 18
Improper Integrals (contd.)
Go back to the example of an integral where the integrands is f (x) =
on the interval [b, 1], where 0 < b 1. For a choice of b here, we get
1
1
1
11
= 1 + > 0.
dx =
110.109 CALCULUS II
Week 3 Lecture Notes: February 14 - February 18
lecture 1
Today, I started with some basics about dierential equations (called ordinary dierential equations, or
ODEs). I began with the denition of the order of an ODE, dened as the numb
110.109 CALCULUS II
Week 4 Lecture Notes: February 21 - February 25
lecture 1
Today, I decided to go over some of the content of last Fridays lecture, given by my guest Professor
Nero Budur. The topic was Section 9.5 Linear Dierential Equations. The most
110.109 CALCULUS II
Week 5 Lecture Notes: February 28 - March 4
lecture 1
Today, we start with an example of how to use a parameterization to calculate the area between a
parameterized curve and the x-axis.
Example 1. Calculate the area between the upper
110.109 CALCULUS II
Week 6 Lecture Notes: March 7 - March 11
Arc-length in Polar Coordinates
Today is a short day, due to the fact that for the second half of this lecture, I want to focus on the midterm
exam coming up next class, its format and the areas
110.109 CALCULUS II
Week 8 Lecture Notes: March 28 - April 1
Lecture 1: Section 10.2 Series
Today we start the discussion on a series, basically the sum of the terms of a sequence:
Denition 1. The sum of all of the terms in a sequence cfw_an is called an