On Sunday morning, I went to gym to workout for an hour but hadn't stopped by McDonald's because I wasn't very hungry. It's Seafair weekends and Blue Angels' performances always draw locals' attentions. Since we went to Genesis Park to watch last year, we didn't go this year but may go next year or the year after. We generally participate this big event once every three years.
I planned to have my son catching up 2 sections of Chapter 5 of Calculus textbook, but I hadn't had chance to walk him through one section before we went to watch Ant-Man. There are two movie theaters at Alderwood Mall, one is AMC we generally go, another is Regals, which is older and smaller we used to go a lot. Ant-Man was only played at latter, so we went there this time. I had checked out a 3D show to be on at 3:50pm, but we were confused by the term of RPX on the panel and almost left. This wasn't our first time to watch 3D movie at this theater, our minds were just wired abnormally at that moment. Eventually, we bought the tickets and sat in the auditorium.
We were the only two audiences sitting in the auditorium until the play time was very close. It's a very fun movie and the environment in the auditorium was super. Tiny creatures can be as the same great heros as giants. This is sort of anti-Iron Man or Hulk.
After coming home, we had dinner and took rest. When I was ready to walk my son through Section 5.2, he was too distracted to follow my instructions. I didn't think he wanted to study and would be able to keep doing this everyday during this summer break though he proactively asked me to help him. Desire is always great but action is hard to take. I dismissed him for the night and told him that he didn't need to do this if he felt suffered.
However, I had gone through the text and formulas for Section 5.2 myself and been interested in the contents. Reviewing the book, I recalled that the first time I studied Differentiations & Integrals was at my first college as Civil Engineering major, I didn't have any clue and hated them, but second time was for pursuing economics/finance degrees, I started loving the theories, especially the practices; Third time was for the preparation of PHD in Economics entrance exams, I even thought about to utilize the knowledge to save the crisis all over the world. This time, I purely appreciate the beauties of calculus.
For instance, I wrote down the procedure of this example on a piece of paper myself to practice:
f(x) = x^(3) - 6x, taking the sample points to be right endpoints and a=0, b=3, and n=6.
DeltaX = (3-0)/6 = 1/2, then X1=0.5, X2=1.0, X3=1.5, X4=2.0, X5=2.5, X6=3.0
So, Limit from 0 to 3, (X^(3)-6X)dx = (0.5^(3)-0.5*6)*0.5+(1^(3)-1*6)*0.5+(1.5^(3)-1.5*6)*0.5 + (2^(3)-2*6)*0.5 + (2.5^(3)-2.5*6)*0.5 + (3^(3)-3*6)*0.5
= -3.9375
In addition, these algebraic representations are very useful in real world:
Sum of positive integers: 1+2+3+......+n = n(n+1)/2
(Knew this as teen)
Sum of square of positive integers: 1^(2)+2^(2)+3^(2)+......+n^(2) = n(n+1)(2n+1)/6
(Learned this when I was in college and remember it all the time)
Sum of cub of positive integers: 1^(3)+2^(3)+3^(3)+......+n^(3)=(n(n+1)/2)^(2)
(Might learn it when I was in college but totally forgot until on this Sunday)
However, the most practical knowledge I learned for my professional jobs was from my MBA.
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