The Manga Guide to Calculus
Hiroyuki Kojima
Language: English
Pages: 256
ISBN: 1593271948
Format: PDF / Kindle (mobi) / ePub
Noriko is just getting started as a junior reporter for the Asagake Times. She wants to cover the hard-hitting issues, like world affairs and politics, but does she have the smarts for it? Thankfully, her overbearing and math-minded boss, Mr. Seki, is here to teach her how to analyze her stories with a mathematical eye.
In The Manga Guide to Calculus, you'll follow along with Noriko as she learns that calculus is more than just a class designed to weed out would-be science majors. You'll see that calculus is a useful way to understand the patterns in physics, economics, and the world around us, with help from real-world examples like probability, supply and demand curves, the economics of pollution, and the density of Shochu (a Japanese liquor).
Mr. Seki teaches Noriko how to:
- Use differentiation to understand a function's rate of change
- Apply the fundamental theorem of calculus, and grasp the relationship between a function's derivative and its integral
- Integrate and differentiate trigonometric and other complicated functions
- Use multivariate calculus and partial differentiation to deal with tricky functions
- Use Taylor Expansions to accurately imitate difficult functions with polynomials
Whether you're struggling through a calculus course for the first time or you just need a painless refresher, you'll find what you're looking for in The Manga Guide to Calculus.
This EduManga book is a translation from a bestselling series in Japan, co-published with Ohmsha, Ltd. of Tokyo, Japan.
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quantity determined by the intersection point E ? Loss of benefit to society The overall benefit to society is reduced by the amount corresponding to the empty area in the figure. pf F E G xf Do you get it? Yes, I will report my stories using calculus, too. I also think velocity and falling bodies are good topics to write about. I’m going to look into them! Applying the Fundamental Theorem 105 The Calculus News-Gazette ¥50 The Integral of Velocity Proven to Be Distance!
same data that you used in your article, isn’t it? It’s from Burnham CHemical. We received the document itself from a whistleblower. We've already checked its credibility with other sources. I can’t publish my new story yet. Ah, yes...what’s the source of this data? But I will lend you the data that I have collected so far. The similarities are encouraging. 148 Chapter 5 Let’s Learn About Taylor Expansions! Wipe Wipe I was so anxious to know...I’m sorry. I never imagined you would be
and gn(x)gnabout x = ... n 2 n 2 2 gn ( x ) gn ( n2 ) = dividing gn(x) by this... we get hn , the scaled function Cx n Cn n 2 Since S c r ib b le hn ( x ) = n Sc ri bb le n Cx = n! x ! (n − x ) ! n Ah, so many coasters... So then... Cn = 2 ( n 2 n! ) ! ( n2 ) ! Divide: n we consider gn( ) 2 instead of gn(x). ( n2 ) ! ( n2 ) ! ( n ) ! ( n2 ) ! n! = 2 × hn ( x ) = x ! (n − x ) ! n ! x ! (n − x ) ! What Does Taylor
Expansion Tell Us? 169 So many...wasted coasters... Well, we now n convert the unit into 2 since x is away n from the center . 2 n 2 is the standard deviation. If you don’t know statistics, simply regard it as a magic word!* r Ig. .. no re d... Ab a ad ac * Standard deviation is an index we use to describe the scattering of data. 170 Chapter 5 Let’s Learn About Taylor Expansions! br a! In other words, n n z=x + 2 2 and substitute x in hn . We set in this way, we change the
variable. The new one, z, is the number of standard deviations away from the center. n n 2 ! 2 ! and get hn ( x ) = n n n n z ! − z! + 2 2 2 2 n n z n − + 2 2 We take a ln of each side.* ln hn ( x ) n n n n n n z ! − ln − = ln ! + ln ! − ln + z ! 2 2 2 2 2 2 * We use ln ab = ln a + ln b d ln = ln d − ln c c Now we need to calculate this,
