DickCappels
- Joined Aug 21, 2008
- 7,453
Yes it does cover both.
A link to the book, which is out of copyright protection is in OBW0549's post #16.
A link to the book, which is out of copyright protection is in OBW0549's post #16.
If I may - about two years ago, I was at a point where I needed to increase greatly my calculus skillset, which I had hated since my undergraduate days. Then I barely scraped through (yes, I admit, I got C's in each class), and stayed away as much as possible - and avoided it where possible.The highest math classes that I took WAY back were technical math (for electronics technology) and pre-Calculus. I recall not enjoying pre-Calc so much, but I think I did like things like trigonometry. Playing with micro-controllers has rekindled my interest in electronics. How would I go about gaining functional ability in Calculus so I could work with and understand circuits better? Or would I be better off just cobbling things together?
Yes, now I am able to address the problems I needed to understand to describe the mode of electromagnetic emissions from a plasma jet. Why? Well, I helped develop a miniature electric propulsion system from scratch for a cubesat --- did all the work, etc. from concept to flight hardware, and AFTER it was done realized I didn't have a clue of how to describe the RF/EM being emitted from the system's plasma jet. And that was after 2 years of hw/fw/sw development -- and the RF/EM being emitted was a primary cause of communications blackout whenever the system was energized which cost me an arm and a leg to learn how to mitigateCalculus was an aha moment for me, like pulling the curtain away from the wizard of Oz. So for me personally, I'd recommend learning it even if you barely use it. It's a great tool for viewing the world, like learning some history or philosophy.
Please see the book reference I posted just now in my earlier message. Morris took the time to write out in long hand all of the reasoning of early calculus and his book was written in the sixty's for students at college level.I don't have Thompson's book. Does it explain what a derivative or integral are, or does it just show how to evaluate expressions that contain them?
I found it to be very much the opposite. But I was very fortunate to have teachers, both in high school and in college, that emphasized understanding the fundamentals and learning how to apply them to problems in general. Take your cone example. You say that, yes, you can use calculus to find the volume but you could also just look it up. Well, if you need to know the volume of a cone, look it up. Learning to do so using calculus isn't with the aim of repeating common results that are tabulated in tables, but to solve similar problems that AREN'T in the tables.This has been an interesting thread, that I have been wanting to reply too. It turns out that Calculaus has a lot of memorization.
Sometimes Kindle books don't reproduce equations and images well. I like paper sometimes, but, yeah, if the book is huge, the Kindle version is probably more practical!If you are kindle user (recommended) also try out the kindle edition so your big fat book (heavy) is absolutely portable wherever you need it.
I did come across the concept of PID for motor control and a heater control and noticed the the "C" connection. heh As I play with an Arduino more, I run into more math. So, if it isn't at the circuit level, it's in the code. Can't escape. hehNumerical integration and differentiation will allow you to write/understand a PID controller. I wrote a couple of unusual PID controllers.
Nope. I'm writing neural network code and the core of the learning algorithm is error back-propagation which requires using what is known as the chain rule and the partial derivatives of the outputs with respect to not only each of the inputs but also each of the weights. Considering that each layer typically has well over a thousand of these, it is important not only to be able to take the partials, but also to be able to generalize them so that they can be put into a loop structure.I did come across the concept of PID for motor control and a heater control and noticed the the "C" connection. heh As I play with an Arduino more, I run into more math. So, if it isn't at the circuit level, it's in the code. Can't escape. heh
I don't know about your specific case, but things like the sin of 45° shouldn't be too dependent on memorization. If you sketch (even just in your mind) a 45°-45°-90° triangle with sides of length 1 then the hypotenuse is, by the Pythagorean Theorem, equal to √2. Now you use the definition of the sine of an angle and you get 1/√2 (or √2/2). I almost always have to do an exercise like this if asked for the values of the basic trig functions for 30° of 60°. About all I remember reliably is that either the sine or the cosine is 1/2, but a quick mental sketch immediately lets me figure out all of them with confidence.Wbahn:
The memorization just killed me. Stuff like the basic integrals. Or even stuff like the sin of 45 degrees. I had to spend most of my time memorizing to be able to do the problems without the book in front of me. It took me 2-3 times longer to learn. There wasn't enough time on an exam to derive them. So, if you asked me what's the indefinite integral of sin(x); I'd know it contains cos(x) and it might have minus sign or what is the formula for integrate by parts.
Algebra has rules and since I learn kinesthetically or by repetition, every subsequent math class required Algebra so repetition was satisfied.
I really feed sorry for you -- you were done a serious disservice by the educational system you were in.I know that trick now, but I wasn't taught it. I was given a table to memorize. If someone would have taught me in 3rd or 4th grade that the digits in the 9x table add up to 9 in 4th grade. then I would not have had trouble with 54, 56, 63 and 64 for the 8x and 9x table. e.g 6*9 or even the product of 2 even number has to be even. Those sorts of rules would have helped me a lot. No, we had to memorize the times tables.
Sounds like learning how to take a test using a TI-83 calculator!I've looked at recent (well, actually about 15 years old at this point) trig texts and was very disheartened to find that how they taught trig functions was via a picture of a TI-83 calculator showing which buttons to press. Nowhere that I could find did they even mention the notion that the sine of an angle was defined as the ratio of two particular sides of a right triangle. I didn't have time to look to see what kinds of problems they expected students to be able to solve with that level of understanding.
It explains them in clear, concise, and accessible language. It was my intoduction and helped immensely when I encountered the more theoretical approach replete with theorems and delta-neighborhoods (shudder!).I don't have Thompson's book. Does it explain what a derivative or integral are, or does it just show how to evaluate expressions that contain them?
After being re-introduced to Calculus properly by Morris (see book reference above), I learnt a great way to learn the subject matter: Practice by hand, literally on pen and paper. And do this from time to time to focus your brain on the steps -- not at once, only in certain chunks at certain times. He literally gives narration about topics from various subject areas, and then gives the ANSWERS to the questions, leaving readers to take out their NOTEBOOK and pen (suggest, pencil and rubber to work out he steps -- if you succeed, you get the answer, if not, you work through the preceding examples contained in the associated chapters !I don't know about your specific case, but things like the sin of 45° shouldn't be too dependent on memorization. ... Others (myself included) would counter that concepts at this level are foundational and just like we "memorize" that 2 + 2 is 4, we should be able to internalize these concepts so that they become core knowledge that we can recall decades after last using them as things we simply "know" as opposed to things we have "memorized" and that thus have a shelf life before we forget them.
No kidding. An open book exam meant you had to know things much better and deeper. Anybody searching the textbook for a piece of information was already lost, and you knew who these people were immediately.OMG, where I went to school there was nothing so dreaded as an open book exam. It meant you had to know things at a much higher level.
http://djm.cc/library/Calculus_Made_Easy_Thompson.pdfI don't have Thompson's book. Does it explain what a derivative or integral are, or does it just show how to evaluate expressions that contain them?
by Jake Hertz
by Jake Hertz