Post by Admin on Jul 17, 2018 22:30:23 GMT
Discovering calculus with the HP-28 and the HP-48 / Robert T. Smith, Roland B. Minton ( 1991 )
www.amazon.com/Discovering-Calculus-Hp-28-Hp-48-Robert/dp/0070591792/ref=sr_1_1?ie=UTF8&qid=1531864515&sr=8-1&keywords=Discovering+calculus+with+the+HP-28+and+the+HP-48
And remember those HP-28's, unfolding with buttons on both sides:
www.hpmuseum.org/hp28c.htm
www.hpmuseum.org/img/28cs.jpg
www.hpmuseum.org/img/28cm.jpg
www.hpmuseum.org/3qs/28c3q.jpg
Now first of all, about the book, it is more about calculus than it is about calculators. But when it comes to people like these authors, who have earned doctorates in Mathematics, they are going to command my respect in a way which few others ever could.
It sounds like the 28 came out a couple of years before the 48. The book talks about RPN (Reverse Polish Notation), but never about RPL (Reverse Polish Language). But these machines are clearly using RPL.
They are very much different from my HP-41. With that you had the standard 4 level stack, they called it, from the bottom, x, y, z, t. But these newer machines have nearly infinite stacks, having 32k bytes of memory.
So in the stack you can enter a real number. You can also use the hash tag to make it binary. Leading 0 to make it Octal, leading with Ox to make it hexadecimal. It shows this on the front face of the model 28, that it is 'objects' which go on the stack. Lead with double quotes for strings, and single quotes for variables, parentheses for complex, square braces for vectors and double square braces for a matrix.
Curly braces for a list. single quotes for an algebraic equation, and double less than for a program.
In my opinion this is all very interesting, but they have gone beyond the point where this is really workable. A calculator will always have limits in size of keyboard and display, and that it does not have disk drives. Beyond a point, you want a desk top computer instead.
And I feel somewhat vindicated in this in that as I know, HP followed on with the 49, and it did more than the 48. Then the 50, which presumably did more, and it was the first to have an ARM processor, instead of a fully custom chip. But then they have dropped all these. And now they have the HP-PRIME, which undoubtedly does much, but they don't talk about RPL any more, only RPN. So I feel that they have scaled back.
I also notice that in their stored equations and programs on the 48 and 28, they are algebraic, not RPN. With my 41, it as all RPN keystrokes, nothing algebraic at all.
And then as much as their 28 and 48 do, with all the various data objects, I feel that it still does not go far enough to do all which is commonly required in applied mathematics.
In particular, it often goes to matrices where the elements are not just polynomials in a complex varialble, but rational polynomial functions in a complex variable. So you need to be able to do all manner of root finding, factoring, multiplications, and then root locus diagrams. And this is for Frequency Domain. For Time Domain you also get into similar types of math.
And then there are newer things too, and some stuff starting to use Tensor Analysis, formerly reserved only for General Relativity, and there is still more which has come in.
So while it has gone beyond workability for a calculator, I feel that it still does not go anywhere's near what is really needed. MATLAB and Mathematic do much, but I feel that there is still a vacuum.
And then so much of the 28 and 48 is about graphing. And then TI does this too, and the new HP-Prime also.
But if you are taking a test you can use a calculator to get high precision answers easily. But if you need it to show you how to graph stuff, and with asymptotes and all, you are in deep shit. You do not understand the material. The calculator then will just waste you time.
If on the other hand you want to explore a new and interesting topic in graphs, a desktop computer can do a better job.
So enough said.
www.amazon.com/Discovering-Calculus-Hp-28-Hp-48-Robert/dp/0070591792/ref=sr_1_1?ie=UTF8&qid=1531864515&sr=8-1&keywords=Discovering+calculus+with+the+HP-28+and+the+HP-48
And remember those HP-28's, unfolding with buttons on both sides:
www.hpmuseum.org/hp28c.htm
www.hpmuseum.org/img/28cs.jpg
www.hpmuseum.org/img/28cm.jpg
www.hpmuseum.org/3qs/28c3q.jpg
Now first of all, about the book, it is more about calculus than it is about calculators. But when it comes to people like these authors, who have earned doctorates in Mathematics, they are going to command my respect in a way which few others ever could.
It sounds like the 28 came out a couple of years before the 48. The book talks about RPN (Reverse Polish Notation), but never about RPL (Reverse Polish Language). But these machines are clearly using RPL.
They are very much different from my HP-41. With that you had the standard 4 level stack, they called it, from the bottom, x, y, z, t. But these newer machines have nearly infinite stacks, having 32k bytes of memory.
So in the stack you can enter a real number. You can also use the hash tag to make it binary. Leading 0 to make it Octal, leading with Ox to make it hexadecimal. It shows this on the front face of the model 28, that it is 'objects' which go on the stack. Lead with double quotes for strings, and single quotes for variables, parentheses for complex, square braces for vectors and double square braces for a matrix.
Curly braces for a list. single quotes for an algebraic equation, and double less than for a program.
In my opinion this is all very interesting, but they have gone beyond the point where this is really workable. A calculator will always have limits in size of keyboard and display, and that it does not have disk drives. Beyond a point, you want a desk top computer instead.
And I feel somewhat vindicated in this in that as I know, HP followed on with the 49, and it did more than the 48. Then the 50, which presumably did more, and it was the first to have an ARM processor, instead of a fully custom chip. But then they have dropped all these. And now they have the HP-PRIME, which undoubtedly does much, but they don't talk about RPL any more, only RPN. So I feel that they have scaled back.
I also notice that in their stored equations and programs on the 48 and 28, they are algebraic, not RPN. With my 41, it as all RPN keystrokes, nothing algebraic at all.
And then as much as their 28 and 48 do, with all the various data objects, I feel that it still does not go far enough to do all which is commonly required in applied mathematics.
In particular, it often goes to matrices where the elements are not just polynomials in a complex varialble, but rational polynomial functions in a complex variable. So you need to be able to do all manner of root finding, factoring, multiplications, and then root locus diagrams. And this is for Frequency Domain. For Time Domain you also get into similar types of math.
And then there are newer things too, and some stuff starting to use Tensor Analysis, formerly reserved only for General Relativity, and there is still more which has come in.
So while it has gone beyond workability for a calculator, I feel that it still does not go anywhere's near what is really needed. MATLAB and Mathematic do much, but I feel that there is still a vacuum.
And then so much of the 28 and 48 is about graphing. And then TI does this too, and the new HP-Prime also.
But if you are taking a test you can use a calculator to get high precision answers easily. But if you need it to show you how to graph stuff, and with asymptotes and all, you are in deep shit. You do not understand the material. The calculator then will just waste you time.
If on the other hand you want to explore a new and interesting topic in graphs, a desktop computer can do a better job.
So enough said.