(15C) Applied Analysis …

08172023, 11:53 AM
(This post was last modified: 08182023 09:46 PM by SlideRule.)
Post: #1




(15C) Applied Analysis …
The publication Applied Analysis by the Hilbert Space Method, Samuel S. Holland Jr., Dover Publications (1990) contains numerous examples of HP15C programs.
"A substantial number of the exercises involve numerical calculations. All the computations required in these exercises are within range of a good handheld programmable scientific electronic, calculator. … But the text does not require knowledge of a programming language nor does it require access to a computer. All the numerical exercises can be done on a good, programmable handheld calculator. To show the feasibility of this, I have included several sample programs for the Hewlett–Packard HP15C. The following programs, written for the HP15C, compute this polynomial (pg. 29) These calculations were done on the HewlettPackard HP15C, a relatively inexpensive programmable scientific electronic calculator. Exercises 5 through 11, which ask you to do similar calculations, can also all be done on a handheld calculator having capabilities comparable to those of the 15C. … Sample programs for the HP15C are provided in the appendix to this section (pgs. 120/121) Calculating and Graphing Partial Sums of Fourier Series See Appendix 3.2.A for sample HP15C programs. (pg. 122) Appendix 3.2.A Calculating and Graphing Partial Sums of Fourier Series This appendix provides some general suggestions and some sample HP15C programs for the calculation and graphing Exercises 5 through 11. … Sample Program # 1 In this case the HP15C is programmed to do the calculation just as you would do it by hand. (pgs. 124125) Sample Program # 2 In this program we take advantage of a counting function in the HP15C, the “ISG” command (Increment and Skip if Greater than). Using this command, we can put a selfterminating loop in the program and so make the program sum as many terms of the series as we wish. (pg. 126) On the HP15C one can evaluate the Legendre polynomials via subroutines. The first two, P_{0} = 1 and P_{1} = x are no problem. Programs to evaluate P_{2} through P_{5} are listed below. (pg. 273) FourierHermite expansions for other functions are dealt with in the exercises. For these exercises, one will need means for evaluating the Hermite polynomials. Here are HP15C subroutines for evaluating … HP15C subroutines for the Hermite polynomials (pgs. 313314) On the HP15C we can use the ISG command (Increment, and Skip if Greater Than) to control the number of terms we compute in the series (5.2.10). Refer to Section 10 of the HP15C manual. Here is a sample program for the 15C. (pgs. 365366) The following HP15C program can be used to compute Ψ_{3}(u)^{2}. (pgs. 396397)[/i] The approximation (6.4.2) is easily programmed. An HP15C program looks like this: (pg.453) The formula on the right side of equation (6.4.5) is easily programmed (be sure your calculator is in radian mode). For the HP15C: (pg. 458) The truncated power series (6.4.2) together with the asymptotic formula (6.4.5) gives us a reasonably effective means of calculating the values of J_{0}(x). The following HP15C program, labeled “C”, combines the two approximations, branching automatically to “A” or “B” according as x ≤ 4 or x > 4. (Use only positive x as J_{0} is even.) So this one program will compute J_{0}(x). (pgs. 459460) Here are some suggestions for doing practical calculations with the FourierBessel expansion (6.5.5). In the exercises we will use fourterm approximations … If you use the HP15C and have inserted into your machine the program labeled “C” given in Section 6.4 to calculate the values of J_{0}(x) then the following program will calculate the right side of (6.5.10). Note that I avoid using the memory registers 0 and .0 because they are used in the subroutines A and B. (pg. 471) 8. (Continuation) Suppose the plate in Exercise 7 is made of steel and is heated to an initial temperature … don’t attempt to use your series at t = 0. [Hints for an HP15C program: Put time t in register 0 (hours). Punch in xENTERy (x, y in meters). The following program takes it from there. … With 10 nonzero terms, the HP15C takes about 30 seconds per value (pgs. 577578) BEST! SlideRule edit: fixed two minor inconsistencies. 

08182023, 07:15 PM
Post: #2




RE: (15C) Applied Analysis …
Wowwwwwwwwwwwwwwwwwwwwww!!! How did this book remain a secret for us calculator programmers! I looked at a downloaded copy and was impressed on how much the HP15C is used in various examples!!!
Namir 

08182023, 09:44 PM
Post: #3




RE: (15C) Applied Analysis …
You're welcome, Namir; sorry I won't be at this years get together in FL  still, more to come.
BEST! SlideRule 

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