(15C) Applied Analysis …

[SlideRule]

The publication Applied Analysis by the Hilbert Space Method, Samuel S. Holland Jr., Dover Publications (1990) contains numerous examples of HP-15C 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 hand-held calculator. To show the feasibility of this, I have included several sample programs for the Hewlett–Packard HP-15C.

The following programs, written for the HP-15C, compute this polynomial (pg. 29)

These calculations were done on the Hewlett-Packard HP-15C, 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 HP-15C 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 HP-15C programs. (pg. 122)

Appendix 3.2.A Calculating and Graphing Partial Sums of Fourier Series
This appendix provides some general suggestions and some sample HP-15C programs for the calculation and graphing Exercises 5 through 11.
…
Sample Program # 1
In this case the HP-15C is programmed to do the calculation just as you would do it by hand. (pgs. 124-125)

Sample Program # 2
In this program we take advantage of a counting function in the HP-15C, the “ISG” command (Increment and Skip if Greater than). Using this command, we can put a self-terminating loop in the program and so make the program sum as many terms of the series as we wish. (pg. 126)

On the HP-15C one can evaluate the Legendre polynomials via subroutines. The first two, P₀ = 1 and P₁ = x are no problem. Programs to evaluate P₂ through P₅ are listed below. (pg. 273)

Fourier-Hermite expansions for other functions are dealt with in the exercises. For these exercises, one will need means for evaluating the Hermite polynomials. Here are HP-15C subroutines for evaluating … HP-15C subroutines for the Hermite polynomials (pgs. 313-314)

On the HP-15C 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 HP-15C manual. Here is a sample program for the 15C. (pgs. 365-366)

The following HP-15C program can be used to compute |Ψ₃(u)|². (pgs. 396-397)[/i]

The approximation (6.4.2) is easily programmed. An HP-15C 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 HP-15C: (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 J₀(x). The following HP-15C 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 J₀ is even.) So this one program will compute J₀(x). (pgs. 459-460)

Here are some suggestions for doing practical calculations with the Fourier-Bessel expansion (6.5.5). In the exercises we will use four-term approximations … If you use the HP-15C and have inserted into your machine the program labeled “C” given in Section 6.4 to calculate the values of J₀(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 HP-15C 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 HP-15C takes about 30 seconds per value (pgs. 577-578)

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SlideRule

edit: fixed two minor inconsistencies.

[Namir]

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

[SlideRule]

You're welcome, Namir; sorry I won't be at this years get together in FL - still, more to come.

BEST!
SlideRule