NATIONAL BUREAU OF STANDARDS REPORT

2369

A NUMERICAL ANALYST’S FIFTEEN-FOOT SHELF

by

George E 0 Forsythe

National Bureau of Standards s Los Angeles

<50>

U. $. DEPARTMENT OF COMMERCE

NATIONAL BUREAU OF STANDARDS
NATIONAL BUREAU OF STANDARDS

A. V. Astin, Director

U. S. DEPARTMENT OF COMMERCE

Charles Sawyer, Secretary

cover of this report.

Electricity. Resistance Measurements. Inductance and Capacitance. Electrical Instruments. Magnetic Measurements. Applied Electricity. Electrochemistry.

Optics and Metrology. Photometry and Colorimetry. Optical Instruments. Photographic

Technology. Length. Gage.

Heat and Power. Temperature Measurements. Thermodynamics. Cryogenics. Engines and

Lubrication. Engine Fuels. Cryogenic Engineering.

Atomic and Radiation Physics. Spectroscopy. Radiometry. Mass Spectrometry. Solid State

Physics. Electron Physics. Atomic Physics. Neutron Measurements. Infrared Spectroscopy.

Nuclear Physics. Radioactivity. X-Rays. Betatron. Nucleonic Instrumentation. Radiological Equipment. Atomic Energy Commission Instruments Branch.

Chemistry. Organic Coatings. Surface Chemistry. Organic Chemistry. Analytical Chemistry.

Inorganic Chemistry. Electrodeposition. Gas Chemistry. Physical Chemistry. Thermochemistry. Spectrochemistry. Pure Substances.

Mechanics. Sound. Mechanical Instruments. Aerodynamics. Engineering Mechanics. Hydraulics. Mass. Capacity, Density, and Fluid Meters. Organic and Fibrous Materials. Rubber. Textiles. Paper. Leather. Testing and Specifications. Polymer Structure. Organic Plastics. Dental Research.

Metallurgy. Thermal Metallurgy. Chemical Metallurgy. Mechanical Metallurgy. Corrosion.

Mineral Products. Porcelain and Pottery. Glass. Refractories. Enameled Metals. Concreting Materials. Constitution and Microstructure. Chemistry of Mineral Products.

Budding Technology. Structural Engineering. Fire Protection. Heating and Air Conditioning. Floor, Roof, and Wall Coverings. Codes and Specifications.

Applied Mathematics. Numerical Analysis. Computation. Statistical Engineering. Machine

Development.

Electronics. Engineering Electronics. Electron Tubes. Electronic Computers. Electronic

Instrumentation.

Radio Propagation. Upper Atmosphere Research. Ionospheric Research. Regular Propagation Services. Frequency Utilization Research. Tropospheric Propagation Research. High

Frequency Standards. Microwave Standards.

Ordnance Development. These three divisions are engaged in a broad program of research

Electromechanical Ordnance, and development in advanced ordnance. Activities include

Electronic Ordnance. basic and applied research, engineering, pilot production, field testing, and evaluation of a wide variety of ordnance materiel. Special skills and facilities of other

NBS divisions also contribute to this program. The activity is sponsored by the Department of

Defense.

Missile Development. Missile research and development: engineering, dynamics, intelligence,

instrumentation, evaluation. Combustion in jet engines. These activities are sponsored by the

Department of Defense.

© Office of Basic Instrumentation • Office of Weights and Measures.
NATIONAL BUREAU OF STANDARDS REPORT

NSS PROJECT NBS REPORT

1101-10-5100 March 12 f 1953 2369

A NUMERICAL ANALYST’S FIFTEEN”FOOT SHELF*

by

George E„ Forsythe

National Bureau of Standards s Los Angeles

PREPRINT

*This compilation was sponsored (in part) by the Office of

Naval Research,, USN„

The publication, reprl

unless permission Is o

25, D, C. Such perml

cally prepared if that

Approved for public release by the

Director of the National Institute of

Standards and Technology (NIST) on October 9, 2015

n part, Is prohibited

indards, Washington

lort has been speclfiort for Its own use,

A NUMERICAL ANALYST'S FIFTEEN-FOOT SHELF*"

by

George E 0 Forsythe

National Bureau of Standards, Los Angeles

Imagine a laboratory of numerical analysis, with computers, coders,

problem analysts, and research mathematicians . The group varies in

mathematical experience from new college graduates to professionals

with long research records,. Disappointingly few can profitably consult

a book not in English but, pooling talents, the group can read English,

French, German, Italian, Russian, and Hebrew quite well. Quite as

important as a comprehensive libraiy (assumed to lie within a few miles)

is a small library in the laboratory building. What should such a

working library contain?

Clearly the library needs a diversity of material, of which at

least five classes can be distinguished:

A. Mathematics books.

Bo Books on computing machines.

C„ Tables of functions.

Do Periodicals.

E. General references (e 0 g., language dictionaries).

"This compilation was sponsored (in part) by the Office of Naval

Research, USN. It represents the opinions of the author only, and not

those of the National Bureau of Standards nor the Office of Naval

Research
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This article is a proposed list of about II4.O essential books in

class Ao The reader is warned that the list has been hastily prepared and is very tentative 5 its inclusions and omissions should

not be taken too seriously <,

Glass A was divided into the following five categories,, of

which four have been split into subcategories:

1 o Bibliographies on mathematics.

2. Collections of formulas

»

3 0 Books on numerical analysis

»

l+o Other books on applied mathematics

„

5 o Books on pure mathematics 0

In selecting the titles five qualities were explicitly considered: (a) adequacy of material in topics likely to be needed;

(b) use of English language; (c) completeness of bibliography;

(d) readability; (e) recency 0 The order of precedence given to

these qualities depended on the book user; for mature research men

it was perhaps a $ c, e^ b 9 d5 (most important first) 9 while for

junior computers,, perhaps b 3 d 9 a9 e 5 c. In categories 1 5 and 3

a considerable proportion of the available books has been listed,,

so that any enlargement of the library would occur mainly in categories U and 3 «
'
The bibliographical citations came from the books themselves 3 from the Library of Congress cards,, or from Parke's very helpful

Guide (see p„ U below) „ Mrs„ Mildred Martinolich helped prepare

the citations.,

u

1. BIBLIOGRAPHIES

ENGINEERING RESEARCH ASSOCIATES, High-speed computing devices , McGraw-Hill, New York, 1990, U9l pp.

FLETCHER, A., MILLER, J. C. P., and RGSENHEAD, L., An index of

mathematical tables, McGraw-Hill, New York, 19)46. l&O pp.

FRANKLIN, A.D., and HANKAM, E„ V. , Bibliography on the use of IBM

machines in science , statistics , and education 9 International Business

Machines Corp., New York, 1992. 90 pp.

GRINTER, L. E., Numerical methods of analysis in engineering ,

Macmillan, New York, 19li9« 207 pp. [The article by T. J. Higgins

contains a comprehensive bibliography on numerical solution of

partial differential equations.]

HARVARD UNIVERSITY, Staff of the Computation Laboratory, A manual

of operation for the automatic sequence controlled calculator .

Harvard University Press, 19)46. 96l pp„

KUROSH, A. G 0 , MARKUSHEVICH, A. I., and RASHEVSKII, P. K. (editors).

Mathematics in the U. S„ S. R. in the thirty years 1917-19 U7 (Russian),

Moscow-Leningrad, 19I4.8. 10hh pp. [Surveys and bibliographies of most

Soviet work in this period.]

PARKE, N. G. Ill, Guide to the literature of mathematics and

physics , McGraw-Hill, New York, 19 Ll7. 209 pp.

SHOHAT, J. A., HILLE, E„, and WALSH, J. L., A bibliography on

orthogonal polynomials , National Research Council of the National

Academy of Sciences, Washington, I9I4O. 20 U pp.
.

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.
VLASOV , V 0 Z,, GOLUBEV, V G V,, and MOISEEV, N, D, (editor).

Me chanics in the U, S, S, R, in the thirty years 1917-19 b7 (Russian),

Moscow-Leningrad, 1990, hl6 pp„ [Companion volume to that of Kurosh

and others,

]

2, COLLECTIONS OF FORMULAS

a. General

ADAMS, E. P, and HIPPISLEY, R, L,, Smithsonian mathematical formulae and tables of elliptic functions „ Smithsonian Institution,

Washington, 19 U7 • 31 b PP°

BIERENS DE HAAN, D,, Nouvelles table s d

8 integrates definies,

corrected edition, Stechert, New York, 1939° 716 pp,

DWIGHT, H, Bo, Table s of integrals and other mathematical data ,

Macmillan, 19 b7- 290 pp,

DOETSCH, G,, Tabellen zur Laplace- Trans formation and Anleitung

zum Gebrauch, Springer, Berlin and Gottingen, 19b7° 189 pp,

GR0BNER, W,, and HCFREITER, N,, Integraltafel , Erster Teil ,

Unbestimmte Integrate , Springer, Vienna and Innsbruck, 19b9 » 166 pp,

HALD, A,, Statistical tables and formulas, Wiley, New York, 1992,

97 pp,

HASTINGS, Cecil Jr„, Approximations in numerical analysis , Looseleaf sheets being published by the RAND Corporation, Santa Monica,

California, 1990 ff, 7b sheets so far,

JOLLEY, L, B, W, , Summation of series . Chapman and Hall,

London, 1929 . 232 pp.
.
6

MADELUNG, E 0

, Die mathematischen Hilfsmittel des Physikers n

3rd edition, American reprint, Dover, New York, 19h3« 38 Ll pp»

MAGNUS, W., and OBERHETTINGER, F 0 , (translated by J e Wermer),

Formulas and theorems for the special functions of mathematical physics,

Chelsea, New York, 19)i9<= 172 pp„

NAUTICAL ALMANAC OFFICE (Great Britain), Interpolation and allied

tables , H„ M„ Stationery Office, London, 1936c lj.9 pp«

PAPELIER, G„, Formulaire de mathematique

s

speciales, 11th edition,

Librairie Vuibert, Paris, 19 h7« 208 pp» [Formulas from algebra,

analysis, trigonometry, analytical geometry 0 ]

bo Bound with numerical tables

COMRIE, L. T„, Chambers 1 s shorter six-figure mathematical tables.

Chambers, Edinburgh and London, 1990 « 3^7 PP°

DAVIS, H„ To, Tables of the higher mathematical functions ,

Principia Press, Bloomington, Indiana, vol. 1, 1933, 377 PP»; volo 2

1939 s 391 pp.

JAHNKE , E o , and EMDE , F „ , Tables of functions with formulae and

curves , Irth edition, Dover, New York, 19 h5° 306 + 76 pp„

NATIONAL BUREAU OF STANDARDS, Tables of Chebyshev polynomials

C n

(x) and S (x). Applied Mathematics Series, vol„ 9 S Government

Printing Office, Washington, 1992 0 l6l pp» [The introduction by

Lanczos is a valuable reference,,]

7

3° REFERENCES ON NUMERICAL METHODS

a. General

HARTREE, D. R„ , Numerical analysis ,, Oxford University Press, 1992.

287 pp.

HOUSEHOLDER, A„ S„, Numerical analysis , to be published by

McGraw-Hill, New York, autumn 1993

«

KOPAL, Z„ Notes on numerical a nalysis „ M„ I. T„, hectographed,

c. 1990 ?, c o 200 pp 0

MILNE, W„ E„, Numerical Calculus , Princeton University Press,

19 U9. 393 PP»

00 00 RUNGE, Co, and KONIG, H„, Vorlesungen uber numerisches Rechnen,

Springer, Berlin, 192li. 371 pp„

SCARBOROUGH, J» B„, Numerical mathematical analysis , 2^ edition,

John Hopkins Press, Baltimore, 1990 , $11 pp 0

VON SANDEN, H c

, Praktische Analysis , 2nd edition, Teubner,

Leipzig, 1923o 199 PP°

WHITTAKER, E. T. # and ROBINSON, G., The calculus of observations ,

Lith edition, Blackie, London and Glasgow, 19Un 397 pp<> WELLERS, Fo A., (translated by R 0 To Beyer), Practical analysis ,

Dover, New York, 19 U8. h22 pp Q

b. Matrix problems

DWYER, P. S», Linear computations, Wiley, New York, 1991° 3hh PP»

FADDEEVA, V 0 N„ , Computational methods of linear algebra (Russian),

Moscow-Leningrad, 1990 . 2h0 pp D
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FRAZER, R. A., DUNCAN, W. J,, and COLLAR, A„ R c

, Elementary

matrices , and some applications to dynamics and differential

equations , Cambridge Univ. Press , 1938, ljl6 pp.

NATIONAL BUREAU OF STANDARDS,, Proceedings of a symposium on

simultaneous linear equations and the determination of eigenvalues,

August 1991, Government Printing Office, to appear in 1993.

ZURMUHL, R. , Matrizen , Springer, Berlin, Gottingen, and

Heidelberg, 19^0 o lj.27 PPo [A very useful book.]

Co Differential equations

BENNETT, A. A,, MILNE, ¥. E„, BATEMAN, H 0 , Numerical integration

of differential equations , National Research Council of the National

Academy of Sciences, Washington, 1933 ° 108 pp 0 [Extensive

bibliographies.

]

COLLATZ, L., Eigenwertaufgaben mit technischen Anwendungen ,

Akademische Verlag„, Leipzig, 19b9o U66 pp 0

COLLATZ , L. , Numerische Behandlung von Differential gleichungen .

Springer, Berlin, Gottingen and Heidelberg, 1991. If? 8 pp.

KANTOROVICH, L. V 0

, and KRILOV, V 0 I 0, Approximate methods of

higher analysis (Russian), 3rd edition, Moscow-Leningrad, 19?0» 697 PP»

MILNE, W„ E. , Numerical solution of differential equations ,

Wiley, New York, 1993° 275? PP° [Extensive bibliography.]

SOUTHWELL R. V D , Relaxation methods in engineering science ,

Oxford University Press, 19li0. 292 pp.
• 'l'J V

.
9

SOUTHWELL, R« V 0

, Relaxation methods in theoretical physics , Clarendon Press , Oxford , 19 h6. 2)4.8 pp D

d„ “Monte Carlo 11 methods

NATIONAL BUREAU OF STANDARDS, Monte Carlo methods. Applied

Mathematics Series 12, U„ S 0 Government Printing Office, Washington,

19S1. h2 pp„

he REFERENCES ON APPLIED MATHEMATICS

a„ Engineering mathematics

BRONWELL, A. , Advanced mathematics in physics and engineering , McGraw-Hill, New York, 1953® U75 pp.

CHURCHILL, R„ V 0

, Fourier series and boundary value problems , McGraw-Hill, New York, 19 Ip-., 206 pp c

CHURCHILL, Ro V„, Modern operational mathematics in engineering ,

McGraw-Hill, New York, 19 UU. 306 pp D

DOHERTY, Re E„, and KELLER, E 0 G„, Mathematics of modern engineering , Wiley, New York, vol® 1, 1936, 31U PP»5 vol„ 2 (by Keller only),

19)j 2, 309 pp®

GARDNER, M 0 F 0

, and BARNES, J. L 0 , Transients in linear systems,

vol 0 1, Wiley, New York, 19 h.2, 389 PP®

MARGENAU, H. , and MURPHY, G. M„ , The mathematics of physics and

chemistry , van No strand. New York, 19h3° 58l pp®

OLDENBURGER, R», Mathematical engineering analysis , Macmillan,

New York, 1950® I4.26 pp„
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S0K0LNIK0FF, I. S„, and S0K0LNIK0FF , E 0 S 0

, Higher mathematics

for engineers and physicists , 2nd edition , McGraw-Hill, New York,

19 111 o <87 pp„

b» Theoretical physics

BLATT, J. M„, and WEISSKOPF, V. F c , Theoretical nuclear physics , Wiley , New York, 1992 » 86 b PP-.

BORN, Mo , Qptik . Ein Lehrbuch der elektromagnetischen

Lichttheorie , reprint, Edwards, Ann Arbor, 19b3° 991 pp„

JEFFREYS, H„, and JEFFREYS, B„ S„, Methods of mathematical physics ,

2nd edition, Cambridge University Press, 1990- 708 pp.

J00S, G„ s (translated by I, M„ Freeman), Theoretical physics ,

Hafner, New York, 193b. 7b8 pp e

MORSE, P„ Mo, and FESHBACH, H 0 , Methods of theoretical physics , multigraphed. Technology Press, Cambridge, 19b6» b97 pp® [Being

published by McGraw-Hill „

]

SCHIFF, L 0 Io, Quantum mechanics , McGraw-Hill, New York, 19 b9.

hOb PPc

SMYTHE , W0 R 0

, Static and dynamic electricity , McGraw-Hill,

New York, 1939 o 960 pp D

STRATTON, J„ A 0

, Electromagnetic theory , McGraw-Hill, New York,

19 bio 6l9 pp 0

ZEMANSKY, M„ Wc

, Heat and thermodynamics , 2d edition, McGrawHill, New York, 19b3° 390 pp
'

/isnlfiK


11

g s Mechanics

GOLDSTEIN, H„ s Classical mechhnics , Addison-Wesley,

Cambridge , 1990 . 399 pp.

MILNE- THOMSON , L. M. , Theoretical hydrodynamics 3 2d edition

Macmillan, London , 19 U9. 600 pp.

RAYLEIGH, Lord (J. W„ STRUTT ) , The theory of sound , 2d edition,

2 vols„ reprinted in one, Dover , 19 U9. L8o + 90b pp 0

SCANLAN, R. H„, and ROSENBAUM, R., Introduction to the study of

aircraft vibration and flutter fl Macmillan, New York, 1991 « h.28 pp,

WHITTAKER, E„ T., A treatise on the analytical dynamics of

particles and rigid bodies , Ijth edition, Dover, New York, 19UU®

Ll96 pp.

d 0 Statistics

BOWKER, A 0 Ho, and GOODE, H 0 P 0

, Sampling inspection by variables ,

McGraw-Hill, New York, Toronto, and London, 1992 0 216 pp D

COCHRAN, Wo G 0

, and COX, G 0 M0 , Experimental designs , Wiley,

New York, 1990. l&h pp.

DIXON, Wo J., and MASSEY, F. J., Introduction to statistical

analysis , McGraw-Hill, New York, Toronto, and London, 1991° 370 pp.

KENDALL, Mo G 0 , The advanced theory of statistics , Griffin,

London, vol„ 1, 3rd edition, 19)|6, L97 pp.; vol c 2, 191x6, 921 pp.

WALD, A., Sequential analysis , Wiley, New York, 19b7° 212 pp D

12

e 0 Economics

KOQPMANS, To Jo (editor) , Activity analysis of production

and allocation , Wiley, New York, 1951. bOh pp. [RAND Report R-193o]

McKINSEY, J„ Co Co, Introduction to the theory of games , McGraw-Hill,

New York, Toronto, and London, 1952. 371 pp,

5. REFERENCES ON PURE MATHEMATICS

a. Logic

ROSSER, J. Bo, Logic for mathematicians , McGraw-Hill, New York,

1953. 530 pp.

b. Algebra

BIRKHOFF, Go, and MacLANE, S. , A survey of modern algebra , Macmillan, New York, 19 hi. h50 pp 0

PkcDUFFEE, C„ Co, The theory of matrices , reprint, Chelsea,

New York, 19h6. 110 pp„

PERRON, 0o, Die Lehre von den Ke ttenbruchen , 2d edition,

Teubner, Leipzig, 1929. 520 pp.

PERLIS, S 9 , Theory of matrices , Addison-Wesley, Cambridge, 1952.

237 PP.

USPENSKY, Jo V„, Theory of equations , McGraw-Hill, New York,

Toronto, and London, 19h8. 353 PP.

VAN DER WAERDEN, B. L. (translated by F 0 Blum), Modern algebra ,

Ungar, New York, vol Q 1, 19 h9, 26)4 pp.; vol 0 2, 1950, 222. pp 0
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c. Number theory

HARDY, G. H t> and WRIGHT, E. M„ , An introduction to the theory

of numbers , Clarendon Press, Oxford, 1938. )|03 pp 0

do Analysis in general

/ GOURSAT, E„ (translated by E„ R. Hedrick), A course in mathematical analysis , Ginn, Boston, vol 1, 190li, 9U8 pp.; vol. 2, part 1,

1916, 299 pp.; vol. 2, part 2, 1917, 300 pp„ [For vol, 3 see next entry,]

GOURSAT, E„, Cours d * analyse mathematique , edition, GauthierVillars, Paris, 19 Ll2o 702 pp.

/ 00 POLYA, Go, and SZEGO, G B , Aufgaben und Lehrsatze aus der Analysis ,

reprint, Dover, New York, 19b$ s vol. 1, 3 L.2 pp.; vol„ 2, bl2 pp.

e. Calculus

COURANT, R. (translated by E. J. McShane), Differential and

integral calculus , Interscience , New York, vol. 1, 1937, 6l6 pp„;

vol. 2, 1936, 682 pp.

HARDY, G„ Ho, A course of pure mathematics , lQth edition,

Cambridge University Press, 1992. 909 pp°

0STR0WSKI, A., Vorlesungen uber Differential- und Integralrechnung ,

Birkhauser, Basel, vol. 1, 19h9, 373 PP°$ vol. 2, 1991, U82 pp.

[Chapter 6 of vol. 2 contains a rigorous treatment of numerical

interpolation^ integration, etc.]

SHERWOOD, G. E. F., and TAYLOR, A. E., Calculus , Prentice-Hall

,

revised edition, 19ii7. 903 PP«
v
fo Real variables

GRAVES, Lo Mo, The theory of functions of real variables Q McGraw-Hill, New York, 19l|6 e 300 pp„

TITCHMARSH, E„ C„, The theory of functions „ 2d edition, Oxford

University Press, London, 1939° Li5b PP»

g 0 Complex variable ; conformal maps

BECKENBACH, E 0 F 0 (editor). Construction and applications of

conformal maps 9 National Bureau of Standards, Applied Mathematics

Series, vol„ 18, Government Printing Office, 1952o 280 pp s

[Bibliography by Seidel on numerical methods,,]

BERGMAN, S c

, The kernel function and conformal mapping , American

Mathematical Society, [now] Providence, 1950 » l6l pp c

KNOPP, Ko (translated by F„ Bagemihl), Theory of functions ,

Dover, New York, vol„ 1, 19 U5 , 1U6 pp 0 j vol 0 2, 19b7 s 150 pp»

NEHARI, Z„, Conformal mapping , McGraw-Hill, New York, Toronto,

and London, 1952 „ 396 pp e

h 0 Series , etc e

BROMWICH, T„ Jo I'Ao, An introduction to the theory of infinite

series , 2d edition, reprint, Macmillan, London, 19b2. 535 PP«

KNOPP, Ko (translated by R. 0 o Young), Theory and application

of infinite series , Blackie, London, 1928 0 571 pp„
ip
WALL 5 H„ S„ , Analytical theory of continued fractions n van

15

Nostrand, New York, Toronto, and London,, 19Li8 e U33 pp e

i 0 Fourier series ; transforms

ROGOSINSKI, W0 (translated by H c Cohn and F 0 Steinhardt), Fourier

series , Chelsea, 1950 o 176 pp 0

WIDDER, D. V„, The Laplace transform , Princeton University Press,

19bl« U06 pp„

ZYGMUND, A„, Trigonometrical series ,, Warsaw, 1935c 331 pp c

Polynomials and approximation

AKHIEZER, No I», Lectures on the theory of approximation (Russian),

Mo scow"Leningrad, 19177. 323 PP° [The compiler has not seen this book,

but the author is an expert on the Russian work in this fields which is

so important for numerical analysis,,]

JACKSON, Do, The theory of approximation , American Mathematical

Society, [now] Providence, 1930. 17 8 pp 0

WARDEN , Mo, The geometry of the zeros of a polynomial in a

complex variable , American Mathematical Society, [now] Providence,

19 U9

o

183 PP°

SZEGO, Go, Orthogonal polynomials , American Mathematical Society,

[now] Providence, 1939. IjOl pp 0

WALSH, Jo Lo, Interpolation and approximation by rational functions

in the complex domain , American Mathematical Society, [now] Providence

1935, 382 pP o
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16

WHITTAKER, J 0 M c

, Interpolat ory function theory , Cambridge

University Press, 193^» 107 pp»

k„ Special functions

HOBSON, E. The theory of spherical and ellipsoidal harmonics n Cambridge University Press , 1931 » £00 pp„

McLACHLAN, N 0 W0 , Theory and application of Mathieu functions 0 Clarendon Press s Oxford , 19li7° I4.OI pp»

OBERHETTINGER, F«, and MAGNUS, Anwendungen der elliptischen

Funktionen in Physik und Te chnik „ Springer, Berlin, Gottingen, and

Heidelberg, 19h9o 126 pp c z _ x

2 ROSSER, Jo Bo, Theory and application of ! e

" dx and

J o

z _

2 2 y _2

j e P ^ dy P e X dx , Mapleton, Brooklyn, I9I480 192 pp D Jo Jo

SNOW, C o , The hypergeometric and Legendre functions with

applications to integral equations of potential theory. National Bureau

of Standards, Washington, 19h2 0 319 PP°

STRUTT, Mo J„ 0o, Lamesche, Mathieusche und verwandte Funktionen

in Physik und Te chnik , reprint, Edwards, Ann Arbor, 19l|lu 116 pp«

TANNERY, J.-, and MOLK, J n

, Elements de la theorie des fonctions

elliptiques , Gauthier-Villars, Paris, vol 0 1, l893 s 2)46 pp„j vol 0 2,

I896, 299 PPo

WATSON, G„ No, A treatise on the theory of Bessel functions ,

2nd edition, Cambridge University Press, 19 Wi. 80)4 pp c
< r*— ftn * »
17

WHITTAKER, E„ T 0j and WATSON, G 0 N 0

, A course of modern analysis n American edition, Cambridge University Press , and Macmillan , New York,

I9 I4.3 ® 608 pp„

lo Potential theory

KELLOGG, 0 o D» s Foundations of potential theory , reprint,

Ungar, New York, 19 Uu 38 I4 pp 0

m0 Differential equations

BATEMAN, H0j Partial differential equations of mathematical

physics , reprint, Dover, New York, 19 hlu £22 pp„

FORD, L„ R 0j Differential equations n McGraw-Hill, New York, 1933®

263 pp 0

FRANK, P„, and VCN MISES, Ro s Die Differential- und Inte gral gle i chunge

n

der Mechanik und Physik ; 2d edition, 2 vols 0 , reprint, Rosenberg, New

York, 19b3® 916 + 1106 pp 0

INCE, Eo L., Ordinary differential equations fl reprint, Dover,

New York, c„ ±9l&<- 5£8 PP®

KAMKE, E 0 , Differential gleichungen , Lbsungsmethoden und Lbsungen ,

2 volSo, reprint, Edwards, Ann Arbor, I9 L1F 0 6L.2 + 2h3 PP®

LEFSCHETZ, S 0

, Lectures on differential equations , Princeton

University Press, 19U8 0 210 pp0

MINORSKY, N 0 , Introduction to non-linear mechanics , Edwards,

Ann Arbor, 19 U7® I46 L1 pp

18

PIAGGIO, Ho To H°, An elementary treatise on differential

equations and their application . 7th edition, G„ Bell, London,

1938 0 2<6 pp„

SGMMERFELD , A 0 (translated by E 0 G c Straus) , Partial differential

equations in physics „ Academic Press , New York, 19b9» 339 pp.

STOKER, Jo Jo, Nonlinear vibrations in mechanical and electrical

systems s Interscience , New York, 1990° 273 pp°

TAMARKIN , J c Do, and FELLER, ¥„ , Partial differential equations , Brown University , Providence, I9 I4I. 268 pp 0 [Mimeographed notes.]

WEBSTER, A, G„ , Partial differential equations of mathematical

physics , 2d edition, Ste chert. New York, 1933° UHO pp.

ne Difference equations ; integral equations

LOVITT, Wo V„, Linear inte gral equations , McGraw-Hill, New York

and London, 192lu 293 PP°

MILNE- THOMSON, L 0 Mo, The calculus of finite differences ,

Macmillan, London, 1933° 998 pp«

NORLUND, No E 0 , Vorlesungen uber Differenzenrechnung , reprint,

Edwards, Ann Arbor, 1999° 991 pp»

°o Inequalities

HARDY, G. Ho, LITTLEWGOD, T„ E c , and POLYA, G 0 , Inequalities ,

Cambridge University Press, 1939° 3lU PP°
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MOTZKIN, T» s Beitrage zur Theorie der line are n Ungle i ohunge

n

„ Azriel, Jerusalem, 19360 71 pp» [Translated by D 0 R» Fulkerson,

Publication T-22, The RAND Corporation, Santa Monica, Calif

7

March

1952, 86 pp„]

p„ Calculus of variations , etc P

COURANT, R„, and HILBERT, D„, Methoden der mathematischen Physik ,

2d edition, 2 vols 0 , reprint, Interscience, New York, 19li3o

Ii69 + 5U9 pp a

q c Probability

( CRAMER, Ho, Mathematical methods of statistics „ Princeton

University Press, 19l|6o 975 PP<>

FELLER, Wo , An introduction to probability theory and its

applications , vol, 1, Wiley, New York, 1950<, hi9 PP«

USPENSKY, Jo Vo, Introduction to mathematical probability n

McGraw-Hill, New York, 1937 ° Ijll pp c

r 0 Topology

NEWMAN, Mo Ho A» , Elements of the topology of plane sets of

points, 2nd edition, Cambridge University Press, 1951* 21 ppD

20

So Geometry

KELLY s P 0 Jo, and BUSEMANN, H„, Projective geometry and projective metrics „ Academic Press , 1953° about 300 PP<>

S0K0LNIK0FF , I„ So s Tensor analysis 9 theory and applications fl

Wiley, 1991. 33£ PP»

STRUIK, D, Ho, Lectures on classical differential geometry ,

Addison-Wesley, Cambridge, 1950. 221 pp„

March 12, 1953

THE NATIONAL BUREAU OF STANDARDS

Functions and Activities

The functions of the National Bureau of Standards are set forth in the Act

of Congress, March 3, 1901, as amended by Congress in Public Law 619, 1950.

These include the development and maintenance of the national standards of

measurement and the provision of means and methods for making measurements

consistent with these standards; the determination of physical constants and

properties of materials; the development of methods and instruments for testing

materials, devices, and structures; advisory services to Government Agencies on

scientific and technical problems; invention and development of devices to serve

special needs of the Government; and the development of standard practices,

codes, and specifications. The work includes basic and applied research, development, engineering, instrumentation, testing, evaluation, calibration services

and various consultation and information services. A major portion of the

Bureau’s work is performed for other Government Agencies, particularly the

Department of Defense and the Atomic Energy Commission. The scope of activities is suggested by the fisting of divisions and sections on the inside of the

front cover. Reports and Publications

The results of the Bureau’s work take the form of either actual equipment and

devices or published papers and reports. Reports are issued to the sponsoring

agency of a particular project or program. Published papers appear either in the

Bureau’s own series of publications or in the journals of professional and scientific

societies. The Bureau itself publishes three monthly periodicals, available from

the Government Printing Office: The Journal of Research, which presents complete papers reporting technical investigations; the Technical News Bulletin, which

presents summary and preliminary reports on work in progress; and Basic Radio

Propagation Predictions, which provides data for determining the best frequencies

to use for radio communications throughout the world. There are also five series

of nonperiodical publications: The Applied Mathematics Series, Circulars, Handbooks, Building Materials and Structures Reports, and Miscellaneous Publications.

Information on the Bureau’s publications can be found in NBS Circular 460,

Publications of the National Bureau of Standards ($1.00). Information on cali- bration services and fees can be found in NBS Circular 483, Testing by the National

Bureau of Standards (25 cents). Both are available from the Government Printing Office. Inquiries regarding the Bureau’s reports and publications should be

addressed to the Office of Scientific Publications, National Bureau of Standards,

Washington 25, D. C.