### Complete Bibliography

[1] : “The motion of a heavenly body in a resisting medium,” Pop. Astron. 6 (1898), pp. 20–29.

[2] : The geodesic lines on the anchor ring. Ph.D. thesis, University of Chicago, 1900. Advised by O. Bolza. MR 2936782

[3] : “The second variation of a definite integral when one end-point is variable,” Trans. Amer. Math. Soc. 3 : 1 (1902), pp. 132–141. MR 1500591 JFM 33.0385.01

[4] : “The geodesic lines on the anchor ring,” Ann. of Math. (2) 4 : 1 (October 1902), pp. 1–21. MR 1502291 JFM 33.0670.02

[5] : “Jacobi’s criterion when both end-points are variable,” Math. Ann. 58 : 1–2 (1903), pp. 70–80. MR 1511229 JFM 34.0402.01

[6] : “An existence theorem for a differential equation of the second order, with an application to the Calculus of Variations,” Trans. Amer. Math. Soc. 5 : 2 (1904), pp. 113–125. MR 1500665 JFM 35.0340.01

[7] : “Sufficient condition for a minimum with respect to one-sided variations,” Trans. Amer. Math. Soc. 5 : 4 (1904), pp. 477–492. MR 1500686 JFM 35.0370.02

[8] : “The exterior and interior of a plane curve,” Bull. Amer. Math. Soc. 10 : 8 (1904), pp. 398–404. MR 1558133 JFM 35.0506.01

[9] : “The solutions of differential equations of the first order as functions of their initial values,” Ann. of Math. (2) 6 : 2 (January 1905), pp. 49–68. MR 1503546 JFM 36.0389.01

[10] : “A problem of the Calculus of Variations in which the integrand is discontinuous,” Trans. Amer. Math. Soc. 7 : 2 (1906), pp. 325–336. MR 1500752 JFM 37.0402.01

[11] : “A proof of the fundamental theorem of analysis situs,” Bull. Amer. Math. Soc. 12 : 7 (1906), pp. 336–341. MR 1558345 JFM 37.0495.02

[12] : “Book review: The theory of functions of real variables, by James Pierpont,” Bull. Amer. Math. Soc. 13 : 3 (1906), pp. 119–130. MR 1558414

[13] : “A generalization of the notion of angle,” Trans. Amer. Math. Soc. 7 : 2 (1906), pp. 184–196. MR 1500741 JFM 37.0490.01

[14] : “The construction of a field of extremals about a given point,” Bull. Amer. Math. Soc. 13 : 7 (1907), pp. 321–324. MR 1558473 JFM 38.0408.02

[15] : “A new form of the simplest problem of the Calculus of Variations,” Trans. Amer. Math. Soc. 8 : 3 (1907), pp. 405–414. MR 1500795 JFM 38.0408.01

[16] : “Errata: ‘A new form of the simplest problem of the Calculus of Variations’,” Trans. Amer. Math. Soc. 8 : 4 (October 1907), pp. 536. MR 1500484

[17] : “A note concerning maxima and minima of functions of several variables,” Amer. Math. Monthly 14 : 3 (March 1907), pp. 47–49. MR 1516789 JFM 38.0334.02

[18] : “A method of deriving Euler’s equation in the Calculus of Variations,” Amer. Math. Monthly 15 : 3 (March 1908), pp. 47–54. MR 1516998 JFM 40.1031.08

[19] :
“Book review: Table de caractéristiques relatives a la base __\( 2,310 \)__ des facteurs premiers d’un nombre inférieure a __\( 30,030 \)__, by Ernest Lebon,”
Bull. Amer. Math. Soc.
15 : 3
(1908),
pp. 139–140.
MR
1558702

[20] : “The properties of curves in space which minimize a definite integral,” Trans. Amer. Math. Soc. 9 : 4 (1908), pp. 440–466. MR 1500821 JFM 39.0441.01

[21] : “On the inverse problem of the Calculus of Variations,” Ann. of Math. (2) 9 : 3 (April 1908), pp. 127–140. MR 1502361 JFM 39.0445.01

[22] : “Fields of extremals in space,” Trans. Amer. Math. Soc. 11 : 3 (1910), pp. 325–340. MR 1500866 JFM 41.0437.01

[23] : “A new proof of Weierstrass’s theorem concerning the factorization of a power series,” Bull. Amer. Math. Soc. 16 : 7 (1910), pp. 356–359. MR 1558920 JFM 41.0286.03

[24] : “Book review: An introduction to the study of integral equations, by Maxime Bôcher,” Bull. Amer. Math. Soc. 16 : 4 (1910), pp. 207–213. MR 1558889

[25] : “The function concept and the fundamental notions of the Calculus,” pp. 263–304 in Monographs on topics of modern mathematics relevant to the elementary field. Edited by J. W. A. Young. Longmans Green and Co., 1911. Zbl 0067.03101

[26] : “Eisenhart’s differential geometry,” Bull. Amer. Math. Soc. 18 : 3 (1911), pp. 145–146. MR 1559156

[27] : “A generalization of the preparatory theorem for a power series in several problems,” Bull. Am. Math. Soc. 18 : 2 (1911), pp. 64. Abstract only. JFM 42.0294.03

[28] : “Book review: A treatise on the differential geometry of curves and surfaces, by Luther P. Eisenhart,” Bull. Amer. Math. Soc. 17 : 9 (1911), pp. 470–478. MR 1559100

[29] : “A new proof of the existence theorem for implicit functions,” Bull. Amer. Math. Soc. 18 : 4 (1912), pp. 175–179. MR 1559180 JFM 43.0483.04

[30] : “A generalization of Weierstrass’ preparation theorem for a power series in several variables,” Trans. Amer. Math. Soc. 13 : 2 (April 1912), pp. 133–145. MR 1500910 JFM 43.0504.02

[31] : “Fundamental existence theorems,” pp. i–ii,1–107 in The Princeton Colloquium (Princeton University, 15–17 September 1909), part 1. American Mathematical Society (New York), 1913. JFM 44.0365.01

[32] :
“A method of subdividing the area enclosed by a plane curve, with an application to Cauchy’s theorem,”
Bull. Am. Math. Soc.
19
(1913),
pp. 453.
Abstract only; published in *Bull. Sci. Lab. Denison Univ.* **17** (1914), pp. 375–389.
JFM
44.0568.04

[33] : “Note on Pierpont’s theory of functions,” Bull. Amer. Math. Soc. 20 : 3 (1913), pp. 146–147. MR 1559438 JFM 44.0333.01

[34] : “The relation satisfied by two dependent functions near a point at which both are singular,” Bull. Am. Math. Soc. 19 (1913), pp. 286. Abstract only; article unpublished. JFM 44.0509.05

[35] : “A method of subdividing the interior of a simply closed rectifiable curve with an application to Cauchy’s theorem,” Bull. Sci. Lab. Denison Univ. 17 (1914), pp. 375–389.

[36] :
“A note on symmetrical matrices,”
Bull. Am. Math. Soc.
20
(1914),
pp. 453–454.
Abstract only; published in *Ann. of Math.* **16** (1914–1915), pp. 43–44.
JFM
45.0266.08

[37] :
“The Weierstrass __\( E \)__-function for problems of the Calculus of Variations in space,”
Trans. Amer. Math. Soc.
15 : 4
(October 1914),
pp. 369–378.
MR
1500985
JFM
45.0604.03

[38] : “The minimum of a definite integral for unilateral variations in space,” Trans. Amer. Math. Soc. 15 : 3 (1914), pp. 291–310. MR 1500981 JFM 45.0605.03

[39] : “A note on symmetric matrices,” Ann. of Math. (2) 16 : 1–4 (1914–1915), pp. 43–44. MR 1502486 JFM 45.0262.05

[40] : “A substitute for Duhamel’s theorem,” Ann. of Math. (2) 16 : 1–4 (1914–1915), pp. 45–49. MR 1502487 JFM 45.0452.02

[41] : “Generalizations of geodesic curvature and a theorem of Gauss concerning geodesic triangles,” Amer. J. Math. 37 : 1 (January 1915), pp. 1–18. MR 1507894 JFM 45.0859.02

[42] : “Book review: Leçons sur les fonctions des lignes, by Vito Volterra,” Bull. Amer. Math. Soc. 21 : 7 (1915), pp. 345–355. MR 1559651

[43] : “A note on functions of lines,” Proc. Natl. Acad. Sci. USA 1 : 3 (March 1915), pp. 173–177. JFM 45.0550.01

[44] : “A note on the problem of Lagrange in the Calculus of Variations,” Bull. Amer. Math. Soc. 22 : 5 (1916), pp. 220–225. MR 1559765 JFM 45.0605.01

[45] : “Book review: Topics in the theory of functions of several complex variables, by William Fogg Osgood,” Bull. Amer. Math. Soc. 23 : 1 (1916), pp. 35–44. MR 1559859

[46] : “Jacobi’s condition for problems of the Calculus of Variations in parametric form,” Trans. Amer. Math. Soc. 17 : 2 (April 1916), pp. 195–206. MR 1501037 JFM 46.0758.03

[47] : “A necessary and sufficient condition for the existence of a Stieltjes integral,” Proc. Natl. Acad. Sci. USA 3 : 11 (November 1917), pp. 633–637. JFM 46.1458.03

[48] : “Integrals of Lebesgue,” Bull. Amer. Math. Soc. 24 : 1 (1917), pp. 1–47. MR 1560001 JFM 46.0383.01

[49] : “A device applicable to the problems of Lagrange and Mayer in the Calculus of Variations,” Bull. Am. Math. Soc. 23 (1917), pp. 255–256. Abstract only; article unpublished. JFM 46.0758.02

[50] : “The problem of Mayer with variable end points,” Trans. Amer. Math. Soc. 19 : 3 (1918), pp. 305–314. MR 1501104 JFM 46.0758.04

[51] : “Solutions of differential equations as functions of the constants of integration,” Bull. Amer. Math. Soc. 25 : 1 (1918), pp. 15–26. MR 1560139 JFM 47.0940.01

[52] : “A method of computing differential corrections for a trajectory,” J. U.S. Artillery 51 (1919), pp. 445–449. Corrected copy of earlier printing in vol. 50 (pp. 455–460).

[53] : “The use of adjoint systems in the problem of differential corrections for a trajectory,” J. U.S. Artillery 51 (1919), pp. 296–311.

[54] : Differential corrections for anti-aircraft guns. Technical report, Aberdeen Proving Ground, 1919.

[55] : “Functions of lines in ballistics,” Trans. Amer. Math. Soc. 21 : 2 (1920), pp. 93–106. MR 1501138 JFM 47.0382.02

[56] : “Differential equations containing arbitrary functions,” Trans. Amer. Math. Soc. 21 : 2 (1920), pp. 79–92. MR 1501137

[57] : “Some recent developments in the Calculus of Variations,” Bull. Amer. Math. Soc. 26 : 8 (1920), pp. 343–361. MR 1560316 JFM 47.0471.04

[58] : “Birational transformations simplifying singularities of algebraic curves,” Trans. Amer. Math. Soc. 24 : 4 (1922), pp. 274–285. MR 1501226 JFM 50.0266.02

[59] : “A letter from the president,” Bull. Amer. Math. Soc. 28 : 1–2 (January–February 1922), pp. 16. Letter to members of the American Mathematical Society. MR 1560495

[60] : “The reduction of singularities of plane curves by birational transformation,” Bull. Amer. Math. Soc. 29 : 4 (1923), pp. 161–183. Presidential address delivered before the American Mathematical Society, December 28, 1922. MR 1560693 JFM 49.0264.01

[61] : “Book review: Vorlesungen über Differentialgeometrie und geometrische Grundlagen von Einstein’s Relativitätstheorie, vol. 1: Elementare Differentialgeometrie, by W. Blaschke,” Bull. Amer. Math. Soc. 29 : 7 (1923), pp. 322–325. MR 1560739

[62] : “Algebraic functions and their divisors,” Ann. of Math. (2) 26 : 1–2 (September–October 1924), pp. 95–124. MR 1502680 JFM 50.0699.03

[63] : “Boundary value problems for systems of linear differential equations of the first order,” Bull. Am. Math. Soc. 31 (1925), pp. 215. Abstract only; article unpublished. JFM 51.0343.02

[64] : Calculus of Variations. Carus Mathematical Monographs 1. MAA/Open Court (Chicago), 1925. JFM 51.0372.01

[65] : “A boundary value problem in the Calculus of Variations,” Bull. Amer. Math. Soc. 32 : 4 (1926), pp. 317–331. MR 1561219 JFM 52.0509.02

[66] : “A boundary value problem for a system of ordinary linear differential equations of the first order,” Trans. Amer. Math. Soc. 28 : 4 (1926), pp. 561–584. MR 1501366 JFM 52.0453.13

[67] : “Book review: Elementi del calcolo delle variazioni, by G. Vivanti,” Bull. Amer. Math. Soc. 32 : 4 (1926), pp. 392–393. MR 1561233

[68] : “Contributions that have been made by pure science to the advancement of engineering and industry. Mathematics.,” Sci. Mon. 24 (1927), pp. 308–319. JFM 52.0036.11

[69] : “Book review: Calculus of Variations, by A. R. Forsyth,” Bull. Amer. Math. Soc. 34 : 4 (1928), pp. 512–514. MR 1561597

[70] : “The visiting lectureship of the American Mathematical Society,” Bull. Amer. Math. Soc. 34 : 1 (1928), pp. 22. MR 1561501

[71] : “The transformation of Clebsch in the Calculus of Variations,” pp. 589–603 in Proceedings of the International Mathematical Congress (Toronto, 11–16 August 1924), vol. 1. Edited by J. C. Fields. University of Toronto Press, 1928. JFM 54.0532.03

[72] : “Expansions for implicit functions near a very general type of singularity,” Bull. Am. Math. Soc. 35 : 4 (July–August 1929), pp. 459–460. Abstract only; article unpublished. JFM 55.0135.05

[73] : “An integral inequality,” J. London Math. Soc. S1-5 : 1 (1930), pp. 40–46. MR 1574997 JFM 56.0434.02

[74] : “The problem of Lagrange in the Calculus of Variations,” Amer. J. Math. 52 : 4 (October 1930), pp. 673–744. MR 1506783 JFM 56.0435.01

[75]Contributions to the Calculus of Variations, 1930. Edited by G. A. Bliss and L. M. Graves. University of Chicago Press, 1931. Zbl 0003.40002

[76] : “On separation, comparison and oscillation theorems for self-adjoint systems of linear second order differential equations,” Amer. J. Math. 53 : 4 (October 1931), pp. 781–800. MR 1506854 JFM 57.0528.01 Zbl 0003.25702

[77] : “The Calculus of Variations and the quantum theory,” Bull. Amer. Math. Soc. 38 : 4 (1932), pp. 201–224. MR 1562365 JFM 58.0530.01 Zbl 0004.15601

[78] : “The problem of Bolza in the Calculus of Variations,” Ann. of Math. (2) 33 : 2 (April 1932), pp. 261–274. MR 1503050 JFM 58.0535.02 Zbl 0004.15502

[79] : “On the derivation of necessary conditions for the problem of Bolza,” Bull. Amer. Math. Soc. 38 : 12 (1932), pp. 858–864. MR 1562533 JFM 58.0535.01 Zbl 0006.25902

[80]Topics of the Calculus of Variations. Edited by G. Bliss. University of Chicago, 1932. Principally a report on lectures by E. J. McShane and Richard Courant.

[81] : Variationsrechnung. Edited by F. Schwank. B. G. Teubner (Leipzig and Berlin), 1932. JFM 58.0529.08 Zbl 0003.34803

[82] : “Ernest Julius Wilczynski,” Science 76 : 1971 (October 1932), pp. 316–317. JFM 58.0995.07

[83] : Algebraic functions. AMS Colloquium Publications 16. American Mathematical Society (New York), 1933. JFM 59.0384.03 Zbl 0008.21004

[84] : The Calculus of Variations, multiple integrals. University of Chicago, 1933. MR 2936825

[85]Contributions to the Calculus of Variations, 1931–32. Edited by G. A. Bliss and L. M. Graves. University of Chicago Press, 1933. Zbl 0006.40401

[86] : “Sufficient conditions for a problem of Mayer in the Calculus of Variations,” Trans. Amer. Math. Soc. 35 : 1 (1933), pp. 305–326. MR 1501685 JFM 59.0497.02 Zbl 0006.25903

[87] : “Eliakim Hastings Moore,” Bull. Amer. Math. Soc. 39 : 11 (1933), pp. 831–838. MR 1562740 JFM 59.0038.02

[88] : “Eliakim Hastings Moore,” Univ. Rec. 19 (1933), pp. 130–134.

[89] :
“Mathematical interpretations of geometrical and physical phenomena,”
Amer. Math. Monthly
40 : 8
(October 1933),
pp. 472–480.
Reprinted as Chapter 8 of *A mathematician explains* by M. I. Logsdon (University of Chicago Press, 1936) pp. 146–158.
MR
1522896
JFM
59.0060.01

[90] : “The scientific work of Eliakim Hastings Moore,” Bull. Amer. Math. Soc. 40 : 7 (1934), pp. 501–514. MR 1562892

[91] : Fundamental existence theorems. AMS Colloquium Publications 3: The Princeton Colloquium 1909. American Mathematical Society (New York), 1934. Princeton University, 15–17 September 1909. JFM 60.1092.01

[92] : The Calculus of Variations in three space. University of Chicago, 1934. Lecture notes, Spring 1934.

[93] : The problem of Bolza in the Calculus of Variations. University of Chicago, 1935. Lecture notes, Winter 1935.

[94] : “Beginnings of the Calculus,” Natl. Math. Mag. 10 : 3 (December 1935), pp. 103. MR 1569267

[95] : “Abnormality in the Calculus of Variations,” Bull. Am. Math. Soc. 41 : 5 (May 1935), pp. 343–344. Abstract only. JFM 61.0556.12

[96] : “Book review: ‘Inequalities’, by Hardy, Littlewood, and Pólya,” Science 81 (1935), pp. 565–566.

[97] : “The evolution of problems of the Calculus of Variations,” Amer. Math. Monthly 43 : 10 (December 1936), pp. 598–609. MR 1523791 Zbl 0015.35702

[98] : “Biographical memoir of Eliakim Hastings Moore, 1862–1932,” Proc. Natl. Acad. Sci. USA 17 (1936), pp. 83–102.

[99]Contributions to the Calculus of Variations, 1933–37. Edited by G. A. Bliss, L. M. Graves, and W. T. Reid. University of Chicago Press, 1937.

[100] : “Herbert Ellsworth Slaught,” Science 86 (1937), pp. 72–73.

[101] :
“Herbert Ellsworth Slaught,”
Univ. Chicago Mag.
1937 : Mid–summer
(1937),
pp. 22–24.
Reprinted in *Bull. Kans. Assoc. Math. Teach.* 12:3, 9–12.

[102] : “Herbert Ellsworth Slaught — In memoriam,” Bull. Amer. Math. Soc. 43 : 9 (1937), pp. 595–597. MR 1563596

[103] : “Eliakim Hastings Moore: 1862–1932,” Biographical Memoirs of the National Academy of Sciences 17 (1937), pp. 83–102. article

[104] : “Herbert Ellsworth Slaught — teacher and friend,” Amer. Math. Monthly 45 : 1 (January 1938), pp. 5–10. MR 1524156 JFM 64.0023.14

[105] : “Normality and abnormality in the Calculus of Variations,” Trans. Amer. Math. Soc. 43 : 3 (1938), pp. 365–376. MR 1501950 JFM 64.0510.01 Zbl 0019.12303

[106] : “Definitely self-adjoint boundary value problems,” Trans. Amer. Math. Soc. 44 : 3 (1938), pp. 413–428. MR 1501974 JFM 64.0438.02 Zbl 0020.03204

[107]Contributions to the Calculus of Variations, 1938–41. Edited by G. A. Bliss, M. R. Hestenes, and W. T. Reid. University of Chicago Press, 1942.

[108] : “The Calculus of Variations for multiple integrals,” Amer. Math. Monthly 49 : 2 (February 1942), pp. 77–89. MR 0006022 Zbl 0063.00455

[109] : “Oskar Bolza,” Science 97 : 2509 (1943), pp. 108–109. article

[110] : Mathematics for exterior ballistics. John Wiley and Sons (New York), 1944. MR 0010480 Zbl 0063.00457

[111] : “Oskar Bolza — in memoriam,” Bull. Amer. Math. Soc. 50 : 7 (1944), pp. 478–489. MR 1564626

[112] : Lectures on the calculus of variations. University of Chicago Press (Chicago, IL), 1946. MR 0017881 Zbl 0063.00459

[113] : “Autobiographical notes,” Amer. Math. Monthly 59 (1952), pp. 595–606. MR 0050513

[114] : Algebraic functions. AMS Colloquium Publications 16. Dover Publications (New York), 1966. MR 0203007 Zbl 0141.05002

[115] : Calculus of Variations, 6th edition. Carus Mathematical Monographs 1. The Mathematical Association of America (Washington, DC), 1971. Zbl 0317.49001