# An appreciation of professor M. R. Hestenes

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## Publications of Professor M. R. Hestenes

- 1.
*Sufficient Conditions for a Problem of Mayer in the Calculus of Variations*, Transactions of the American Mathematical Society, Vol. 35, pp. 305–326, 1933 (with G. A. Bliss).Google Scholar - 2.
*Sufficient Conditions for a Problem of Mayer in the Calculus of Variations*, Contributions to the Calculus of Variations, 1931–32, The University of Chicago Press, Chicago, Illinois, 1933 (with G. A. Bliss).Google Scholar - 3.
*Sufficient Conditions for the General Problem of Mayer with Variable Endpoints*, Transactions of the American Mathematical Society, Vol. 35, pp. 479–490, 1933.Google Scholar - 4.
*Sufficient Conditions for the General Problem of Mayer with Variable Endpoints*, Contributions to the Calculus of Variations, 1931–32, The University of Chicago Press, Chicago, Illinois, 1933.Google Scholar - 5.
*Sufficient Conditions for the Problem of Bolza in the Calculus of Variations*, Transactions of the American Mathematical Society, Vol. 36, pp. 793–818, 1934.Google Scholar - 6.
*A Note on the Jacobi Conditions for Parametric Problems in the Calculus of Variations*, Bulletin of the American Mathematical Society, Vol. 40, pp. 297–302, 1934.Google Scholar - 7.
*Generalized Minimax Principle in the Calculus of Variations*, Proceedings of the National Academy of Sciences, Vol. 21, pp. 96–99, 1935 (with G. D. Birkhoff).Google Scholar - 8.
*Natural Isoperimetric Conditions in the Calculus of Variations*, Duke Mathematical Journal, Vol. 1, pp. 198–286, 1935.Google Scholar - 9.
*Natural Isoperimetric Conditions in the Calculus of Variations*, Proceedings of the National Academy of Sciences, Vol. 21, pp. 99–102, 1935.Google Scholar - 10.
*Generalized Minimax Principle in the Calculus of Variations*, Duke Mathematical Journal, Vol. 1, pp. 413–432, 1935 (with G. D. Birkhoff).Google Scholar - 11.
*Minimax Principle for Functions*, Proceedings of the National Academy of Sciences, Vol. 22, pp. 115–119, 1935.Google Scholar - 12.
*On Sufficient Conditions in the Problems of Lagrange and Bolza*, Annals of Mathematics, Vol. 37, pp. 543–551, 1936.Google Scholar - 13.
*The Problem of Bolza in the Calculus of Variations in Parametric Form*, American Journal of Mathematics, Vol. 58, pp. 391–406, 1936.Google Scholar - 14.
*A Direct Sufficiency Proof for the Problem of Bolza in the Calculus of Variations*, Transactions of the American Mathematical Society, Vol. 42, pp. 141–154, 1937.Google Scholar - 15.
*A Sufficiency Proof for Isoperimetric Problems in the Calculus of Variations*, Bulletin of the American Mathematical Society, Vol. 44, pp. 662–667, 1938.Google Scholar - 16.
*Generalized Problem of Bolza in the Calculus of Variations*, Duke Mathematical Journal, Vol. 5, pp. 309–324, 1939.Google Scholar - 17.
*A Note on the Weierstrass Condition in the Calculus of Variations*, Bulletin of the American Mathematical Society, Vol. 45, pp. 471–473, 1939.Google Scholar - 18.
*A Theorem on Quadratic Forms with Applications in the Calculus of Variations*, Transactions of the American Mathematical Society, Vol. 47, pp. 501–502, 1940 (with E. J. McShane).Google Scholar - 19.
*Extension of the Range of a Differentiable Function*, Duke Mathematical Journal, Vol. 8, pp. 183–192, 1941.Google Scholar - 20.
*An Analogue of Green's Theorem in the Calculus of Variations*, Duke Mathematical Journal, Vol. 8, pp. 300–311, 1941.Google Scholar - 21.
*The Problem of Bolza in the Calculus of Variations*, Bulletin of the American Mathematical Society, Vol. 48, pp. 57–75, 1942.Google Scholar - 22.
*A Theory of Critical Points*, American Journal of Mathematics, Vol. 67, pp. 521–562, 1945.Google Scholar - 23.
*The Weierstrass E-Function in the Calculus of Variations*, Transactions of the American Mathematical Society, Vol. 60, pp. 51–71, 1946.Google Scholar - 24.
*Theorem of Lindeberg in the Calculus of Variations*, Transactions of the American Mathematical Society, Vol. 60, pp. 72–92, 1946.Google Scholar - 25.
*Sufficient Conditions for the Isoperimetric Problem of Bolza in the Calculus of Variations*, Transactions of the American Mathematical Society, Vol. 60, pp. 93–118, 1945.Google Scholar - 26.
*An Alternate Sufficiency Proof for the Normal Problem of Bolza*, Transactions of the American Mathematical Society, Vol. 61, pp. 256–264, 1946.Google Scholar - 27.
*An Indirect Sufficiency Proof for the Problem of Bolza in Nonparametric Form*, Transactions of the American Mathematical Society, Vol. 62, pp. 509–535, 1947.Google Scholar - 28.
*Sufficient Conditions for Multiple Integral Problems in the Calculus of Variations*, American Journal of Mathematics, Vol. 70, pp. 239–276, 1948.Google Scholar - 29.M. R. Hestenes
*Numerical Methods of Obtaining Solutions of Fixed Endpoint Problems in the Calculus of Variations*, The RAND Corporation, Research Memorandum No. 102, 1949.Google Scholar - 30.M. R. Hestenes
*A General Problem in the Calculus of Variations with Applications to the Paths of Least Time*, The RAND Corporation, Research Memorandum No. 100, 1950.Google Scholar - 31.
*An Elementary Introduction to the Calculus of Variations*, Mathematics Magazine, Vol. 24, pp. 250–267, 1950.Google Scholar - 32.
*Applications of the Theory of Quadratic Forms in Hilbert Space to the Calculus of Variations*, Pacific Journal of Mathematics, Vol. 1, pp. 525–581, 1951.Google Scholar - 33.
*A Method of Gradients for the Calculation of the Characteristic Roots and Vectors of a Real Symmetric Matrix*, Journal of Research, National Bureau of Standards, Vol. 47, pp. 45–61, 1951 (with W. E. Karush).Google Scholar - 34.
*The Separation of Close Eigenvalues of a Real Symmetric Matrix*, Journal of Research, National Bureau of Standards, Vol. 47, pp. 291–297, 1951 (with J. B. Rosser, C. Lanczos, and W. E. Karush).Google Scholar - 35.
*Solution of the Equation Ax = λBx*, Journal of Research, National Bureau of Standards, Vol. 47, pp. 471–478, 1951 (with W. E. Karush).Google Scholar - 36.
*Method of Conjugate Gradients for Solving Linear Systems*, Journal of Research, National Bureau of Standards, Vol. 49, pp. 409–438, 1952 (with E. Stiefel).Google Scholar - 37.
*Determination of Eigenvalues and Eigenvectors of Matrices*, Simultaneous Linear Equations and the Determination of Eigenvalues, Edited by L. J. Paige and O. Tausky, National Bureau of Standards, Applied Mathematics Series, Vol. 29, US Government Printing Office, Washington, DC, 1953.Google Scholar - 38.
*Hilbert Space Methods in Variational Theory and Numerical Analysis*, Proceedings of the International Congress of Mathematicians, Vol. 3, Edited by J. Gerretsen and J. De Groot, North Holland Publishing Company, Amsterdam, Holland, 1954.Google Scholar - 39.
*Iterative Computational Methods*, Communications on Pure and Applied Mathematics, Vol. 8, pp. 85–96, 1956.Google Scholar - 40.
*Elements of the Calculus of Variations*, Modern Mathematics for the Engineer, Edited by E. F. Beckenbach, McGraw-Hill Book Company, New York, New York, 1956.Google Scholar - 41.
*The Conjugate-Gradient Method for Solving Linear Systems*, Proceedings of the Sixth Symposium in Applied Mathematics, Vol. 6, Edited by J. H. Curtis, American Mathematical Society, Providence, Rhode Island, 1956.Google Scholar - 42.
*Inversion of Matrices by Biorthogonalization and Related Results*, SIAM Journal on Applied Mathematics, Vol. 6, pp. 51–90, 1958.Google Scholar - 43.
*Relative Hermitian Matrices*, Pacific Journal of Mathematics, Vol. 11, pp. 225–245, 1961.Google Scholar - 44.
*Relative Self-Adjoint Operators in Hilbert Space*, Pacific Journal of Mathematics, Vol. 11, pp. 1315–1357, 1961.Google Scholar - 45.
*Quadratic Variational Theory and Linear Elliptic Partial Differential Equations*, Transactions of the American Mathematical Society, Vol. 101, pp. 306–350, 1961.Google Scholar - 46.
*A Ternary Algebra with Applications to Matrices and Linear Transformations*, Archive for Rational Mechanics and Analysis, Vol. 2, pp. 138–194, 1962.Google Scholar - 47.
*Variational Theory and Optimal Control Theory*, Computing Methods in Optimization Problems, Edited by A. V. Balakrishnan and L. W. Neustadt, Academic Press, New York, New York, 1964.Google Scholar - 48.
*On Variational Theory and Optimal Control Theory*, SIAM Journal on Control, Vol. 3, pp. 23–48, 1965.Google Scholar - 49.
*Calculus of Variations and Optimal Control Theory*, John Wiley and Sons, New York, New York, 1966.Google Scholar - 50.
*Elements of Calculus of Variations and Optimum Control Theory*, Space Mathematics, Part 2, Edited by J. B. Rosser, American Mathematical Society, Providence, Rhode Island, 1966.Google Scholar - 51.
*An Embedding Theorem for Differential Equations*, Journal of Optimization Theory and Applications, Vol. 2, pp. 87–101, 1968.Google Scholar - 52.
*Pairs of Quadratic Forms*, Linear Algebra and Its Applications, Vol. 1, pp. 397–407, 1968.Google Scholar - 53.
*Multiplier and Gradient Methods*, Computing Methods in Optimization Theory, Edited by A. V. Balakrishnan*et al.*, Academic Press, New York, New York, 1969.Google Scholar - 54.
*Multiplier and Gradient Methods*, Journal of Optimization Theory and Applications, Vol. 4, pp. 303–320, 1969.Google Scholar - 55.
*Quadratic Variational Theory*, Control Theory, and the Calculus of Variations, Edited by A. V. Balakrishnan, Academic Press, New York, New York, 1969.Google Scholar - 56.
*Iterative Methods for Solving Linear Equations*, Journal of Optimization Theory and Applications, Vol. 11, pp. 323–334, 1973.Google Scholar - 57.
*The Solution of Linear Equations by Minimization*, Journal of Optimization Theory and Applications, Vol. 11, pp. 335–359, 1973 (with M. L. Stein).Google Scholar - 58.
*On a Ternary Algebra*, Scripta Mathematics, Vol. 29, pp. 253–272, 1973.Google Scholar

## Copyright information

© Plenum Publishing Corporation 1974