Brief but intriguing, this monograph on the theory of elliptic functions was written by one of America's most prominent and widely read mathematicians. Richard Bellman encompasses a wealth of material in a succession of short chapters, spotlighting high points of the fundamental regions of elliptic functions and illustrating powerful and versatile analytic methods.Suitable for advanced undergraduates and graduate students in mathematics, this introductory treatment is largely self-contained. Topics include Fourier series, sufficient conditions, the Laplace transform, results of Doetsch and Kober-Erdelyi, Gaussian sums, and Euler's formulas and functional equations. Additional subjects include partial fractions, mock theta functions, Hermite's method, convergence proof, elementary functional relations, multidimensional Poisson summation formula, the modular transformation, and many other areas.

A Brief Introduction to Theta Functions

Science & Math

Richard Bellman

Mathematics

HOLT.

Perturbation Techniques in Mathematics, Physics, and Engineering

HOLT. RINEHART AND WINSTON

In this book, we study theoretical and practical aspects of computing methods for mathematical modelling of nonlinear systems. A number of computing techniques are considered, such as methods of operator approximation with any given accuracy; operator interpolation techniques including a non-Lagrange interpolation; methods of system representation subject to constraints associated with concepts of causality, memory and stationarity; methods of system representation with an accuracy that is the best within a given class of models; methods of covariance matrix estimation; methods for low-rank matrix approximations; hybrid methods based on a combination of iterative procedures and best operator approximation; and methods for information compression and filtering under condition that a filter model should satisfy restrictions associated with causality and different types of memory. As a result, the book represents a blend of new methods in general computational analysis, and specific, but also generic, techniques for study of systems theory ant its particular branches, such as optimal filtering and information compression. - Best operator approximation, - Non-Lagrange interpolation, - Generic Karhunen-Loeve transform - Generalised low-rank matrix approximation - Optimal data compression - Optimal nonlinear filtering

Methods of Nonlinear Analysis, Vol. 1 (Mathematics in Science and Engineering Series, Vol. 61)

Academic Press

Differential-Difference Equations [hardcover] Richard Bellman,Kenneth L. Cooke [Apr 19, 2012]

Differential-Difference Equations

Computers & Technology

Kenneth L. Cooke

Computer Science

Perturbation techniques in mathematics, physics, and engineering

Dover Publications. Inc.

This classic book is an introduction to dynamic programming, presented by the scientist who coined the term and developed the theory in its early stages. In Dynamic Programming, Richard E. Bellman introduces his groundbreaking theory and furnishes a new and versatile mathematical tool for the treatment of many complex problems, both within and outside of the discipline.
 The book is written at a moderate mathematical level, requiring only a basic foundation in mathematics, including calculus. The applications formulated and analyzed in such diverse fields as mathematical economics, logistics, scheduling theory, communication theory, and control processes are as relevant today as they were when Bellman first presented them. A new introduction by Stuart Dreyfus reviews Bellman's later work on dynamic programming and identifies important research areas that have profited from the application of Bellman's theory.

Dynamic Programming (Princeton Landmarks in Mathematics and Physics, 33)

Princeton University Press

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Books by Richard Bellman