1. The real variable 2. Scalars and vectors 3. Tensors 4. Matrices 5. Multiple integrals 6. Potential theory 7. Operational methods 8. Physical applications of the operational method 9. Numerical methods 10. Calculus of variations 11. Functions of a complex variable 12. Contour integration and Bromwich's integral 13. Contour integration 14. Fourier's theorem 15. The factorial and related functions 16. Solution of linear differential equations of the second order 17. Asymptotic expansions 18. The equations of potential, waves and heat conduction 19. Waves in one dimension and waves with spherical symmetry 20. Conduction of heat in one and three dimensions 21. Bessel functions 22. Applications of Bessel functions 23. The confluent hypergeometric function 24. Legendre functions and associated functions 25. Elliptic functions Notes Appendix on notation Index.

Methods of Mathematical Physics. By Harold Jeffreys and Bertha Swirles Jeffreys. Pp. viii, 679. 63s. 1946. (Cambridge University Press)

Determinants, First Minors, and Cofactors.- A Summary of Basic Determinant Theory.- Intermediate Determinant Theory.- Particular Determinants.- Further Determinant Theory.- Applications of Determinants in Mathematical Physics.

http://inis.jinr.ru/sl/m_mathematics/ma_algebra/mal_linear%20algebra/vein%20r.,%20dale%20p.%20determinants%20and%20their%20applications%20in%20mathematical%20physics%20(springer,%201998)(isbn%200387985581)(393s).pdf

Determinants and their applications in mathematical physics

Sturmian comparison theorems for three-term recurrence equations

We express a weigthed generalization of the Delannoy numbers in terms of shifted Jacobi polynomials. A specialization of our formulas extends a relation between the central Delannoy numbers and Legendre polynomials, observed over 50 years ago, to all Delannoy numbers and certain Jacobi polynomials. Another specialization provides a weighted lattice path enumeration model for shifted Jacobi polynomials and allows the presentation of a combinatorial, non-inductive proof of the orthogonality of Jacobi polynomials with natural number parameters. The proof relates the orthogonality of these polynomials to the orthogonality of (generalized) Laguerre polynomials, as they arise in the theory of rook polynomials. We also find finite orthogonal polynomial sequences of Jacobi polynomials with negative integer parameters and expressions for a

Shifted Jacobi polynomials and Delannoy numbers

In Section 3, since relation (6) is valid only for n ≥ 2 r , the condition n ≥ r in relation (9) should be replaced by n ≥ 2 r . When r ≤ n ≤ 2 r − 1, relation (9) still holds but now relations (6) and (7) should be replaced, respectively, by the relations and the asterisk again denoting omission of the last column. The proof of (9) for r ≤ n ≤ 2 r − 1 is exactly similar to its proof for n ≥ 2 r .

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Solution of a general homogeneous linear difference equation

A solution is given for un + 1 in terms of u1 and u0, where the elements of the sequence {un} satisfy the linear difference equation Two linearly independent solutions of the equation are written as determinants and relations are given which can be used to check the evaluation of these determinants.

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Solution of a linear difference equation

/pdf/solutions-of-period-seven-for-a-logistic-difference-equation-2z4c98yodi.pdf

Solutions of period seven for a logistic difference equation

The paper discusses the differential equation from a fresh point of view, to supplement an earlier discussion by Noye. In particular, for n = 1 the equation can be transformed to the equation for a pendulum with viscous damping, with corresponding to critical damping. At the end of the paper, some related equations are considered.

On the differential equations for tide-well systems

The paper extends a theorem given by Entringer on the asymptotic expansion of a composite function.

Functions of asymptotic expansions

A proof is given of a result deduced from numerical work on the conformal mapping of the region exterior to a quadrilateral possessing an axis of symmetry. It is shown that the result follows from known relationships between hypergeometric functions.

A. Brown

Papers

Solution of a linear difference equation

Solutions of period seven for a logistic difference equation

On the differential equations for tide-well systems

Functions of asymptotic expansions

Proof of a conformal mapping relationship