BooksAnalysis and university
Analysis and university books
Kiselev’s Calculus, Fikhtengolts’s analysis, the Demidovich and Gunter & Kuzmin problem collections, and other university-level classics.
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Analysis and university books: 11 books
Fuss's Pure Mathematics, Part III
by N. I. Fuss
US grades 11–12 and university · UK Years 12–13 and undergraduate
The third part of Fuss's course of pure mathematics, after the Algebra and the Geometry, in first faithful English translation from the original Russian edition. Four divisions, 32 chapters and 480 numbered sections. The application of algebra to geometry: geometric questions solved by equations of the first to the fourth degree. Plane trigonometry: the trigonometric lines and their properties, the solution of triangles, questions of practical geometry, further formulas, and the solution of cubic equations by trigonometry. Conic sections: the sections of a cone, curved lines in general, the circle, the ellipse, the parabola and the hyperbola. The foundations of the differential and integral calculus: differentials of algebraic and transcendental functions, tangents, points of inflection, greatest and least quantities, integrals, the length and quadrature of curves, the surfaces and volumes of solids of revolution, and the inverse method of tangents. 219 questions are worked with full solutions; the 157 figures are reproduced on twelve engraved plates.
Markov: Probabilities
by Andrei A. Markov
US grades 12 and university · UK Year 13 and university
The foundational 1900 work on probability theory by the mathematician who gave us Markov chains. A modern annotated English translation.
Fikhtengol'ts' Analysis, Vol. I
by G. M. Fikhtengol'ts
US grades University 1–2 · UK Undergraduate 1–2
The university course in mathematical analysis by the founder of the Leningrad school of the theory of functions, in first faithful English translation from the original Russian edition. Fourteen chapters run from the real numbers through functions, limits and the number e, continuity, the derivative and the differential, the mean-value theorems and Taylor's formula, the study of functions by their derivatives, functions of several variables and their differentiation and extrema, the indefinite and the definite integral, geometric and mechanical applications, curvature, and a historical survey of the origins of analysis from its prehistory to Newton and Leibniz. 390 pages with an alphabetical index.
Gunter & Kuzmin
by N. M. Gunter & R. O. Kuzmin
US grades University 1–4 · UK Undergraduate
The standard Russian problem collection for higher mathematics — the book used across Soviet technical universities. 814 pages spanning mathematical analysis, differential and integral calculus, series, differential equations, and probability theory, in the first complete English translation.
Gunter & Kuzmin, Part I
by N. M. Gunter & R. O. Kuzmin
US grades University 1–2 · UK Undergraduate
The first half of the standard Russian problem book for higher mathematics, as a volume on its own: analytic geometry in the plane and in space, differential calculus and its applications including differential geometry, higher algebra, and indefinite and definite integration. 448 pages.
Gunter & Kuzmin, Part II
by N. M. Gunter & R. O. Kuzmin
US grades University 2–4 · UK Undergraduate 2–3
The second half completes the collection: multiple, curvilinear and surface integrals, field and potential theory, ordinary and partial differential equations, improper integrals and special functions, series and Fourier series, approximate computation, functions of a complex variable, mathematical physics, the calculus of variations and probability. 379 pages.
Demidovich's Analysis Problems
by B. P. Demidovich
US grades University 1–2 · UK Undergraduate 1–2
Demidovich's university problem book in mathematical analysis, in first faithful English translation from the original Russian edition. Two parts, eight chapters and 82 numbered sections hold 4,683 numbered problems, each section opening with a short summary of theory: real numbers, sequences, limits and continuity, O-notation, uniform continuity and functional equations; the differential calculus of one variable, from the theorems of Rolle, Lagrange and Cauchy to curvature and evolutes; indefinite and definite integrals with their geometric and physical applications; numerical, functional, power and Fourier series, infinite products and Stirling's formula; the differential calculus of several variables; integrals depending on a parameter, Euler's integrals and the Fourier integral formula; and double, triple, many-fold, line and surface integrals, through the formulas of Green, Stokes and Ostrogradsky to the elements of field theory. Answers, with hints, are at the back. Fourteen figures.
Kiselev's Calculus
by A. P. Kiselev
US grades 11–12 · UK Years 12–13
The first complete English translation of Kiselev's calculus — the final volume in his school course. Single-variable differential and integral calculus, proof-based, with classical applications to mechanics and physics. The bridge from Algebra II into the analysis tradition that produced Markov's probability theory.
Fikhtengol'ts' Analysis, Vol. II
by G. M. Fikhtengol'ts
US grades University 1–2 · UK Undergraduate 1–2
The second volume of the university course in mathematical analysis by the founder of the Leningrad school of the theory of functions, in a faithful new English edition. Ten chapters continue directly from Volume I: numerical series and infinite products; sequences and series of functions, power series and approximate computation; improper integrals and integrals depending on a parameter, with the Eulerian integrals; implicit functions and functional determinants; line, double, surface and triple integrals, the formulas of Green, Ostrogradsky and Stokes, and the elements of field theory; Fourier series and the Fourier integral. A concluding sketch points towards differential equations, the calculus of variations, complex and real analysis and functional analysis. 192 numbered articles (Nos. 234–425), 88 figures, 412 pages with an alphabetical index.
Yushkevich: Mathematics in Russia
by A. P. Yushkevich
US grades University and adult · UK Undergraduate and adult
A. P. Yushkevich’s history of mathematics in Russia from its beginnings to 1917, in first faithful English translation from the original Russian edition. Four parts and 26 chapters: numeration, metrology and the arithmetic and geometric manuscripts of old Rus’; Magnitsky’s Arithmetic and the schools of Peter the First; the Petersburg Academy of Sciences, with five chapters on Euler — infinite series, his trilogy on analysis, differential equations and the calculus of variations — and one on his students and successors, Fuss among them; Lobachevsky and the discovery of non-Euclidean geometry; Ostrogradsky and Bunyakovsky; Chebyshev and the Petersburg school, with chapters on number theory, probability theory, the approximation of functions, differential equations, series, analytic functions, geometry and algebra; and the rise of the Moscow school of function theory under Egorov and Luzin. The school textbooks of Kiselev, Davidov, and Malinin and Burenin appear in their place. Fifty numbered figures with portraits and facsimiles, and a name index. 673 pages.
Demidovich's Analysis Problems for Engineers
by B. P. Demidovich (editor)
US grades University 1–2 · UK Undergraduate 1–2
The problem collection in mathematical analysis written for engineering colleges by ten authors under the editorship of B. P. Demidovich, in faithful English translation from the original Russian edition. Ten chapters and 102 numbered sections hold 3,199 numbered problems, each section opening with a summary of theory and worked examples: functions, limits and continuity; differentiation and its geometrical and mechanical applications; extrema, asymptotes and curve sketching; the indefinite and the definite integral, with areas, volumes, centres of gravity and physical problems; functions of several variables, through directional derivatives, envelopes and the curvature and torsion of space curves; multiple, line and surface integrals and the elements of field theory; number, functional, Taylor and Fourier series; a full chapter of 404 problems on differential equations; and a chapter of approximate calculations — interpolation, real roots of equations, numerical integration of functions and of differential equations. Answers follow, with hints and, for the problems marked with two asterisks, solutions. 107 numbered figures and six appendix tables.