Piskunov’s Differential and Integral Calculus, Volume I: Limits, Derivatives and Integrals — A Faithful English Edition (Russian Math Classics — English Editions)

Nikolai Piskunov's Differential and Integral Calculus is the classic Russian calculus course written for engineers. For decades it was the standard textbook at technical universities, it was translated into several languages, and it is still recommended to students who want a complete, rigorous and practical course. Volume I covers the differential calculus of one and several variables and the indefinite and definite integral, with their applications.

Piskunov introduces every concept through a concrete problem before defining it in general: the derivative through the velocity of a moving point, the definite integral through the area under a curve. Every theorem is proved, and every method is put to work at once in worked examples that show each step of the computation. Approximate methods are taught alongside the theory they rest on: roots of equations, Lagrange's and Newton's interpolation formulas, numerical differentiation, the method of least squares, and the rectangle, trapezoidal, Simpson and Chebyshev formulas for definite integrals. Each chapter ends with exercises, most with answers, which makes the book well suited to independent study.

Volume I contains twelve chapters: Number, Variable, Function; Limit and Continuity; The Derivative and the Differential; Theorems on Differentiable Functions; Investigation of the Behavior of Functions; Curvature of a Curve; Complex Numbers and Polynomials; Functions of Several Variables; Applications of the Differential Calculus to Geometry in Space; The Indefinite Integral; The Definite Integral; and Geometric and Mechanical Applications of the Definite Integral, including work, centers of mass and moments of inertia.

This is a new, faithful English translation, complete and unabridged: every chapter, all 249 figures and all the exercises and answers, newly typeset with a full English subject index. Piskunov's notation and his chapter, section and formula numbering are kept, so the volume pairs directly with Volume II. A translator's preface introduces the author and the book.

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