Undergraduate Texts in Mathematics Series

This fifth edition of Lang's book covers all the topics traditionally taught in the first-year calculus sequence. Divided into five parts, each section of A FIRST COURSE IN CALCULUS contains examples and applications relating to the topic covered. In addition, the rear of the book contains detailed solutions to a large number of the exercises, allowing them to be used as worked-out examples -- one of the main improvements over previous editions.

Undergraduate Algebra

by Serge Lang

Published 22 December 1986

The companion title, Linear Algebra, has sold over 8,000 copies

The writing style is very accessible

The material can be covered easily in a one-year or one-term course

Includes Noah Snyder's proof of the Mason-Stothers polynomial abc theorem

New material included on product structure for matrices including descriptions of the conjugation representation of the diagonal group

Introduction to Linear Algebra

by Serge Lang

Published 22 May 1970

This is a short text in linear algebra, intended for a one-term course. In the first chapter, Lang discusses the relation between the geometry and the algebra underlying the subject, and gives concrete examples of the notions which appear later in the book. He then starts with a discussion of linear equations, matrices and Gaussian elimination, and proceeds to discuss vector spaces, linear maps, scalar products, determinants, and eigenvalues. The book contains a large number of exercises, some of the routine computational type, while others are conceptual.

Renewable Energy Integration: Challenges and Solutions

by Serge Lang and S. Lang

Published 1 January 2014

Calculus of Several Variables

by Serge Lang

Published December 1973

This is a new, revised edition of this widely known text. All of the basic topics in calculus of several variables are covered, including vectors, curves, functions of several variables, gradient, tangent plane, maxima and minima, potential functions, curve integrals, Green's theorem, multiple integrals, surface integrals, Stokes' theorem, and the inverse mapping theorem and its consequences. The presentation is self-contained, assuming only a knowledge of basic calculus in one variable. Many completely worked-out problems have been included.

Linear Algebra

by Serge Lang

Published December 1971

This book begins with an exposition of the basic theory of vector spaces and proceeds to explain the fundamental structure theorem for linear maps, including eigenvectors and eigenvalues, quadratic and hermitian forms, diagnolization of symmetric, hermitian, and unitary linear maps and matrices, triangulation, and Jordan canonical form. Material in this new edition has been rewritten and reorganized and new exercises have been added.

Undergraduate Analysis

by Serge Lang

Published 31 December 1983

This is a self-contained introduction to analysis for students who have had two years of calculus. Topics discussed include the classical test for convergence of series, Fourier series, polynomial approximation, the Poisson kernel, and the construction of harmonic functions on the disc. Other topics discussed include ordinary differential equations, curve integrals, derivatives in vector spaces, multiple integrals, and others. The text aims to achieve a balance between concrete examples and general theorems, augmented by a variety of examples.

Short Calculus

by Serge Lang

Published 29 November 2001

From the reviews "This is a reprint of the original edition of Lang's 'A First Course in Calculus', which was first published in 1964....The treatment is 'as rigorous as any mathematician would wish it'....[The exercises] are refreshingly simply stated, without any extraneous verbiage, and at times quite challenging....There are answers to all the exercises set and some supplementary problems on each topic to tax even the most able." --Mathematical Gazette