An advanced calculus book primarily aimed at students majoring in mathematics.

Mathematical Analysis: A Modern Approach to Advanced Calculus.

Science & Math

Apostol, Tom M.

Mathematics

Addison-Wesley Publishing Co.

"This book is the first volume of a two-volume textbook for undergraduates and is indeed the crystallization of a course offered by the author at the California Institute of Technology to undergraduates without any previous knowledge of number theory. For this reason, the book starts with the most elementary properties of the natural integers. Nevertheless, the text succeeds in presenting an enormous amount of material in little more than 300 pages."-―MATHEMATICAL REVIEWS

Introduction to Analytic Number Theory (Undergraduate Texts in Mathematics)

Springer

Modular functions and Dirichlet series in number theory (Graduate texts in mathematics)

Springer, Verlag

A new edition of a classical treatment of elliptic and modular functions with some of their number-theoretic applications, this text offers an updated bibliography and an alternative treatment of the transformation formula for the Dedekind eta function. It covers many topics, such as Hecke’s theory of entire forms with multiplicative Fourier coefficients, and the last chapter recounts Bohr’s theory of equivalence of general Dirichlet series.

Modular Functions and Dirichlet Series in Number Theory (Graduate Texts in Mathematics, 41)

Linear Algebra: A First Course with Applications to Differential Equations

Developed from the author's successful two-volume Calculus text this book presents Linear Algebra without emphasis on abstraction or formalization. To accommodate a variety of backgrounds, the text begins with a review of prerequisites divided into precalculus and calculus prerequisites. It continues to cover vector algebra, analytic geometry, linear spaces, determinants, linear differential equations and more.

Wiley-Interscience

An introduction to the Calculus, with an excellent balance between theory and technique. Integration is treated before differentiation--this is a departure from most modern texts, but it is historically correct, and it is the best way to establish the true connection between the integral and the derivative. Proofs of all the important theorems are given, generally preceded by geometric or intuitive discussion. This Second Edition introduces the mean-value theorems and their applications earlier in the text, incorporates a treatment of linear algebra, and contains many new and easier exercises. As in the first edition, an interesting historical introduction precedes each important new concept.

Calculus, Vol. 1: One-Variable Calculus, with an Introduction to Linear Algebra

wiley

An introduction to the calculus, with an excellent balance between theory and technique. Integration is treated before differentiation -- this is a departure from most modern texts, but it is historically correct, and it is the best way to establish the true connection between the integral and the derivative. Proofs of all the important theorems are given, generally preceded by geometric or intuitive discussion. This Second Edition introduces the mean-value theorems and their applications earlier in the text, incorporates a treatment of linear algebra, and contains many new and easier exercises. As in the first edition, an interesting historical introduction precedes each important new concept.

Calculus, Vol. 2: Multi-Variable Calculus and Linear Algebra with Applications to Differential Equations and Probability

Calculus, Volume 1

The Mechanical Universe: Introduction to Mechanics and Heat

This important textbook is based on, though independent of, an educational TV series The Mechanical Universe broadcast on public television in the United States. Its aim is to guide students and general readers to an understanding of how the physical world works; physics is presented as a human endeavour, with historical development forming a thread throughout the text. The prerequisites are minimal, only basic algebra and trigonometry since the necessary calculus is developed in the text, with physics providing the motivation. New concepts are introduced at the natural, logical point with many historical references to place physics in a social perspective. Many topics from twentieth-century physics are included, for example energy, low temperature physics, relativity and black holes. The book is attractively and profusely illustrated and will be welcomed by students and also by general readers for whom this will be a stimulating alternative to other, less-thorough treatments.

Olenick, Richard P.

Goodstein, David L.

Astronomy & Space Science

Cambridge University Press

This second volume of the Mechanical Universe studies electricity and magnetism, their relation to each other and light, and shows how the problem of light led to the special theory of relativity. Then, it moves on to modern physics, where particles may behave like waves and where some of the great verities of Newtonian physics appear less certain. Along with the first volume, this book is based on, though independent of, a public television series broadcast in the United States. Physics is presented as a human endeavor, with historical development forming a thread throughout the text. The prerequisites are minimal, only basic algebra and trigonometry since the necessary calculus is developed in the text, with physics providing the motivation. New concepts are introduced at the natural, logical point with many historical references to place physics in a social perspective. Many topics from twentieth-century physics are included. The book is attractively illustrated and will be a stimulating alternative to other, less-thorough treatments.

Beyond the Mechanical Universe: From Electricity to Modern Physics

Physics

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Books by Apostol, Tom M.