# Elements of the Differential and Integral Calculus

ELEMENTS OF THE DIFFERENTIAL

AND INTEGRAL CALCULUS

*(REVISED EDITION)*

BY

WILLIAM ANTHONY GEANVILLE, PH.D., LL.D.

PRESIDENT OF PENNSYLVANIA COLLEGE

WITH THE EDITORIAL COÖPERATION OF

PERCEY F. SMITH, PH.D.

PROFESSOR OF MATHEMATICS IN THE SHEFFIELD SCIENTIFIC SCHOOL YALE UNIVERSITY

GINN AND COMPANY

BOSTON - NEW YORK - CHICAGO - LONDON

MATHEMATICAL TEXTS

Edited by Percey F. Smith, Ph.D.

Professor of Mathematics in the Sheffield Scientific School

of Yale University

**Elements of the Differential and Integral Calculus (Revised Edition)**

By W. A. Granville, Ph.D., LL.D.

**Elements of Analytic Geometry**

By P. F. Smith and A. S. Gale, Ph.D.

**New Analytic Geometry**

By P. F. Smith and A. S. Gale, Ph.D.

**Introduction to Analytic Geometry**

By P. F. Smith and A. S. Gale, Ph.D.

**Advanced Algebra**

By H. E. Hawkes, Ph.D.

**Text-Book on the Strength of Materials (Revised Edition)**

By S. E. Slocum, Ph.D., and E. L. Hancock, M.Sc.

**Problems in the Strength of Materials**

By William Kent Shepard, Ph.D.

**Plane and Spherical Trigonometry and Four-Place Tables of Logarithms**

By W. A. Granville, Ph.D., LL.D.

**Plane and Spherical Trigonometry**

By W. A. Granville, Ph.D., LL.D.

**Plane Trigonometry and Four-Place Tables of Logarithms**

By W. A. Granville, Ph.D., LL.D.

**Four-Place Tables of Logarithms**

By W. A. Granville, Ph.D., LL.D.

**Theoretical Mechanics**

By P. F. Smith and W. R. Longley, Ph.D.

**First Course in Algebra**

By H. E. Hawkes, Ph.D., William A. Luby, A.B., and Frank C. Touton, Ph.B.

**Second Course in Algebra**

By H. E. Hawkes, Ph.D., William A. Luby, A.B., and Frank C. Touton, Ph.B.

**Complete School Algebra**

By H. E. Hawkes, Ph.D., William A. Luby, A.B., and Frank C. Touton, Ph.B.

**Elementary Analysis**

By P. F. Smith and W. A. Granville, Ph.D., LL.D.

**Plane Geometry**

By William Betz, A.M., and Harrison E. Webb, A. B.

COPYRIGHT, 1904, 1911, BY

WILLIAM ANTHONY GRANVILLE AND PERCEY F. SMITH

ALL RIGHTS RESERVED

813.9

__The Athenæum Press__

GINN AND COMPANY • PRO-

PRIETORS • BOSTON • U.S.A.

This work is in the **public domain** in the **United States** because it was published before January 1, 1928.

The longest-living author of this work died in 1943, so this work is in the **public domain** in countries and areas where the copyright term is the author's **life plus 79 years or less**. This work may be in the **public domain** in countries and areas with longer native copyright terms that apply the **rule of the shorter term** to *foreign works*.

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