Analytical Geometry and Calculus by Elias Loomis

Analytical Geometry and Calculus - Table of Contents

DIFFERENTIAL CALCULUS. 1. DEFINITIONS. LIMITING RATIOS. DIFFERENTIATION OF ALGEBRAIC FUNCTIONS. 2. DIFFERENTIATION OF TRANSCENDENTAL FUNCTIONS. 3. SUCCESSIVE DIFFERENTIATION. EXPANSION OF FUNCTIONS IN SERIES. FUNCTIONS OF SEVERAL INDEPENDENT VARIABLES. VANISHING FRACTIONS. 4. GEOMETRICAL REPRESENTATION OF THE FIRST DIFFERENTIAL COEFFICIENT. MAXIMA AND MINIMA VALUES OF A FUNCTION. 5. TANGENTS AND NORMALS TO PLANE CURVES. ASYMPTOTES. 6. CONVEXITY AND CONCAVITY. SINGULAR POINTS OF CURVES. TRACINGOF CURVES. 7. DIFFERENTIAL COEFFICIENT OF AN ARC, AREA, ETC. 8. CONTACT. CURVATURE. EVOLUTES AND INVOLUTES. THE CYCLOID. INTEGEAL CALCULUS. 1. INTEGRATION OF MONOMIAL DIFFERENTIALS. OF CERTAIN BINOMIAL DIF- FERENTIALS. DEFINITE INTEGRALS. TRIGONOMETRICAL FUNCTIONS. 2. RATIONAL FRACTIONS. INTEGRATION OF CERTAIN IRRATIONAL DIFFERENTIALS. How a Rational Fraction can be Integrated 197 3. INTEGRATION OF BINOMIAL DIFFERENTIALS. INTEGRATION BY PARTS. FORMULAS OF REDUCTION. 4. INTEGRATION BY INFINITE SERIES. INTEGRATION OF LOGARITHMIC, 5. SUCCESSIVE INTEGRATION. INTEGRATION OF FUNCTIONS OF TWO ORMORE VARIABLES. DIFFERENTIAL EQUATIONS. Page Successive Integration 243Integration of Differential Functions of Two Variables 244Differential Equations, how Classified 246How Differential Equations may be Solved 248Geometrical Applications of Differential Equations 251 6. QUADRATURE OF PLANE SURFACES. RECTIFICATION OF PLANE CURVES.SURFACES AND VOLUMES OF SOLIDS OF REVOLUTION. 7. APPLICATIONS OF THE DIFFERENTIAL AND INTEGRAL CALCULUS TOMECHANICS.

What You Will Learn in Analytical Geometry and Calculus

The book The Elements of Analytical Geometry; Elements of the Differential and Integral Calculus by Elias Loomis is a classic mathematics textbook that bridges "analytic geometry and calculus". It provides a structured introduction to the study of "lines, planes, curves, surfaces, and conic sections", while integrating fundamental principles of differential and integral calculus. Designed for students, educators, and self-learners, Loomis’ text emphasizes both clarity and rigor, making complex mathematical concepts accessible. The book systematically explores geometric and algebraic relationships, including tangents, normals, intersections, and transformations. It also introduces essential calculus techniques, illustrating methods of differentiation and integration applied to geometric problems. Each chapter includes examples, proofs, and exercises, helping learners develop a strong foundation in both geometry and calculus. Loomis’ methodical approach ensures that readers can progress from basic principles to advanced problem-solving confidently. Published in the 19th century, this textbook is now in the "public domain", making it freely available for educational and research purposes. Its combination of "analytic geometry and calculus" continues to make it a valuable resource for mathematics, physics, and engineering students. Loomis’ work remains influential, offering a clear and rigorous framework for understanding classical mathematical methods and their applications.

Book Details & Specifications

Title: Analytical Geometry and Calculus by Elias Loomis
Publisher: Harper & Brothers
Year: 1874
Pages: 318
Type: PDF
Language: English
ISBN-10 #: B009T3IZCY
ISBN-13 #: N/A
License: Public Domain Work
Amazon: Amazon

About the Author: Elias Loomis

The author Elias Loomis (1811–1889) was a prominent American mathematician and educator known for his contributions to "analytic geometry, calculus, and mathematics education". He authored several influential textbooks that combined clarity with rigor, making advanced mathematical concepts accessible to students and teachers alike. Loomis served as a professor at institutions like "Western Reserve College" and played a key role in shaping 19th-century mathematics education in the United States. His work, including "The Elements of Analytical Geometry; Elements of the Differential and Integral Calculus", remains a "public domain classic" and continues to serve as a valuable resource for learning and teaching mathematics.

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