Analytical Geometry and Calculus by Elias Loomis
Analytical Geometry and Calculus - Table of Contents
- PART I: DIFFERENTIAL CALCULUS
- 1. Definitions, Limiting Ratios, and differentiation of algebraic functions
- 2. Differentiation of transcendental functions
- 3. Successive Differentiation, Expansion of Functions, and functions of several independent variables
- 4. Geometrical Representation and maxima and minima values of a function
- 5. Tangents and normals to plane curves and Asymptotes
- 6. Convexity, Concavity, Singular Points, and tracing of curves
- 7. Differential Coefficient of an Arc, Area, etc.
- 8. Contact, curvature evolutes and involutes, and the Cycloid
- PART II: INTEGRAL CALCULUS & APPLICATIONS
- 1. Integration of Monomial Differentials and definite integrals evaluation
- 2. Integration of rational fractions and irrational differentials
- 3. Integration by parts and reduction formulas
- 4. Integration by Infinite Series and Logarithmic Functions
- 5. Successive Integration and solving ordinary differential equations
- 6. Quadrature and rectification of plane curves and Volumes of Solids
- 7. Applications of differential and integral calculus to Mechanics
What You Will Learn in Analytical Geometry and Calculus
Elements of Analytical Geometry and of the Differential and Integral Calculus by Elias Loomis is a historic 19th-century American textbook that provided thousands of early science and engineering students with their first rigorous introduction to higher analysis. Designed for clarity, logical succession, and immediate practical application, this volume systematically covers core subjects including co-ordinate axes, equations of the straight line, properties of the circle, parabola, ellipse, hyperbola, limits, explicit differentiation, and fundamental integration.
Tailored for students of classical mathematics, physics historians, and educators, Prof. Loomis emphasizes concise geometric demonstrations alongside precise algebraic manipulation. The text leads readers step-by-step through tangents, normals, curvature, maxima and minima, transcendental functions, arc length determination, and area quadrature. Whether analyzing planar loci or evaluating early physical applications of the definite integral, learners will find this lucid presentation invaluable.
Widely celebrated for its historic pedagogical influence, elegant proofs, and classic problem sets, it stands as one of the best historical analytical geometry and calculus textbooks pdf available for independent study. It systematically equips students with essential reasoning tools for mastering classical analysis with confidence.
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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