Analytical Geometry & Differential and Integral Calculus by Horatio Robinson
Elements of Analytical Geometry & Diff. & Int. Calculus - Table of Contents
- PART I. DIFFERENTIAL CALCULUS
- 1. General Principles and Definitions
- 2. differential coefficients of explicit functions of a single variable
- 3. Differential Coefficients of Inverse Functions, Functions of Functions, and Complex Functions
- 4. Successive Differential Coefficients
- 5. Relation between Real Functions and Differential Coefficients; Taylor's and Maclaurin's theorems application
- 6. Expansion of Functions
- 7. Application of Series to Trigonometric and Logarithmic Expressions
- 8. differentiation of explicit functions of two variables and implicit functions
- 9. Successive Differentiation of Functions of Two or More Variables
- 10. Investigation of the True Value of Expressions under Forms of Indetermination
- 11. maxima and minima values of functions of one variable
- 12. Expansion of Functions of Two or More Variables and Maxima/Minima Loci
- 13. Change of Independent Variables in Differentiation
- 14. Elimination of Constants and Arbitrary Functions by Differentiation
- PART II. GEOMETRICAL APPLICATIONS
- 1. tangents normals and sub-tangents to plane curves
- 2. Asymptotes of Plane Curves; Singular Points; Concavity and Convexity
- 3. Polar Coordinates; Differential Coefficients of Arcs, Areas, and Solids
- 4. radius of curvature evolutes and involutes and Osculatory Circle
- PART III. INTEGRAL CALCULUS
- 1. Meaning of Integration; integration by parts and substitution techniques
- 2. integration of rational fractions by partial fractions
- 3. Formulae for Integration of Binomial Differentials by Successive Reduction
- 4. Geometric Significance and Properties of Definite Integrals
- 5. quadrature of plane curves in polar coordinates
- 6. Rectification of Plane Curves
- 7. Double Integration and Triple Integration
- 8. Quadrature of Curved Surfaces and Cubature of Solids
- 9. Differentiation and Integration under the Sign; Eulerian Integrals
- 10. Introduction to Elliptic Functions
What You Will Learn in Elements of Analytical Geometry & Diff. & Int. Calculus
Elements of Analytical Geometry & Differential and Integral Calculus by Horatio Nelson Robinson is a classical 19th-century American mathematics treatise engineered to provide students with a clear, logical progression from planar coordinate systems to higher analytical calculus. Written during a foundational period in American technical education, this volume systematically breaks down core subjects including co-ordinate axes, straight line equations, properties of the circle, parabola, ellipse, hyperbola, limit definitions, explicit differentiation, and fundamental integration.
Tailored for undergraduate students, physical science scholars, and historical mathematics educators, Prof. Robinson balances intuitive geometric representations with rigorous algebraic demonstrations. The text leads readers step-by-step through tangents, normals, curvature, maxima and minima, transcendental functions, area quadrature, and solid geometry. Whether investigating conic equations or evaluating early physical applications of the definite integral, learners will find this presentation highly lucid.
Widely respected for its structural elegance, historical influence, and classic exercise sets, it stands as one of the best historical analytical geometry and calculus textbooks pdf available for independent study. It systematically equips learners with foundational analytical tools for mastering classical analysis with confidence.
Book Details & Specifications
Title:
Analytical Geometry & Differential and Integral Calculus by Horatio Robinson
Publisher:
J. Ernst
Year:
1856
Pages:
366
Type:
PDF
Language:
English
ISBN-10 #:
028296830X
ISBN-13 #:
978-0282968304
License:
Public Domain Work
Amazon:
Amazon
About the Author: Horatio Nelson Robinson
The author Horatio Nelson Robinson
(1806–1867) was an eminent American mathematician and educator who served as Professor of Mathematics in the United States Navy and authored the celebrated "Robinson's Mathematical Series."
A pioneer in North American scientific textbook writing, Prof. Robinson authored comprehensive works spanning arithmetic, algebra, geometry, trigonometry, calculus, and astronomy that served as standard university and military academy curricula throughout the 19th century.
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