Elements of Analytical Geometry & Diff. & Int. Calculus by Horatio Robinson - PDF

About this book :-
"Elements of Analytical Geometry & Differential and Integral Calculus" by Horatio Nelson Robinson is a 19th-century "mathematics textbook" that combines the study of "analytical geometry" and "calculus". Robinson designed the book to provide a clear and practical approach, connecting algebraic methods with geometric interpretation. It covers points, lines, conic sections, and surfaces, and demonstrates how coordinate geometry underpins calculus concepts. The text reflects the teaching style of the 1800s, emphasizing logical progression and step-by-step explanations to make complex topics accessible to students. The calculus portion of the book includes both differential and integral calculus. Topics include derivatives, maxima and minima, curve tracing, integration techniques, areas, volumes, and applications to geometrical figures. Robinson emphasizes the connection between geometry and calculus, showing that differential and integral methods are natural extensions of algebraic geometry. His work aimed to make higher mathematics comprehensible without requiring prior advanced study, making it widely used in schools and academies during his time. Today, Robinson’s book serves as a valuable historical reference, illustrating how 19th-century educators taught "mathematical concepts". It demonstrates the evolution of pedagogy in analytic geometry and calculus and provides insight into classical approaches to teaching. Collectors, historians, and mathematics enthusiasts appreciate it for its thoroughness, clarity, and historical significance.

Book Detail :-
Title: Elements of Analytical Geometry & Diff. & Int. Calculus by Horatio Robinson - PDF
Publisher: J. Ernst
Year: 1856
Pages: 366
Type: PDF
Language: English
ISBN-10 #: 028296830X
ISBN-13 #: 978-0282968304
License: Public Domain Book
Amazon: Amazon

About Author :-
The author Horatio Nelson Robinson (1806–1867) was an American "mathematics educator" and textbook author. He served as a professor of mathematics in the United States Navy and wrote numerous instructional books covering arithmetic, geometry, and "analytical geometry". His teaching emphasized clarity, practicality, and logical progression. Robinson is best known for his textbooks, including "Elements of Analytical Geometry & Differential and Integral Calculus". His works made advanced mathematics accessible, influencing generations of students.

Book 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 of a Single Variable 4. Successive Differential Coefficients 5. Relation between Real Functions of a Single Variable and Their Differential Coefficients; Taylor's and Maclaurin's Theorems 6. Expansion of Functions 7. Application of Some of the Preceding Series to Trigonometric and Logarithmic Expressions 8. Differentiation of Explicit Functions of Two or More Independent Variables, of Functions of Functions, and of Implicit Functions of Several Variables 9. Successive Differentiation of Functions of Two or More Independent Variables, and of Implicit Functions 10. Investigation of the True Value of Expressions Presented under Forms of Indetermination 11. Determination of the Maxima and Minima Values of Functions of One Variable 12. Expansion of Functions of Two or More Independent Variables, and Investigation of the Maxima and Minima of Such Functions 13. Change of Independent Variables in Differentiation 14. Elimination of Constants and Arbitrary Functions by Differentiation PART II. GEOMETRICAL APPLICATIONS 1. Tangents, Normals, Sub-Tangents, and Sub-Normals to Plane Curves 2. Asymptotes of Plane Curves; Singular Points; Concavity and Convexity 3. Polar Coordinates; Differential Coefficients of the Arcs and Areas of Plane Curves, Solids, and Surfaces of Revolution 4. Different Orders of Contact of Plane Curves; Osculatory Curves; Osculatory Circle; Radius of Curvature; Evolutes and Involutes PART III. INTEGRAL CALCULUS 1. Meaning of Integration; Notation; Definite and Indefinite Integrals; Direct Integration of a Sum; Integration by Parts; Integration by Substitution 2. Integration of Rational Fractions by Decomposition into Partial Fractions 3. Formulae for the Integration of Binomial Differentials by Successive Reduction 4. Geometric Significance and Properties of Definite Integrals; Another Demonstration of Taylor's Theorem; Definite Integrals with Infinite Limits or Indeterminate Forms; Integration by Series 5. Geometrical Applications: Quadrature of Plane Curves (Rectilinear and Polar Coordinates) 6. Rectification of Plane Curves 7. Double Integration; Triple Integration 8. Quadrature of Curved Surfaces; Cubature of Solids 9. Differentiation and Integration under the Sign ?; Eulerian Integrals; Determination of Definite Integrals by Differentiation and by Integration under the Sign ? 10. Elliptic Functions

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