Elementary Treatise on Differential and Integral Calculus by Silvestre Lacroix
An Elementary Treatise on the Differential and Integral Calculus - Table of Contents
Part-I DIFFERENTIAL CALCULUS
- 1. On Successive Differentiations
- 2. On the Differentiation of Transcendental Functions
- 3. On the Differentiation of Equations of Two Variables
- 4. On the Investigation of the Maxima and Minima of Functions
- 5. On the Values of Differential Coefficients in Certain Circumstances
- 6. On the Application of the Differential Calculus to the Theory
- 7. On the Determination of the Nature and Positions of Remarkable Points
- 8. Example of the Analysis of a Curve
- 9. On Osculating Curves
- 10. On Transcendental Curves
- 11. On the Manner of Changing the Independent Variable or the Form of the Function
- 12. On the Differentiation of Functions of Two or More Variables
- 13. On the Maxima and Minima of Functions of Two Variables
- 14. General Remarks upon the Application of the Differential Calculus
- 15. On the Separation of the Variables in Differential Equations
- 16. Investigation of a Factor necessary to render integrable a Differential Equation
- 17. On Equations of the First Order in which the Differentials are Separable
- 18. Methods of Resolving Differential Equations of the First Order
- 19. On the Particular Solutions of Differential Equations of the First Order
- 20. Resolution of some Geometrical Problems depending upon the Integral Calculus
- 21. Investigation of a Function of More than One Variable when the Differentials are of Several Variables
- 22. On the Integration of Partial Differential Equations of the First Order
Part-II INTEGRAL CALCULUS
- 1. On the Integration of Irrational Functions
- 2. On the Integration of Binomial Differentials
- 3. On Integration by Series
- 4. On the Integration of Logarithmic and Exponential Quantities
- 5. On the Integration of Circular Functions
- 6. A General Method of obtaining Approximate Values of Integrals
- 7. On the Application of the Integral Calculus to the Rectification of Curves
- 8. On Equations of Total Differentials which do not satisfy the Condition of Exactness
- 9. On the Maxima and Minima of Indeterminate Integrals
- 10. On Differences and Series
- 11. On the Direct Method of Differences when applied to Functions defined Implicitly in terms of the Independent Variable
- 12. On the Determination of a Function whose Difference is Expressed by a Given Function
- 13. On the Integration of Equations of Differences
- 14. On Equations of Mixed Differences
- 15. On Recurring Series
- 16. On the Connexion between the Differential Calculus and that of Differences
- 17. On Interpolations
- 18. On the Numbers of Bernoulli
- 19. Application of the Integral Calculus to the Theory of Series
- 20. Notes
What You Will Learn in An Elementary Treatise on the Differential and Integral Calculus
An Elementary Treatise on Differential and Integral Calculus by Silvestre François Lacroix is one of the most influential calculus textbooks in mathematical history. Synthesizing the analytical breakthroughs of Euler, Lagrange, and Laplace, this landmark volume made Continental calculus accessible worldwide, serving as an essential resource for classical calculus foundational study practice.
The monograph systematically presents differential coefficients, series expansions, integration techniques, geometric applications, and differential equations. By combining rigorous logical proofs with clear geometric illustrations, Lacroix enables students and scholars to understand foundational analysis and perform step-by-step classical integration methods with absolute mathematical clarity.
Historians of mathematics and educators praise this treatise for modernizing 19th-century scientific education and shaping modern calculus notation. Lacroix’s structured exposition equips readers with the deep analytical reasoning required for mastering historical differential calculus principles across advanced mathematical research.
Book Details & Specifications
Title:
Elementary Treatise on Differential and Integral Calculus by Silvestre Lacroix
Publisher:
Cambridge: Printed by J. Smith for J. Deighton and Sons
Year:
1816
Pages:
748
Type:
PDF
Language:
English
ISBN-10 #:
1145120636
ISBN-13 #:
978-1145120631
License:
Public Domain Work
Amazon:
Amazon
About the Author: Silvestre François Lacroix
The author Silvestre François Lacroix
(1765–1843) was a prominent French mathematician and educator who served as Professor at the Collège de France and the École Polytechnique. Renowned for his pedagogical clarity, he authored comprehensive textbooks that revolutionized European mathematics instruction.
Translated into English by Cambridge scholars Charles Babbage, George Peacock, and John Herschel, Lacroix’s works introduced Continental calculus to the English-speaking world. His monumental texts remain celebrated milestones for researchers seeking authoritative historical calculus reference resources.
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