Algebra Preliminary to the Differential Calculus by De Morgan
Elements of Algebra Preliminary to the Differential Calculus - Table of Contents
1. Equations of the First Degree
2. On the Symbols of Algebra, as Distinguished from Those of Arithmetic
3. Equations of the First Degree with More Than One Unknown Quantity
4. On Exponents, and on the Continuity of Algebraic Expressions
5. General Theory of Expressions of the First and Second Degrees; Including the Numerical Solution of Equations of the Second Degree
6. On Limits and Variable Quantities
7. Classification of Algebraical Expressions and Consequences. Rule of Division
8. On Series and Indeterminate Coefficients
9. On the Meaning of Equality in Algebra, as Distinguished from its Meaning in Arithmetic
10. On the Notation of Functions
11. On the Binomial Theorem
12. Exponential and Logarithmic Series
13. On the Use of Logarithms in Facilitating Computations
What You Will Learn in Elements of Algebra Preliminary to the Differential Calculus
"Elements of Algebra Preliminary to the Differential Calculus" by Augustus De Morgan is a classic 19th-century textbook designed to provide a strong foundation in "algebra" before progressing to "differential calculus". Written for students and self-learners, the book introduces fundamental algebraic concepts, including equations, functions, and series, in a clear and logical manner. De Morgan emphasizes step-by-step reasoning, making complex topics accessible to learners at various levels.
The text gradually develops more advanced concepts such as indeterminate coefficients, binomial expansions, and polynomial equations. It includes numerous "worked examples" and exercises, allowing students to practice and apply the concepts learned. By bridging the gap between basic algebra and calculus, the book prepares readers for higher mathematical study, including the use of derivatives and analysis of functions.
Valued for its clarity, rigor, and historical significance, De Morgan’s book reflects classical pedagogical methods in mathematics. Its logical progression, emphasis on practical applications, and solid grounding in "algebraic techniques" make it a timeless resource for students and educators. For anyone interested in the history of mathematics or the foundations of calculus, this treatise remains an essential reference in "mathematical education".
Book Details & Specifications
Title:
Algebra Preliminary to the Differential Calculus by De Morgan
Publisher:
Taylor and walton
Year:
1837
Pages:
309
Type:
PDF
Language:
English
ISBN-10 #:
1016357583
ISBN-13 #:
978-1016357586
License:
Public Domain Work
Amazon:
Amazon
About the Author: Augustus De Morgan
The author Augustus De Morgan
was a leading 19th-century British mathematician known for his clear teaching style and major contributions to logic. As the first mathematics professor at University College London, he shaped how mathematical reasoning was taught. His work remains influential for its logical structure and accessible explanations. His book "Elements of Algebra Preliminary to the Differential Calculus" helps students move from basic algebra into early calculus concepts.
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