Differential and Integral Calculus with Examples & Applications by James Tayor
Differential and Integral Calculus with Examples & Applications - Table of Contents
PART I. DIFFERENTIAL CALCULUS
1. Functions; Rates; Differentials
2. Differentiation; Applications
3. Problems of Rates Solved by Limits
4. Successive Differentiation
5. Expansion of Functions
6. Maxima and Minima
7. Points of Inflection; Curvature; Evolutes
8. Envelopes; Order of Contact; Osculating Curves
9. Change of the Independent Variable
10. Functions of Two or More Variables
11. Asymptotes; Singular Points; Curve Tracing
PART II. INTEGRAL CALCULUS
1. Standard Forms; Direct Integration
2. Definite Integrals; Applications
3. Integration of Rational Fractions
4. Integration by Rationalization
5. Integration by Parts; Reduction Formulas
6. Integration of Trigonometric Forms
7. Lengths and Areas of Curves; Surfaces and Volumes of Solids of Revolution
8. Definite Integral as a Limit; Intrinsic Equations of Curves
9. Differential Equations
What You Will Learn in Differential and Integral Calculus with Examples & Applications
"Differential and Integral Calculus with Examples & Applications" by "James Taylor" is a practical and accessible guide to mastering "differential calculus". The book introduces fundamental concepts such as derivatives, limits, and rates of change with clear explanations and step-by-step examples. Taylor’s structured approach emphasizes understanding over memorization, helping learners build a solid foundation in calculus theory and problem-solving techniques.
Beyond differentiation, the text provides comprehensive coverage of "integral calculus", demonstrating how integrals are used to calculate areas, solve equations, and model real-world phenomena. Each chapter includes worked examples and exercises designed to reinforce concepts and strengthen analytical skills. By blending theory with practical applications, Taylor ensures students can see the relevance of calculus in science, engineering, and applied mathematics.
The book also serves as a valuable introduction to "mathematical analysis", linking calculus concepts to broader analytical thinking and problem-solving strategies. Ideal for students, educators, and self-learners, Taylor’s treatise combines clarity, examples, and applications to make complex topics approachable. With its hands-on approach and thorough explanations, this book remains an essential resource for mastering both differential and integral calculus.
Book Details & Specifications
Title:
Differential and Integral Calculus with Examples & Applications by James Tayor
Publisher:
Ginn
Year:
1902
Pages:
296
Type:
PDF
Language:
English
ISBN-10 #:
3337944582
ISBN-13 #:
978-3337944582
License:
Public Domain Work
Amazon:
Amazon
About the Author: James Morford Tayor
The author
James Morford Tayor
was a respected "mathematician" and educator known for his work in "differential calculus" and "integral calculus". He focused on making complex concepts clear and accessible, creating resources that helped students build strong foundations in calculus. Taylor’s approach emphasized step-by-step explanations, worked examples, and practical applications. His contributions to "mathematical analysis" education continue to guide learners and educators, making advanced calculus concepts easier to understand and apply in academic, scientific, and engineering contexts.
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