An Elementary Course in the Integral Calculus by Daniel A. Murray
An Elementary Course in the Integral Calculus - Table of Contents
1. Integration: A Process of Summation
2. Integration: The Inverse of Differentiation
3. Fundamental Rules and Methods of Integration
4. Geometrical Applications of the Calculus
5. Rational Fractions
6. Irrational Functions
7. Integration of Trigonometric and Exponential Functions
8. Successive Integration; Multiple Integrals
9. Further Geometrical Applications; Mean Values
10. Applications to Mechanics
11. Approximate Integration; Integration by Means of Series; Integration by Measurement of Areas
12. Integral Curves
13. Ordinary Differential Equations
What You Will Learn in An Elementary Course in the Integral Calculus
"An Elementary Course in the Integral Calculus" by Daniel A. Murray is a classical "calculus" textbook designed for students and beginners. It introduces the fundamental concepts of "integration", starting with the notion of infinitesimals and the geometric interpretation of "definite integrals". The book emphasizes clear explanations, helping learners understand both the theory and reasoning behind integration.
Murray carefully develops the main "techniques" of integration, including substitution, integration by parts, trigonometric substitutions, and methods for rational and algebraic functions. The text balances rigor with accessibility, offering numerous worked examples and exercises so readers can practice solving problems effectively. It also extends to applications in geometry and physics, such as computing areas, volumes, and surface areas, making the content practical and relatable.
The book’s style is ideal for beginners or intermediate students who want a strong foundation in calculus. By blending theory, problem-solving strategies, and real-world "applications", Murray’s treatise not only teaches how to integrate but also why these methods work. Its structured approach makes it a valuable resource for self-study, classroom use, or anyone seeking a classical introduction to integral calculus.
Book Details & Specifications
Title:
An Elementary Course in the Integral Calculus by Daniel A. Murray
Publisher:
Year:
1898
Pages:
316
Type:
PDF
Language:
English
ISBN-10 #:
1164568353
ISBN-13 #:
978-1164568353
License:
Public Domain Work
Amazon:
Amazon
About the Author: Daniel Alexander Murray
The author Daniel Alexander Murray
(1862–1934) was a Canadian "mathematician" renowned for his contributions to "calculus" education. He studied at Dalhousie University, Johns Hopkins, and in Europe, gaining a strong foundation in "mathematics" that shaped his teaching and writing. Murray held academic positions at Cornell University, New York University, Dalhousie, and McGill, focusing on applied mathematics and education. He authored influential textbooks, including "An Elementary Course in the Integral Calculus", emphasizing "integration" and practical "applications".
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