Integration by Parts: Tutorial and Examples by Graham S McDonald
Integration By parts (Presentation) - Table of Contents
1. Theory
2. Usage
3. Exercises
4. Final solutions
5. Standard integrals
6. Tips on using solutions
7. Alternative notation
What You Will Learn in Integration By parts (Presentation)
"Integration By Parts (Presentation)" by Graham S. McDonald is a concise and focused tutorial on one of the most important "integration techniques" in calculus. Designed for students learning or reviewing calculus, it explains the method of "integration by parts", derived from the "product rule" of differentiation, in a clear and structured way. The presentation breaks down the concept step by step, making it easier to understand the theory and logic behind the formula
? u . dv = u.v - ? vdu
The content emphasizes practical application by teaching how to "choose functions" (u) and (dv) to simplify integrals of function products. Through worked examples and exercises, students can see the technique in action and practice solving a variety of integrals, from polynomials and exponentials to trigonometric functions. The presentation also highlights common pitfalls and strategies to handle more complex integrals, helping learners build confidence and accuracy in their calculations.
Ideal for self-study or classroom use, this presentation is both "student-friendly" and efficient. It focuses on building conceptual understanding while reinforcing problem-solving skills, making it a valuable resource for anyone studying introductory or intermediate calculus. By combining theory, examples, and exercises, McDonald’s guide helps learners master "integration by parts" and apply it effectively to solve challenging integrals.
Book Details & Specifications
Title:
Integration by Parts: Tutorial and Examples by Graham S McDonald
Publisher:
Graham McDonald
Year:
2003
Pages:
39
Type:
PDF
Language:
English
ISBN-10 #:
B072K13R3T
ISBN-13 #:
License:
External Educational Resource
Amazon:
Amazon
About the Author: Graham S McDonald
The author
Graham S McDonald
is a British mathematician and academic with a strong background in "mathematics and physics". He earned a "BSc (Hons) from the University of Glasgow" and a "PhD from the University of Strathclyde", and he has worked at universities across the UK and Europe before becoming an "Associate Professor at the University of Salford". McDonald’s expertise includes "numerical analysis", "mathematics education", and "integral calculus", and he is known for creating "clear tutorial modules" on foundational calculus techniques like integration by parts. His work focuses on making mathematical methods understandable and accessible to students through structured explanations and examples.
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