A fascinating look at higher Mathematics (expanded version)

A serious attempt to make my method and the gamma function accessible to anyone dealing with integral calculus

Elaboration , 2011 , 35 Pages

Mathematics - General, Basics

John Bredakis method and highways without speed limit.
Cook book forumlas for integrals.
A serious attempt to make my method and the gamma function accessible to anyone dealing with integral calculus. The bing bang derivation of innumerous mathematical formulas starting from elementary trigonometrie.

Inhaltsverzeichnis (Table of Contents)

• I. A fascinating look at Higher Mathematics
• The bing bang derivation of innumerous mathematical formulas starting from elementary trigonometry
• At the beginning is the Integral Ip
• Special case:
• And then philosophy starts
• II. John Bredakis method
• Basic property of the gamma function
• Successive derivatives
• III. (a)
• III. (b)
• III. (c)
• John Bredakis method and Highways without speed limit
• The only method providing cook book formulas for a variety of integrals for any non negative integer n and the relevant improper forms.
• The general formula for In
• Something like successive derivatives with alternating sign

Zielsetzung und Themenschwerpunkte (Objectives and Key Themes)

This text aims to demonstrate the application of the John Bredakis method in deriving numerous mathematical formulas from basic trigonometry. The key themes include:

• The power of the John Bredakis method in simplifying complex mathematical operations
• The connection between advanced mathematics and elementary concepts
• The role of the imaginary unit 'i' in expanding mathematical understanding
• The application of geometrical principles in advanced mathematical derivations
• The development of practical formulas for various integral forms

Zusammenfassung der Kapitel (Chapter Summaries)

I. A fascinating look at Higher Mathematics

This chapter introduces the Integral Ip, a fundamental concept in higher mathematics, and explores its derivation from elementary trigonometry. The chapter also highlights the significance of the imaginary unit 'i' and its role in understanding the complexity of the real world.

II. John Bredakis method

This chapter introduces the John Bredakis method, a powerful tool for simplifying complex mathematical operations, particularly in the calculation of integrals. The chapter explains the method's foundation and its application to various forms of integrals.

III. (a)

This chapter presents a key equation that showcases the interconnectedness of various mathematical concepts. It emphasizes the importance of understanding the limitations of conventional mathematical approaches and the need for innovative methodologies.

III. (b)

This chapter delves into the concept of the Beta function, a crucial element in advanced mathematics. It connects the Beta function with the integral representation of the gamma function and highlights its applications in various areas of mathematics.

III. (c)

This chapter focuses on the solutions of Bessel's equation, a differential equation that arises in numerous physics and engineering problems. The chapter explores the relationship between Bessel's equation and trigonometry, highlighting the connection between traditional and advanced mathematical approaches.

John Bredakis method and Highways without speed limit

This chapter emphasizes the practicality and versatility of the John Bredakis method. It showcases the method's ability to derive cook-book formulas for a wide range of integrals and its applicability in handling improper forms.

Schlüsselwörter (Keywords)

The text focuses on the John Bredakis method, a powerful tool for simplifying complex mathematical operations, particularly in the calculation of integrals. Key themes include higher mathematics, integral calculus, trigonometry, imaginary unit, gamma function, Beta function, Bessel's equation, and practical formula derivation.

• Author: Prof. Dr. med. John Bredakis (Author)
• Publication Year: 2011
• Pages: 35
• Catalog Number: V170470
• ISBN (eBook): 9783640895229
• ISBN (Book): 9783640896103
• Language: English
• Tags: mathematics