Euler's e Essentials
N.B. Singh
This audiobook is narrated by a digital voice.
"Euler's e Essentials" is a beginner-friendly guidebook that introduces readers to the fascinating world of mathematics through the lens of Euler's constant, denoted by the symbol e. Written in an accessible and easy-to-understand manner, this book is designed for individuals with little to no mathematical background who are curious about the beauty and significance of mathematical concepts. Through clear explanations, illustrative examples, and real-world applications, readers will embark on a journey to discover the fundamental properties of Euler's constant and its wide-ranging implications in various scientific disciplines, from calculus and physics to finance and biology. Whether you're a high school student exploring mathematics for the first time or an adult learner eager to delve into the mysteries of numbers, "Euler's e Essentials" offers an engaging and enlightening introduction to one of the most important constants in mathematics.
Duration - 7h.
Author - N.B. Singh.
Narrator - Digital Voice Mary G.
Published Date - Monday, 20 January 2025.
Copyright - © 2024 N.B. Singh ©.
Location:
United States
Description:
This audiobook is narrated by a digital voice. "Euler's e Essentials" is a beginner-friendly guidebook that introduces readers to the fascinating world of mathematics through the lens of Euler's constant, denoted by the symbol e. Written in an accessible and easy-to-understand manner, this book is designed for individuals with little to no mathematical background who are curious about the beauty and significance of mathematical concepts. Through clear explanations, illustrative examples, and real-world applications, readers will embark on a journey to discover the fundamental properties of Euler's constant and its wide-ranging implications in various scientific disciplines, from calculus and physics to finance and biology. Whether you're a high school student exploring mathematics for the first time or an adult learner eager to delve into the mysteries of numbers, "Euler's e Essentials" offers an engaging and enlightening introduction to one of the most important constants in mathematics. Duration - 7h. Author - N.B. Singh. Narrator - Digital Voice Mary G. Published Date - Monday, 20 January 2025. Copyright - © 2024 N.B. Singh ©.
Language:
English
Preface
Duración:00:02:20
Introduction to Euler’s e
Duración:00:00:31
Origin of Euler’s Constant
Duración:00:03:11
Early Investigations and Discoveries
Duración:00:03:35
Euler’s Contributions to the Study of e
Duración:00:02:44
Significance of Euler’s e in Mathematics
Duración:00:03:10
Applications of Euler’s e in Real Life
Duración:00:03:37
Notable Properties of Euler’s Number
Duración:00:05:01
Historical Context of Euler’s Constant
Duración:00:03:23
Modern Interpretations and Extensions
Duración:00:03:56
History of Euler’s Constant
Duración:00:00:21
Origins of Logarithms
Duración:00:04:02
Leonhard Euler’s Contributions
Duración:00:03:19
Formalization of Euler’s Constant
Duración:00:03:38
Mathematical Definition of Euler’s e
Duración:00:00:24
Properties of Natural Logarithms
Duración:00:02:55
Exponential Function and Euler’s Constant
Duración:00:02:24
Applications of Euler’s Constant in Calculus
Duración:00:03:12
Geometric Interpretation of Euler’s e
Duración:00:03:27
Properties of Euler’s Number
Duración:00:00:22
Definition of Euler’s Number
Duración:00:00:27
Exponential Growth and Decay
Duración:00:02:46
Relationship with Natural Logarithm
Duración:00:03:00
Limit Representations
Duración:00:02:57
Applications in Calculus
Duración:00:03:12
Connection to Complex Analysis
Duración:00:04:05
Infinite Series Representations
Duración:00:05:04
Historical Development
Duración:00:03:02
Euler’s e in Calculus
Duración:00:00:24
Introduction to Euler’s e in Calculus
Duración:00:02:38
Derivatives Involving Euler’s Number
Duración:00:03:24
Integrals Involving Euler’s Number
Duración:00:02:39
Applications of Euler’s e in Differential Equations
Duración:00:03:39
Euler’s e in Taylor Series
Duración:00:03:43
Euler’s e in Limit Theory
Duración:00:03:49
Euler’s e in Complex Analysis
Duración:00:04:05
Euler’s e in Multivariable Calculus
Duración:00:04:59
Applications in Exponential Growth
Duración:00:00:22
Finance and Compound Interest
Duración:00:02:42
Population Growth Models
Duración:00:03:23
Radioactive Decay and Half-Life
Duración:00:03:05
Epidemiology and Spread of Diseases
Duración:00:03:00
Exponential Growth in Physics
Duración:00:02:41
Technological Advancements and Moore’s Law
Duración:00:03:52
Environmental Studies and Sustainability
Duración:00:03:47
Complex Functions and Analyticity
Duración:00:04:41
Euler’s e in Exponential Functions
Duración:00:02:37
Euler’s e in Logarithmic Functions
Duración:00:02:42
Euler’s e in Trigonometric Functions
Duración:00:02:47
Euler’s e in Power Series
Duración:00:02:34
Euler’s e in Contour Integration
Duración:00:02:33
Residue Theory and Euler’s e
Duración:00:02:18
Applications of Euler’s e in Complex Analysis
Duración:00:02:49
Euler’s e in Differential Equations
Duración:00:00:27
First-Order Ordinary Differential Equations
Duración:00:03:09
Second-Order Ordinary Differential Equations
Duración:00:03:05
Systems of Ordinary Differential Equations
Duración:00:02:44
Partial Differential Equations
Duración:00:02:40
Homogeneous Differential Equations
Duración:00:02:12
Non-homogeneous Differential Equations
Duración:00:02:04
Boundary Value Problems
Duración:00:02:00
Euler’s e in Probability Theory
Duración:00:00:31
Probability Distributions
Duración:00:02:53
Expected Value and Variance
Duración:00:02:15
Cumulative Distribution Functions
Duración:00:01:58
Joint Probability Distributions
Duración:00:01:50
Conditional Probability and Bayes’ Theorem
Duración:00:02:06
Random Variables and Moments
Duración:00:01:49
Limit Theorems
Duración:00:01:55
Euler’s e in Finance
Duración:00:00:21
Compound Interest and Continuous Growth
Duración:00:02:03
Present Value and Future Value
Duración:00:02:35
Continuous Compounding
Duración:00:02:39
Interest Rates and Euler’s e
Duración:00:02:32
Continuous Discounting
Duración:00:02:33
Continuous Return Rates
Duración:00:02:44
Applications in Investment
Duración:00:03:47
Financial Modeling with Euler’s e
Duración:00:02:52
Euler’s e in Physics
Duración:00:00:25
Kinematics and Euler’s e
Duración:00:02:33
Dynamics and Euler’s e
Duración:00:02:34
Thermodynamics and Euler’s e
Duración:00:01:03
Electricity and Magnetism with Euler’s e
Duración:00:02:23
Optics and Euler’s e
Duración:00:02:12
Quantum Mechanics and Euler’s e
Duración:00:02:29
Relativity and Euler’s e
Duración:00:02:26
Statistical Mechanics and Euler’s e
Duración:00:02:24
Euler’s e in Number Theory
Duración:00:00:26
Prime Numbers and Euler’s e
Duración:00:01:56
Fermat’s Little Theorem and Euler’s e
Duración:00:02:06
Cryptography and Euler’s e
Duración:00:05:01
Diophantine Equations and Euler’s e
Duración:00:03:13
Distribution of Primes and Euler’s e
Duración:00:03:26
Euler’s Totient Function
Duración:00:02:35
Residue Theorem and Euler’s e
Duración:00:03:15
Applications in Cryptography
Duración:00:02:37
Euler’s e in Nature
Duración:00:00:21
Population Growth and Euler’s e
Duración:00:03:44
Compound Interest and Euler’s e
Duración:00:03:19
Radioactive Decay and Euler’s e
Duración:00:03:22
Electric Circuits and Euler’s e
Duración:00:03:17
Fluid Dynamics and Euler’s e
Duración:00:03:14
Biological Rhythms and Euler’s e
Duración:00:03:54
Fractals and Euler’s e
Duración:00:03:31
Philosophical Implications of Euler’s e
Duración:00:00:25
Infinity and Limitlessness
Duración:00:04:21
Harmony of Mathematics and Nature
Duración:00:03:52
Beauty in Mathematical Symmetry
Duración:00:03:43
Quest for Universal Truths
Duración:00:04:01
Exploration of the Unknowable
Duración:00:03:53
Role of Mathematics in Human Understanding
Duración:00:04:07
Interconnectedness of Mathematical Concepts
Duración:00:04:03
Future Directions in Euler’s e Research
Duración:00:00:34
Computational Approaches to Euler’s e
Duración:00:05:02
Euler’s e in Machine Learning and Artificial Intelligence
Duración:00:05:18
Euler’s e and Quantum Computing
Duración:00:05:10
Euler’s e and Cryptocurrency
Duración:00:05:16
Euler’s e in Biomedical Modeling and Simulation
Duración:00:05:50
Euler’s e and Climate Modeling
Duración:00:05:08
Philosophical Implications of Euler’s e in the Digital Age
Duración:00:05:08
Conclusion
Duración:00:00:59
The Legacy of Euler’s e
Duración:00:04:32
Challenges and Opportunities
Duración:00:05:53
Implications for Education
Duración:00:05:52
Future Research Directions
Duración:00:05:46
Ethical Considerations
Duración:00:06:03
Integration into Curriculum
Duración:00:05:42
Global Impact
Duración:00:05:23
Call to Action
Duración:00:04:26