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
Duration:00:02:20
Introduction to Euler’s e
Duration:00:00:31
Origin of Euler’s Constant
Duration:00:03:11
Early Investigations and Discoveries
Duration:00:03:35
Euler’s Contributions to the Study of e
Duration:00:02:44
Significance of Euler’s e in Mathematics
Duration:00:03:10
Applications of Euler’s e in Real Life
Duration:00:03:37
Notable Properties of Euler’s Number
Duration:00:05:01
Historical Context of Euler’s Constant
Duration:00:03:23
Modern Interpretations and Extensions
Duration:00:03:56
History of Euler’s Constant
Duration:00:00:21
Origins of Logarithms
Duration:00:04:02
Leonhard Euler’s Contributions
Duration:00:03:19
Formalization of Euler’s Constant
Duration:00:03:38
Mathematical Definition of Euler’s e
Duration:00:00:24
Properties of Natural Logarithms
Duration:00:02:55
Exponential Function and Euler’s Constant
Duration:00:02:24
Applications of Euler’s Constant in Calculus
Duration:00:03:12
Geometric Interpretation of Euler’s e
Duration:00:03:27
Properties of Euler’s Number
Duration:00:00:22
Definition of Euler’s Number
Duration:00:00:27
Exponential Growth and Decay
Duration:00:02:46
Relationship with Natural Logarithm
Duration:00:03:00
Limit Representations
Duration:00:02:57
Applications in Calculus
Duration:00:03:12
Connection to Complex Analysis
Duration:00:04:05
Infinite Series Representations
Duration:00:05:04
Historical Development
Duration:00:03:02
Euler’s e in Calculus
Duration:00:00:24
Introduction to Euler’s e in Calculus
Duration:00:02:38
Derivatives Involving Euler’s Number
Duration:00:03:24
Integrals Involving Euler’s Number
Duration:00:02:39
Applications of Euler’s e in Differential Equations
Duration:00:03:39
Euler’s e in Taylor Series
Duration:00:03:43
Euler’s e in Limit Theory
Duration:00:03:49
Euler’s e in Complex Analysis
Duration:00:04:05
Euler’s e in Multivariable Calculus
Duration:00:04:59
Applications in Exponential Growth
Duration:00:00:22
Finance and Compound Interest
Duration:00:02:42
Population Growth Models
Duration:00:03:23
Radioactive Decay and Half-Life
Duration:00:03:05
Epidemiology and Spread of Diseases
Duration:00:03:00
Exponential Growth in Physics
Duration:00:02:41
Technological Advancements and Moore’s Law
Duration:00:03:52
Environmental Studies and Sustainability
Duration:00:03:47
Complex Functions and Analyticity
Duration:00:04:41
Euler’s e in Exponential Functions
Duration:00:02:37
Euler’s e in Logarithmic Functions
Duration:00:02:42
Euler’s e in Trigonometric Functions
Duration:00:02:47
Euler’s e in Power Series
Duration:00:02:34
Euler’s e in Contour Integration
Duration:00:02:33
Residue Theory and Euler’s e
Duration:00:02:18
Applications of Euler’s e in Complex Analysis
Duration:00:02:49
Euler’s e in Differential Equations
Duration:00:00:27
First-Order Ordinary Differential Equations
Duration:00:03:09
Second-Order Ordinary Differential Equations
Duration:00:03:05
Systems of Ordinary Differential Equations
Duration:00:02:44
Partial Differential Equations
Duration:00:02:40
Homogeneous Differential Equations
Duration:00:02:12
Non-homogeneous Differential Equations
Duration:00:02:04
Boundary Value Problems
Duration:00:02:00
Euler’s e in Probability Theory
Duration:00:00:31
Probability Distributions
Duration:00:02:53
Expected Value and Variance
Duration:00:02:15
Cumulative Distribution Functions
Duration:00:01:58
Joint Probability Distributions
Duration:00:01:50
Conditional Probability and Bayes’ Theorem
Duration:00:02:06
Random Variables and Moments
Duration:00:01:49
Limit Theorems
Duration:00:01:55
Euler’s e in Finance
Duration:00:00:21
Compound Interest and Continuous Growth
Duration:00:02:03
Present Value and Future Value
Duration:00:02:35
Continuous Compounding
Duration:00:02:39
Interest Rates and Euler’s e
Duration:00:02:32
Continuous Discounting
Duration:00:02:33
Continuous Return Rates
Duration:00:02:44
Applications in Investment
Duration:00:03:47
Financial Modeling with Euler’s e
Duration:00:02:52
Euler’s e in Physics
Duration:00:00:25
Kinematics and Euler’s e
Duration:00:02:33
Dynamics and Euler’s e
Duration:00:02:34
Thermodynamics and Euler’s e
Duration:00:01:03
Electricity and Magnetism with Euler’s e
Duration:00:02:23
Optics and Euler’s e
Duration:00:02:12
Quantum Mechanics and Euler’s e
Duration:00:02:29
Relativity and Euler’s e
Duration:00:02:26
Statistical Mechanics and Euler’s e
Duration:00:02:24
Euler’s e in Number Theory
Duration:00:00:26
Prime Numbers and Euler’s e
Duration:00:01:56
Fermat’s Little Theorem and Euler’s e
Duration:00:02:06
Cryptography and Euler’s e
Duration:00:05:01
Diophantine Equations and Euler’s e
Duration:00:03:13
Distribution of Primes and Euler’s e
Duration:00:03:26
Euler’s Totient Function
Duration:00:02:35
Residue Theorem and Euler’s e
Duration:00:03:15
Applications in Cryptography
Duration:00:02:37
Euler’s e in Nature
Duration:00:00:21
Population Growth and Euler’s e
Duration:00:03:44
Compound Interest and Euler’s e
Duration:00:03:19
Radioactive Decay and Euler’s e
Duration:00:03:22
Electric Circuits and Euler’s e
Duration:00:03:17
Fluid Dynamics and Euler’s e
Duration:00:03:14
Biological Rhythms and Euler’s e
Duration:00:03:54
Fractals and Euler’s e
Duration:00:03:31
Philosophical Implications of Euler’s e
Duration:00:00:25
Infinity and Limitlessness
Duration:00:04:21
Harmony of Mathematics and Nature
Duration:00:03:52
Beauty in Mathematical Symmetry
Duration:00:03:43
Quest for Universal Truths
Duration:00:04:01
Exploration of the Unknowable
Duration:00:03:53
Role of Mathematics in Human Understanding
Duration:00:04:07
Interconnectedness of Mathematical Concepts
Duration:00:04:03
Future Directions in Euler’s e Research
Duration:00:00:34
Computational Approaches to Euler’s e
Duration:00:05:02
Euler’s e in Machine Learning and Artificial Intelligence
Duration:00:05:18
Euler’s e and Quantum Computing
Duration:00:05:10
Euler’s e and Cryptocurrency
Duration:00:05:16
Euler’s e in Biomedical Modeling and Simulation
Duration:00:05:50
Euler’s e and Climate Modeling
Duration:00:05:08
Philosophical Implications of Euler’s e in the Digital Age
Duration:00:05:08
Conclusion
Duration:00:00:59
The Legacy of Euler’s e
Duration:00:04:32
Challenges and Opportunities
Duration:00:05:53
Implications for Education
Duration:00:05:52
Future Research Directions
Duration:00:05:46
Ethical Considerations
Duration:00:06:03
Integration into Curriculum
Duration:00:05:42
Global Impact
Duration:00:05:23
Call to Action
Duration:00:04:26