Science and Engineering Mathematics Series
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The world is made up of complex numbers.
Complex functions, woven from complex numbers, inherit the properties of real-number functions, but at the same time, they also perform a magical dance.
Learning the essence of complex functions
Masato Murakami /Ritsuyoshi Yasutomi/Shinobu Kobayashi
Complex function theory is also called function theory.
This reflects the pride of mathematicians who believe that one cannot discuss functions without understanding complex functions.
This book begins with the fundamentals of power series expansion, which bridges the gap between complex and real functions, and then uses the residue theorem to explain...
This book carefully explains the application of complex functions to solving complex real integrals, as well as analytic continuation techniques that can extend the domain of functions.
The Fourier series method, discovered by Fourier in the 19th century, has spread to cutting-edge fields such as quantum mechanics through the Fourier transform.
Fourier Analysis: Fundamentals of Wave Analysis
Masato Murakami /Ritsuyoshi Yasutomi/Shinobu Kobayashi
This book provides a detailed explanation of Fourier analysis techniques and their applications, focusing on the fundamental question of "how to expand a physical phenomenon like a wave into a series of trigonometric functions."
This book carefully explains the process of converting Fourier series to complex exponential functions using Euler's formula, and its extension from discrete to continuous Fourier integrals, including their significance.
Furthermore, it can be understood that the variable transformation function of the Fourier transform allows for the solution of differential equations that are otherwise difficult to solve.
This book allows you to grasp the meaning and utility of the Fourier transform through numerous illustrations and practice problems.
Government approval ratings, stock market forecasts, weather forecasts,
How reliable are the numerical data that influences our lives?
The origin of statistical data analysis
Masato Murakami / Kazuo Inoue / Shinobu Kobayashi
Understanding how these statistics are calculated allows us to identify truly valuable data.
This book begins by reviewing the fundamentals of statistics, such as "mean" and "variance," and then teaches how necessary data can be expressed mathematically through probability density functions such as the normal distribution, binomial distribution, t-distribution, chi-squared distribution, F-distribution, and Poisson distribution.
I sincerely hope you will hone your data statistical analysis skills through practical application.
Nature is written in the language of mathematics.
Natural phenomena are described by differential equations.
The origin of differential equations in science and engineering
Masato Murakami /Ritsuyoshi Yasutomi/Shinobu Kobayashi
Starting with first-order linear differential equations, this course guides you through fundamental techniques and then moves on to solving more complex differential equations.
It effortlessly guides you to understand the solutions to equations that brilliant pioneers in the history of mathematics, such as Bernoulli, Clérot, Euler, Hermite, and Legendre, once tackled.
The first step in analyzing physical phenomena is constructing differential equations. Then, by solving these equations, the phenomena can be described.
Mathematicians, employing ingenious techniques, have tackled and successfully solved difficult differential equations.
That forms the foundation of modern science.
Armed with quantum mechanics, physicists have brought to the end the story of the microscopic world.
Quantum Mechanics III Introduction to magnetism
Masato Murakami / Kazumasa Iida / Shinobu Kobayashi
This is the third installment following "Introduction to Wave Mechanics." Based on the angular momentum operator of quantum mechanics, humanity has succeeded in elucidating magnetism associated with electron orbitals, drawing on classical mechanics.
However, encountering an inexplicable anomalous splitting of the emission spectrum, they finally arrived at the fourth degree of freedom: electron spin. As a result, they succeeded in explaining the anomalous Zeeman effect, which is the complex splitting structure of the spectrum. This led to the elucidation of all magnetic phenomena.
Furthermore, this proved that the quantum mechanical approach of operators and eigenvalues was also valid in the field of magnetism.
With just paper and a pencil, you can understand the essence of quantum mechanics, a treasure of humankind!
Now, let's give it a try!
Quantum Mechanics II: Introduction to Wave Mechanics
Masato Murakami / Kazumasa Iida / Shinobu Kobayashi
This is the second book in the series, following "Introduction to Matrix Mechanics." Based on the idea that electrons are waves, Schrödinger proposed the wave equation. As we seek its solution, the mysterious electron orbitals within atoms gradually become clear.
This book will allow you to thoroughly study the process by which the electron orbitals of the hydrogen atom, a subject of extreme difficulty in matrix mechanics, are brilliantly elucidated. Furthermore, a considerable number of pages are dedicated to explaining the properties of associated differential equations such as Laguerre's and Legendre's, which are essential mathematical foundations for understanding this process.
The solutions to these differential equations reveal the electron orbitals of all the atoms in the periodic table.
Analytical mechanics is neither difficult nor useless, but rather a product of humankind, a realization that it is not something incomprehensible or useless.
analytical mechanics
Masato Murakami / Masato Suzuki / Shinobu Kobayashi
The curve that minimizes the time required for an object to fall along a curve connecting two points is called the brachistochrone curve. Variational calculus is used to determine the shape of this curve.
The foundation of analytical mechanics lies in variational calculus.
An object moves along a path that minimizes a certain physical quantity. This is the principle of least action.
It is precisely because it is abstract that this book allows you to truly appreciate the allure of analytical mechanics, which contributed to the development of quantum mechanics.
This single book will give you a deep understanding of matrix and vector operations and determinants , which are the foundations of data science.
Linear Algebra
Masato Murakami / Ayako Suzuki / Shinobu Kobayashi
I often hear people say they struggle with linear algebra. On the other hand, linear algebra, along with calculus, is a required subject in university mathematics.
This is because matrix and vector operations are widely used in many fields of science and engineering. Above all, they are essential tools for the much-discussed fields of AI, such as deep learning and data science.
Based on the concept that "mathematics can only be understood through practical application," this book aims to help readers understand the fundamentals and applications of linear algebra through numerous practice problems.
This one book explains how quantum mechanics is
It will become clear whether it was constructed.
Quantum Mechanics I: An Introduction to Matrix Mechanics
Masato Murakami / Kazumasa Iida / Shinobu Kobayashi
Quantum mechanics is considered the greatest achievement of 20th-century physics. Many researchers ventured into this uncharted territory, feeling their way through the process.
Then, a ray of light shone through the ideas of Heisenberg and others. That was matrix mechanics.
Nowadays, quantum mechanics is described using wave mechanics, and textbooks dealing with matrix mechanics have almost disappeared. However, the concepts cultivated in matrix mechanics continue to thrive.
This book is a valuable resource for understanding its contents.
The mathematical foundation of artificial intelligence (AI)
You'll be able to master regression analysis!
Regression analysis
Masato Murakami / Kazuo Inoue / Shinobu Kobayashi
Based on existing data,
A detailed explanation of the method for predicting target values!
The basics of statistics are the normal distribution, t-distribution, chi-squared distribution, and F-distribution.
You will be able to understand how it is used in statistical analysis.
And how reliable are the results of regression analysis?
This single book will allow you to experience everything from the basics of data analysis to its applications.
You can also learn statistical testing techniques that are important in data science.
The entire process of deriving the formula will not be omitted.
A wealth of practice problems with detailed answers.
I hope you enjoy the process of understanding and accepting these things in this book.
Now, let's master statistical mechanics!
Applied Statistical Mechanics
Masato Murakami / Kazumasa Iida / Shinobu Kobayashi
A continuation of the basic series.
This will give you a good understanding of the usefulness of statistical mechanics!
Experience the power of statistical mechanics through practical problems.
That's what will happen!
Diatomic gases, specific heat of solids, and the Ising model
We are also exploring the applied fields of phase transitions.
The basic step is to find the partition function.
To find the energy of the system
Substitute into the Boltzmann factor.
The thermodynamic function can then be obtained through mathematical processing.
I hope you enjoy the process of understanding and accepting these things in this book.
The university lecture on statistical mechanics
It's surprisingly easy to understand!
Statistical mechanics basics
Masato Murakami / Kazumasa Iida / Shinobu Kobayashi
Statistical mechanics breathes life into thermodynamics, which had previously been vague and elusive.
I hope you enjoy the process of how the micro and macro levels merge, revealing even the very essence of thermodynamics.
Microcanonical population, partition function
What are canonical groups and grand canonical groups?
The Fermi and Bose distributions in quantum statistics
It's easy to understand.