Recommendation 4
Introduction 6

PART 1
Chapter 1 Fourier Series 15
Chapter 2 Fourier Coefficients 93
Chapter 3 Discontinuous Fourier Expansion 153
Chapter 4 Voice and Spectrum 189

PART 2
Chapter 5 Differentiation 219
Chapter 6 Differentiation of sinq 253
Chapter 7 Integration 289
Chapter 8 Orthographic and Orthogonal 343

PART 3
Chapter 9 e and i 391
Chapter 10 Euler's Formula 431
Chapter 11 Complex Representation of Fourier Series Expansion 477
Chapter 12: Fourier Transforms and Wave Uncertainty 501
Chapter 13 FFT Method 527

Appendix 557 Answer 571
Ending the Book 576
Reference 584

Recognized as an introductory book on waves in the United States and Japan, "Learning Wave Laws with Mathematics" will guide those interested in various fields, including science, mathematics, and medicine, into the world of waves in an easy-to-understand and enjoyable way!

Waves are an essential field in various fields of study, including theoretical physics, yin-yang, optics, astrophysics, electronics, vibration analysis, signal processing, image processing, data compression, communications engineering, and radiology.
And our daily lives are also full of waves.
That's why waves are a very important field for us.
However, because waves, especially Fourier transforms, are not properly covered in high school, it is said that there are many difficulties when trying to start studying mathematics in earnest in college.

'Fourier' is a powerful mathematical method for interpreting phenomena that are understood as waves, such as light, sound, vibration, and heat conduction.
Sound is perceived as waves of pressure transmitted by vibrating air.
Of course, human speech is also sound, so it can be expressed as waves.
The familiar trigonometric functions such as sin or cos, differentiation that is convenient for finding the speed or acceleration of a moving object, integration that can find the distance moved, i (the imaginary unit) that is convenient for calculations, e (the base of natural logarithms) that has a special meaning even in differentiation or integration, vectors that have two elements of direction and magnitude, Maclaurin expansion that can be applied in the same form to any equation, etc., all of these things that are learned separately in physics or mathematics appear on the stage of the equation for interpreting wavelength called 'Fourier'.
This book teaches in detail and kindly so that you can understand and conquer the Fourier transform, which is by no means easy.
For example, trigonometry and differentiation/integration, which are essential for learning Fourier series, are very easy to learn and are approached from the basics, so even people who are afraid of numbers or formulas can approach them with ease.

By organizing the process of amateurs who did not even know the basics of mathematics gathering together to study and discuss Fourier waves among themselves, and explaining Fourier waves from their perspective, a wonderful introductory book on waves that anyone can easily understand was created.
This book, which was developed through this process, utilizes conversational methods to enable self-study and even includes simple practical exercises.
It is hard to find a book that makes learning Fourier's waves easier than this one, as it explains them with dialogue, numerous pictures, and examples. Even now, more than 30 years after its publication, it is known as one of the easiest introductory books on Fourier in Japan and the United States.

It will be an easy and useful guide for those who are interested in waves, especially young students with big dreams, scientists, medical students, and the general public who are interested in science.