From Alternating Current to the Fourier Transform

di Sandro Ronca (Autore)

Sandro Ronca, 2026

Why does a complex number describe an alternating current? And how does that same idea lead all the way to the Fourier transform? This book answers both questions in ten carefully connected stages. It starts from one of the cornerstones of modern technology, AC circuit theory, and uses it as a gateway to some of the most powerful tools in mathematics. The first six chapters build a solid foundation in AC circuit analysis: sinusoids and phasors, the "magic" of complex numbers, impedance and admittance, resonance and electrical power. Chapter seven tackles transients with Euler's numerical method, an approach that makes differential equations tangible even before the analytical solution. Then the journey opens up: the Fourier series, the vector-space view that unifies it all, and finally the Fourier transform, the indispensable tool of acoustics, signal processing, optics, image processing and quantum mechanics. Written from decades of teaching experience, the book always reasons about concepts before formulas. Where the standard explanation relies on calculus, it often offers an alternative path as well. Dedicated mathematical interludes (complex numbers, derivatives, the exponential function, integrals, the Gaussian, Dirac's delta, Feynman's trick and more) bring every reader up to speed, while giving experts insights rarely highlighted in standard courses. Inside you will find: • 10 chapters, from alternating current to the Fourier transform • 280+ figures and diagrams • Nearly 3,000 formulas, displayed as real mathematical text • Worked examples and end-of-chapter problems • A fully linked analytical index Ideal for students making the leap from high school to university physics or engineering, technicians and engineers who want to truly understand the tools they use every day, and any curious mind who has wondered what lies behind the word "Fourier". Best enjoyed on a tablet or computer, where formulas and figures display at their best.

• Autore: Sandro Ronca
• Anno edizione: 2026
• Editore: Sandro Ronca
• Formato: EPUB3 con DRMFREE
• Lingua: Inglese
• Compatibilità: Tutti i dispositivi (eccetto Kindle)
• Layout: Reflowable
• EAN: 9798237650655