Lectures on Fourier Series: Exploring Harmonic Analysis

Lectures on Fourier Series is a comprehensive, lecture-based textbook that guides readers from the fundamentals of trigonometric polynomials to the advanced applications of Fourier analysis. Designed for advanced undergraduates, engineering students, and early graduate learners, this book blends mathematical rigor with conceptual clarity.

Across ten carefully structured lectures, readers explore the theory, computation, and applications of Fourier series — from orthogonality and convergence to half-range expansions, complex representations, and their role in solving heat and wave equations. Each lecture combines theory, worked examples, and practice problems, culminating in a comprehensive formula sheet and MCQ review section for self-assessment.

The book emphasizes intuition, mathematical precision, and physical interpretation, making it ideal for students of mathematics, physics, and engineering, as well as educators and exam aspirants seeking a clear, modern approach to harmonic analysis.

Key Features:

Structured as a sequence of 10 in-depth lectures for modular or sequential study

Covers trigonometric and complex Fourier series, convergence theorems, and applications

Includes step-by-step derivations, solved examples, and problem sets

Features a comprehensive formula sheet and concept-check questions

Connects classical analysis with modern signal and system theory

Whether you are exploring the mathematical beauty of periodic functions or the analytical power of spectral methods, Lectures on Fourier Series offers a complete and elegant journey through one of mathematics’ most profound tools.