Advanced Calculus of One Variable

Discover a rigorous yet practical approach to series, transforms, and their applications. This book develops sequences and series, power series and Taylor theory, Fourier series, and Fourier and Laplace transforms, with convolution and distributional ideas providing a unifying perspective. It then shows how these tools solve key problems in ODEs, PDEs—including the heat and wave equations—and linear difference equations.Theory is reinforced throughout with reproducible Python examples using SymPy, NumPy/SciPy, and Matplotlib for symbolic computation, numerical exploration, and visualization. Brief “Python with AI” interludes demonstrate responsible use of LLMs for testing conjectures, checking steps, and improving computational workflows without replacing mathematical reasoning. Ideal for graduate students and practitioners seeking a proof-based, computation-friendly reference.