Advanced Integration Techniques

A 440-page, problems-only collection that turns advanced integration into a disciplined practice. Built for honors undergraduates, graduate students, instructors, and independent learners, this book focuses on technique + intuition over exposition, so you spend your time solving.

What’s inside

• Chs. 1–43: Core Practice Sets
  Carefully curated “Practice Problems” from classical topics (change of variables, Fubini/Tonelli, improper and singular integrals, inequalities, asymptotics, differential forms, Stokes/Green/Divergence) plus 8 new, intuition-driven problems per chapter that escalate in difficulty.
• Advanced Thematic Problem Banks
  Open-ended challenges that synthesize methods across:
  Integrals on manifolds • Path integrals • Differential forms & Stokes • Riemannian volume • Coarea & measure-theoretic tools • Stationary phase/Laplace methods • Singular integrals & regularization • Topological/holonomy viewpoints.
• Research-style prompts
  Many problems ask you to justify assumptions, choose a coordinate system, design bounds, or propose an asymptotic scheme—mirroring how real mathematicians and physicists reason.

Why it works

• Pedagogical ramp: each chapter moves from tactical “warm-ups” to multi-step strategy.
• Crossover skill: problems emphasize geometry, symmetry, and invariants—habits that generalize beyond any one trick.
• Assignment-ready: instructors can lift sets directly for proof-oriented courses and qualifying-exam prep.

Audience & prerequisites

• Honors undergrads, graduate students, instructors, and researchers in Mathematics or Physics.
• Prerequisites: proof-based Calculus & Linear Algebra; comfort with multivariable/vector calculus. Helpful (not required): basic measure theory, differential forms, and Riemannian geometry.

Format

• Problems-only (no solutions), 440 pages, clean, readable layout with Table of Contents.
• Ideal for course problem sets, independent study, or exam training.

Author: Jason Mastorakos — blending rigor and geometric insight to develop problem sets that train both computation and proof strategy.