Advanced Integration Techniques
About
About the Book
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 insideChs. 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 worksPedagogical 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 & prerequisitesHonors 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.
- FormatProblems-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.
Author
About the Author
jason Mastorakos
ason Mastorakos is a mathematician, tutor, and author who specializes in helping students bridge the gap between formal theory and real problem-solving in advanced calculus and physics. With a background reaching through second-year honours university mathematics and physics, he works daily with abstract algebra, advanced linear algebra, analysis, differential equations, probability, and elementary functional analysis. His teaching focuses on making these abstract ideas feel concrete, visual, and intuitive, especially for upper-level undergraduates who are encountering rigorous mathematics for the first time.
He runs S.T.E.M. Online, an online mathematics and physics tutoring company dedicated to strengthening critical thinking and visual-spatial reasoning. Jason has extensive experience working one-on-one and in small groups with honours students, engineering undergraduates, graduate-school applicants, and self-learners who want more than formula drills. His style is to start from first principles, insist on clear logic in every step, and then show how those same ideas power real applications in physics, engineering, and quantitative science.
As an author, Jason is particularly interested in turning “problem-only” practice into a complete learning experience. His book Advanced Integration Techniques: Mastering Advanced Integrals & Applications reflects this philosophy: it builds from solid foundations, develops advanced tools (improper integrals, special functions, contour integration, multiple integrals, fractional calculus, and more), and then reinforces them with carefully chosen exercises, theory sections, and detailed solutions. Across his writing and teaching, Jason’s goal is consistent: to give motivated students a rigorous, clear, and deeply satisfying path into higher mathematics.
Contents
Table of Contents
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