The Calculus Bundle

The Ultimate Integration & Special Functions Bundle (5 Books)

SAMPLE PDFs:

https://drive.google.com/drive/u/0/folders/1AYegYpvrMv_ZCxnHKeq9c2BAwhYdvDOj

A complete, rigorous curriculum for mastering integrals, advanced techniques, contest problem-solving, and the special functions that unify modern analysis.

This bundle brings together four comprehensive books designed to build integration skill from the ground up—starting with a solid foundation, advancing through challenging and competition-level integrals, and culminating in a deep, proof-driven understanding of special functions that appear throughout calculus, analysis, physics, and engineering.

Rather than teaching isolated tricks or formula memorization, this bundle trains judgment: how to recognize structure, choose effective methods, and solve integrals and functional problems with confidence and control.

If your goal is to understand integrals and special functions deeply, not just compute them, this bundle is built for you.

What you get in this bundle

1) Art of Indefinite Integration (Complete Handbook)

A rigorous, problem-driven foundation for indefinite integration—built for depth, structure, and real technique selection.

• 850+ pages of carefully organized material
• 250+ fully solved integrals with detailed, step-by-step reasoning
• Large graded problem sets for mastery and speed
• Multiple methods and key insights for difficult integrals

Topics include:
Substitution (standard & non-standard), advanced integration by parts, rational/irrational/trigonometric integrals, logarithmic and exponential forms, reduction and parametric techniques, and more.

2) Art of Advanced Calculus (Complete Edition)

A curated collection of advanced and competition-style integrals focused on developing true integral artistry.

• 140 fully solved advanced integrals (contest + university level) — 600+ pages
• Meticulous solutions that explain strategy, not just execution
• Frequent alternative approaches (clever substitutions, parameter methods, complex-analysis-flavored ideas where appropriate)
• Emphasis on recognizing structure, identities, and special-function appearances

Includes 500+ graded practice problems with answers.

3) Cracking the MIT Integration Bee

A contest-focused training manual designed around what the MIT Integration Bee actually rewards: speed, structure, and decision-making under pressure.

• ~600 Integration Bee problems fully solved (1330+ pages) (From MIT, Carnegie Mellon and Caltech)
• Bee-time shortcuts alongside complete solutions
• Alternative methods and “why this is faster” explanations
• Common pitfalls and strategic warnings

Covers casework mastery (absolute values, piecewise behavior, symmetry, floors/ceilings), fast substitutions, efficient integration by parts, and advanced round tools (parameter differentiation, series ideas, special-function structure).

4) Art of Special Functions

A complete, proof-driven handbook for mastering the functions that shape advanced calculus, analysis, and applied mathematics.

This book builds special functions from first principles, emphasizing structure, derivation, and real problem-solving control—showing where these functions come from, why they work, and how they connect to integrals, differential equations, transforms, and asymptotics.

• 1150 pages, fully self-contained
• 350+ fully solved problems with detailed explanations
• 500+ practice exercises ranging from routine to challenging
• Rigorous proofs of fundamental identities and theorems
• Clear links between theory, computation, and applications

Topics include:
Gamma, Beta, Digamma & Polygamma functions; special integrals; Riemann & Hurwitz zeta; polylogarithms; hypergeometric functions; orthogonal polynomials; Bessel, Legendre & Airy functions; elliptic integrals & functions; theta functions; and integral transforms (Fourier, Laplace, Mellin, Hankel, Hilbert, Abel), with applications to differential equations, probability, wave phenomena, and signal processing.

Who this bundle is for

• Undergraduate and graduate STEM students who want depth beyond routine calculus
• Integration Bee, Putnam, and contest solvers aiming for speed and control
• Self-learners seeking a serious, structured integration curriculum
• Anyone who wants to understand integrals and special functions—not memorize formulas

Format

• PDF (high-resolution, LaTeX typeset)
• Instant download
• Lifetime access

Why this bundle works

Most resources either teach technique without insight, or list results without judgment.

This bundle builds the full analytical stack:

Foundation (Indefinite Integration)
→ Power & breadth (Advanced Calculus)
→ Speed & contest instincts (MIT Integration Bee)
→ Unifying theory & structure (Special Functions)

Together, these books train you to see patterns, make intelligent choices, and solve integrals and functional problems with clarity and confidence.