Calculus & Advanced Problem Solving

By the end

What you'll build

• Evaluate hard limits using standard forms, conjugates, series thinking and the squeeze theorem — and know when L'Hôpital fails
• Crack definite integrals with symmetry, the King's property and Leibniz differentiation, often without finding an antiderivative
• Apply AM–GM and Cauchy–Schwarz with correct equality cases, and treat complex numbers as rotate-and-scale geometry
• Dissect multi-concept problems with the translate–connect–estimate–verify clinic method under timed, negative-marking conditions
• Write structured proof sketches by direct argument, contradiction and induction that survive a hostile reader

Curriculum

What's inside

5 modules · 25 lessons

1. 01

   Rigorous Limits & Continuity

   6 lessons
   • Start Here: Where Formulas End
   • The ε–δ Idea, Demystified
   • Limit Techniques Beyond L'Hôpital
   • Evidence Check: Limitsquiz
   • Python Lab: Verify Limits with SymPypython lab
   • + 1 more lesson
2. 02

   Advanced Integration

   4 lessons
   • The Art of the Definite Integral
   • Evidence Check: Integration Propertiesquiz
   • Hard Integrals: Numerical Drillfill blank
   • Python Lab: Verify Integrals with SymPypython lab
3. 03

   Algebra at Depth: Inequalities & Complex Numbers

   5 lessons
   • Inequalities: AM–GM and Friends
   • Evidence Check: Inequalitiesquiz
   • Complex Numbers as Geometry
   • Inequality & Complex Numericalsfill blank
   • Python Lab: Inequality Checks with SymPypython lab
4. 04

   Multi-Concept Problem Clinics

   5 lessons
   • The Clinic Method: Dissecting Hard Problems
   • Evidence Check: Lateral Thinkingquiz
   • Multi-Concept Numerical Drillfill blank
   • Theorems & Results Flashcardsflashcard sr
   • Timed Clinic Mock (60 min)quiz
5. 05

   Proof Sketches & Structure

   5 lessons
   • Anatomy of a Proof
   • Writing Lab: Prove √3 Is Irrationalwriting lab
   • Induction & Structure Numericalsfill blank
   • The Long Game: Wrap-Up & Next Steps
   • Final Timed Mock (70 min)quiz

The shape of it

How this course works