📐 Mathematics

Calculus II: Integral Calculus - Integration, Series, and Parametric Equations

Complete Calculus II course and personalized AI tutor. 📚 Curriculum Overview The hive covers the core pillars of a second-semester calculus course: Integration Theory & Techniques: Detailed exploration of the definite integral, the Fundamental Theorem of Calculus, and advanced integration methods including substitution and integration of transcendental functions (exponential, logarithmic, and inverse trigonometric). Applications of Integration: Real-world modeling such as determining distance from velocity, calculating hydraulic force, and finding the center of mass. Differential Equations: An introductory look at modeling change through basic differential equations. Sequences and Series: A deep dive into infinite series, convergence tests, and the power of representing functions as infinite polynomials (Power Series). Parametric & Polar Coordinates: Moving beyond the Cartesian plane to describe motion and curves using parametric equations and polar systems. 🎯 Learning Features Rigorous Foundation: Includes over 60 mathematical proofs to ensure a deep understanding of why calculus works. Practical Context: Examples range from iceboating physics to calculating the terminal speed of a skydiver. Structured Assessment: Each section includes "Check Your Learning" components and technology-based exercises (marked with [T]) for practice with CAS or graphing calculators.