Introduction

Why Calculus 2?

Calculus 2 takes the foundations of Calculus 1 and extends them in three major directions: more powerful integration techniques, the theory of infinite series, and new coordinate systems for curves that can't be described with simple y = f(x) equations.

• Integration Applications -- Arc length, surface area, work done by variable forces, and improper integrals that span infinite intervals
• Sequences and Series -- Rigorous theory of convergence: geometric series, p-series, alternating series, and the ratio test
• Taylor Series -- Approximate any smooth function as a polynomial, with quantified error bounds — the computational backbone of numerical computing
• Parametric and Polar -- Curves defined by parameter or angle: circles, spirals, rose curves, and their arc lengths and areas

The Computational Angle

This course implements every concept in C using numerical algorithms — no symbolic algebra. You will:

• Compute arc lengths and surface areas with numerical integration + numerical derivatives
• Approximate improper integrals by integrating to large finite bounds
• Implement partial sums to observe series convergence empirically
• Build a Taylor polynomial engine using recursive central differences
• Compute curvature using the second-derivative formula

Each function you write is a small numerical experiment. When your output matches the analytic formula, you know both the theory and the implementation are correct.

Prerequisites

Calculus 1 (limits, derivatives, integrals) and basic C programming (pointers, loops, structs). The Calculus 1 in C course on this platform is ideal preparation.