Introduction

Why Calculus 3?

Calculus 3 extends single-variable calculus into multiple dimensions. Instead of curves, we study surfaces. Instead of slopes, we study gradients. Instead of integrals over intervals, we integrate over areas and volumes.

  • Vectors in 3D -- Dot products, cross products, magnitudes, and projections — the language of 3D geometry
  • Partial Derivatives -- How a multivariable function changes as each variable moves independently
  • Optimization -- Finding maxima and minima of surfaces using the gradient and the second derivative test
  • Multiple Integrals -- Integrating over 2D regions and 3D volumes, in Cartesian and polar coordinates

The Computational Angle

Every concept is implemented in C as a numerical algorithm. You will:

  • Compute dot and cross products from scratch
  • Approximate partial derivatives using central differences
  • Find and classify critical points with the discriminant
  • Evaluate double and triple integrals using the midpoint rule in 2D and 3D
  • Integrate over polar coordinates using the Jacobian factor r

Prerequisites

Calculus 1 and 2 (limits, derivatives, integrals, series) and basic C programming (pointers, function pointers, loops). Calculus 1 in C and Calculus 2 in C on this platform are ideal preparation.

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