Calculus of Several Variables

Contents

1. The Geometry of Planes and Curves
   • Space Curves - an Introduction to Coordinates in 3D
   • Equations of Planes and Lines
   • General Parametric Curves
   • Velocity and Differentiability
   • Arc Length and Curvature
   • The TNB Frame and Serret–Frenet Formulae
2. Multivariable Functions and Partial Derivatives
   • Scalar Functions
   • Multivariable Functions
   • Multivariable Limits and Continuity
   • Partial Derivatives
   • Directional Derivatives
3. Approximations and Optimization
   • Critical Points
   • The Second Derivative Test
   • Tangent Plane Approximations
   • Total Differential
   • Lagrange Multipliers
4. Integrals of Multivariable Functions
   • Double Integrals
   • Fubini's Theorem
   • Line Integrals
   • Gradient
   • Vector Fields
5. Div, Grad, Curl and all that
   • Curl and Divergence
   • Conservative Fields, Path Independance, Gradient Fields
   • $\vec F$ is conservative $\implies$ curl $\vec F = 0$
   • The Fundamental Theorem of Line Integrals
   • Green's Theorem
6. Triple Integrals and Surface Integrals

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