Professor: Leonardo Colò
Program: Honours Physics
Course code: MATH 227
Section: 001
Workload: Sept-Dec 2024 (12 weeks)
Class Schedule: MWF 11h30 - 12h30 in MC1085

1. Multivariable Vector Functions and Line Integrals (3 weeks):
   - Introduction to Multivariable Vector Calculus.
   - Linear Objects in \(\mathbb{R}^3\).
   - Regions in \(\mathbb{R}^n\).
   - Curves and particle motion.
   - Arc Length.
   - Line Integrals.
2. Multiple Integrals (2 semaine):
   • - Cylinders and Quadric Surfaces.
     - Coordinate Systems.
     - Double integrals.
     - Triple integrals.
3. Gradients and Directional Derivatives (2 weeks):
   • - Partial Derivatives.
     - Linearization.
     - Chain Rule.
     - Directional Derivative and Gradient.
4. Vector Fields (4 weeks):
   • - Introduction to vector fields.
     - Divergence and Curl.
     - Path Independence of Line Integrals.
     - Green's Theorem.
     - Surface integrals.
     - Stokes' Theorem.
     - Divergence Theorem.
5. Optimization (1 week):
   • - Extreme Values.
     - Lagrange Multipliers