MAT291 — Calculus III

Course focuses on multivariable calculus in the context of mathematical physics. Continuation of MAT187 — Calculus II, followed by ECE221 — Electric and Magnetic Fields. We used the Calculus: Early Transcendentals (3rd edition) by William Briggs, et al.

Concepts covered

Vector calculus

• Function (mathematics)
  • Graphing of functions
    • Trace
    • Level curves and surfaces
    • Cylinders
• Point-set topology
• Limit
  • Contrapositive proof
  • Continuity
• Partial differentiation
  • Differentiability
  • Chain rule
  • Implicit differentiation
  • Directional derivative
  • Gradient
  • Tangent plane
    • Linear approximation
    • Taylor series
• Jacobian matrix
• Double integral
• Triple integral
• Change of variables
  • Polar coordinates
  • Spherical coordinates
  • Cylindrical coordinates
• Parametric equation
• Line integral and surface integral
  • Flux
  • Circulation
• Vector field
  • Divergence
  • Curl
• Gradient theorem (fundamental theorem of line integrals)
• Divergence theorem
• Stokes’ theorem
• Green’s theorem

Mathematical physics

• Small signal modelling
  • System model (state space equations)
• Helmholtz’s decomposition theorem
• Maxwell’s equations
• Dirac delta function
• Gauss’ law
  • Gaussian surface
• Ampere’s law
  • Amperian loop

Exam preparation

Things to review:

• Divergence/Stokes’ theorem
• Surface integrals
• Gauss/Ampere’s law

IMO the rest feel okay. Question 1 and 2 need a quick look. Divergence/Stokes could be fucked. Surface integrals in particular are a little messy still.