PH 422 Math Bits

Power Series Basics
Derivatives of Scalar Fields
Divergence (40 min)
Divergence Theorem (20 min)
  • Reading: GVC § Divergence Theorem
  • Derivation of the Divergence Theorem (lecture). We follow “div, grad, curl and all that”, by Schey. The Divergence theorem is almost a lemma based on the definition of divergence. Draw a diagram of an arbitrary volume divided into lots of little cubes. Calculate the sum of all the fluxes out of all the little cubes (isn't this a strange sum to consider!!) and argue that the flux out of one cube is the flux into the adjacent cube unless the cube is on the boundary.
Stokes' Theorem
Product Rules

PH 425 Math Bits

Matrix Manipulations (45 minutes)
Introduction to Bra-ket notation (15 minutes)

Unit: Operators and Transformations in Linear Systems

Linear Transformations (1 1/2 hr)
Tangible Metaphor for Complex Vectors (10 minutes)
Properties of Linear Vector Spaces (30 min)
Inner Products and Norms
  • Calculating Inner Products and Normalization of Vectors (Lecture, ?? minutes)

FIXME Write these lecture notes. Emphasize complex vectors.

Matrix Components (40 min)
Rotation Matrices in 2 and 3 Dimensions (10 min)

Unit: Eigenvalues and Eigenvectors

Eigenvalues & Eigenvectors (2 hr)
Special Properties of Hermitian Matrices (40 min)
Commuting Matrices (10 min)

PH 423 Math Bits

Partial Derivatives (40 minutes)
Potential Energy and the Partial Derivative Machine (1 hour 40 minutes)
Total Differentials and Partial Derivatives (1 hour 30 minutes)
Maxwell Relations and Legendre Transforms

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