PX153 - 0 - mathematics for physicists

term 1

A - vectors

PX153 - A1 - notation and geometrical representation
PX153 - A2 - cartesian coordinates and vector components
PX153 - A3 - position, velocity and acceleration vectors
PX153 - A4 - vector operations
PX153 - A5 - coordinate systems
PX153 - A6 - advanced vector operations
PX153 - A7 - reciprocal vectors
PX153 - A0

B - complex numbers

PX153 - B1 - basic operations and the argand diagram
PX153 - B2 - polar representation
PX153 - B3 - de moivre's theorem
PX153 - B4 - application - first look at smh
PX153 - B5 - application - describing damped smh
PX153 - B5.1 - underdamping
PX153 - B5.2 - overdamping
PX153 - B5.3 - critical damping

C - first order ODEs

PX153 - C1 - introduction and definitions
PX153 - C2 - construction of ODEs
PX153 - C3 - direct integration
PX153 - C4 - separation of variables
PX153 - C5 - substitution
PX153 - C6 - integrating factor

D - second order ODEs

PX153 - D1 - definitions
PX153 - D2 - solving 2nd order homogeneous ODEs
PX153 - D3 - reducing a non-linear ODE to a linear ODE

E - second order inhomogeneous ODEs

PX153 - E1 - recap and introduction
PX153 - E2 - method of undetermined coefficients
PX153 - E3 - driven damped simple harmonic motion
PX153 - E4 - method of variation of parameters

F - series

PX153 - F1 - taylor series
PX153 - F2 - convergence of a series
PX153 - F3 - estimating the sum of a series
PX155 - F4 - power series and taylor series revisited

G - calculus of functions of many variables

PX153 - G1 - partital differentiation
PX153 - G2 - the total differential, and exact and inexact differentials
PX153 - G3 - partial differential equations
PX153 - G4 - taylor expansion of a function of two variables
PX153 - G5 - critical points of a function of two variables

H - gradient of a scalar function

PX153 - H1 - directional derivative and gradient vector of scalar functions
PX153 - H2 - visualising variability of a scalar function - contours
PX153 - H3 - gradients of functions of three variables
PX153 - H4 - application of gradient in physics - the potential of a conservative force
PX153 - H5 - coordinate systems revisited
PX153 - H6 - gradient operator

term 2

I - integration

PX153 - I1 - introduction
PX153 - I2 - multiple integrals
PX153 - I3 - domain of integration
PX153 - I4 - non-rectangular domain of integration
PX153 - I5 - summary of integrals in 3D
PX153 - I6 - volume integrals
PX153 - I7 - other coordinate systems
PX153 - I8 - summary of multidimensional integrals
PX153 - I9 - line integrals
PX153 - I10 - conservative fields
PX153 - I11 - surface integrals

J - fourier series

PX153 - J1 - introduction
PX153 - J2 - convergence
PX153 - J3 - proofs and derivations
PX153 - J4 - periodic extensions
PX153 - J5 - symmetric and antisymmetric functions
PX153 - J6 - parseval's theorem
PX153 - J7 - general interval
PX153 - J8 - fourier sine and cosine series
PX153 - J9 - overshoot and gibbs phenomenon
PX153 - J10 - examples

K - linear algebra

PX153 - K0 - outline
PX153 - K1 - terminology of matrices
PX153 - K2 - matrix operations
PX153 - K3 - solving simultaneous equations
PX153 - K4 - row-reduced echelon form (gaussian elimination)
PX153 - K5 - trace and determinants
PX153 - K6 - properties of determinants
PX153 - K7 - matrix inverse
PX153 - K8 - properties of matrix inverses
PX153 - K9 - LU decomposition method
PX153 - K10 - special matrices
PX153 - K11 - matrix operation on vectors
PX153 - K12 - eigenvectors and eigenvalues
PX153 - K13 - additional properties
PX153 - K14 - basis changes and similarity transformations
PX153 - K15 - similarity transformation
PX153 - K16 - diagonalization
PX153 - K17 - properties of diagonalization