Functions of one real variable. Even and odd functions, even and odd parts
of a generic function.
Polynomials (example: Hermite Polynomials).
Rational functions and partial fractions.
Other common elementary functions (exp, log, sin, cos, tan,sinh,cosh,tanh). Inverse functions.
Integration and the area under a curve. Integrals of elementary
functions and linearity properties of integrals.
Key techniques of integration: integration by parts and
by direct substitution.
Integration of rational functions via partial fraction decomposition.
Functions of more than one variable. Partial differentiation. Implicit partial differentiation.
Differentiating functions of functions. Quantifying small changes.
Introduction to Probability and Statistics. Random variables. Discrete distributions, continuous distributions.
Mean, variance and standard deviation. Statistical measures
from data and errors in data.
Least squares fitting to linear data.