Sequences and series convergence, sums of integers/squares/cubes, method of differences for telescoping series, and recurrence relations.
Roots of polynomials, symmetric functions of roots (sum and product), forming equations from given roots.
Polar coordinates (r,θ), conversion to/from Cartesian, sketching polar curves, and areas in polar form.
Conic sections (parabola, ellipse, hyperbola) in Cartesian and polar forms, equations and sketching.
Maclaurin series for approximating functions, standard series (e^x, sin x, cos x, ln(1+x)), and validity intervals.
Hyperbolic functions sinh, cosh, tanh, their graphs and identities (Osborn's rule), inverse hyperbolic functions, differentiation and integration.
Integration using inverse trigonometric functions arcsin, arctan and inverse hyperbolic functions arsinh, arcosh, artanh.
Using partial fractions for integration, including improper integrals, mean values, and graphs of rational functions
Vector equations of lines and planes, scalar product, angles between vectors/lines/planes, intersections
Vector product (cross product), areas of triangles/parallelograms, shortest distances (point to line, point to plane, between lines), triple scalar product
First order differential equations solved using integrating factor e^(∫P dx) for equations of form dy/dx + Py = Q, and substitution methods.
Complex numbers using Euler's formula e^(iθ) = cosθ + i sinθ, exponential form re^(iθ), De Moivre's theorem, nth roots, roots of unity, trig identities.
Second order differential equations (homogeneous and non-homogeneous), auxiliary equation, particular integrals, SHM and damped oscillations.