[HL] List of Recommended Topics

Big Idea	Analysis	Applications
Calculus	Limits
	Related rates	Related rates
	Solids of revolution	Solids of revolution
	Integration techniques (Partial fractions, integration by parts)
	Linear approximation
	Differential equations Homogeneous diff eqs	Differential equations coupled diff eqs
		Phase portraits Slope fields
	Integrating factor
	Logistic growth
	Maclaurin series Convergence
Linear Algebra	RREF (Gaussian Row Reduction)
		Matrix algebra
		Inverse matrix (Det)
	Vectors & Applications	Vectors & Applications
	Planes
		Eigenvalues & Eigenvectors
		Diagonalization
		Markov chains
Geometry		Affine transformations
		Graph theory
		Voronoi diagrams
Functions	Trigonometric functions/equations	Trigonometric functions
	Modeling with real polynomials
	Inequalities
	Remainder/Factor theorem
Probability & Statistics	Bayes' Theorem	Bayes' Theorem
	Binomial thm for rational exp.
		Central Limit Thm
		Confidence interval

Complex Numbers	Complex plane	Complex plane
	Modulus and arguments	Modulus and arguments
	Geometry in C	Geometry in C
	Polar form	Polar form
	Euler's form
	De Moivre's theorem
Proof	Mathematical logic
	Basic proof techniques (deduction, equivalence, definitions, exhaustion, contrapositive, contradiction)
	Induction
	Principle of Mathematical Induction
Further fields to explore	Number theory, probability theory, calculus II, complex numbers, spherical geometry	Linear algebra, algebraic geometry (Affine/Euclidean), graph theory, calculus II