The Basics
	Numbers
	Sets
	Other Important Sets
	Functions
	Parsing Formulas
	Inverse Functions
Limits
	Drawing Tangents and a First Limit
	Another Limit and Computing Velocity
	The Limit of a Function
	Calculating Limits with Limit Laws
	Limits at Infinity
	Continuity
	(Optional) — Making the Informal a Little More Formal
	(Optional) — Making Infinite Limits a Little More Formal
	(Optional) — Proving the Arithmetic of Limits
Derivatives
	Revisiting Tangent Lines
	Definition of the Derivative
	Interpretations of the Derivative
	Arithmetic of Derivatives - a Differentiation Toolbox
	Proofs of the Arithmetic of Derivatives
	Using the Arithmetic of Derivatives – Examples
	Derivatives of Exponential Functions
	Derivatives of Trigonometric Functions
	One More Tool – the Chain Rule
	The Natural Logarithm
	Implicit Differentiation
	Inverse Trigonometric Functions
	The Mean Value Theorem
	Higher Order Derivatives
	(Optional) — Is limxcf'(x) Equal to f'(c)?
Applications of Derivatives
	Velocity and Acceleration
	Related Rates
	Exponential Growth and Decay — a First Look at Differential Equations
		Carbon Dating
		Newton's Law of Cooling
		Population Growth
	Approximating Functions Near a Specified Point — Taylor Polynomials
		Zeroth Approximation — the Constant Approximation
		First Approximation — the Linear approximation
		Second Approximation — the Quadratic Approximation
		Still Better Approximations — Taylor Polynomials
		Some Examples
		Estimating Change and x, y Notation
		Further Examples
		The Error in the Taylor Polynomial Approximations
		(Optional) — Derivation of the Error Formulae
	Optimisation
		Local and Global Maxima and Minima
		Finding Global Maxima and Minima
		Max/Min Examples
	Sketching Graphs
		Domain, Intercepts and Asymptotes
		First Derivative — Increasing or Decreasing
		Second Derivative — Concavity
		Symmetries
		A Checklist for Sketching
		Sketching Examples
	L'Hôpital's Rule and Indeterminate Forms
		Standard Examples
		Variations
Towards Integral Calculus
	Introduction to Antiderivatives
High School Material
	Similar Triangles
	Pythagoras
	Trigonometry — Definitions
	Radians, Arcs and Sectors
	Trigonometry — Graphs
	Trigonometry — Special Triangles
	Trigonometry — Simple Identities
	Trigonometry — Add and Subtract Angles
	Inverse Trigonometric Functions
	Areas
	Volumes
	Powers
	Logarithms
	Highschool Material You Should be Able to Derive
Origin of Trig, Area and Volume Formulas
	Theorems about Triangles
		Thales' Theorem
		Pythagoras
	Trigonometry
		Angles — Radians vs Degrees
		Trig Function Definitions
		Important Triangles
		Some More Simple Identities
		Identities — Adding Angles
		Identities — Double-angle Formulas
		Identities — Extras
	Inverse Trigonometric Functions
	Cosine and Sine Laws
		Cosine Law or Law of Cosines
		Sine Law or Law of Sines
	Circles, cones and spheres
		Where Does the Formula for the Area of a Circle Come From?
		Where Do These Volume Formulas Come From?
Root Finding
	Newton's Method
	The Error Behaviour of Newton's Method
	The false position (regula falsi) method
	The secant method
	The Error Behaviour of the Secant Method