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Sets and Functions: polynomials, rational functions, absolute value, root functions, exponential and logarithmic functions. Coordinate Geometry on the Plane. Average Rates of Change. Approximating Area under a Curve. Introduction to Limits. Slopes of Tangent Lines and Areas under a Curve. The Definite Integral. Derivatives and Anti-Derivatives. The Fundamental Theorem of Calculus. Further Integration Techniques: Integration by means of substitution, Integration by parts. Trigonometric Functions and their derivatives and anti-derivatives. Curve Sketching. Optimisation. Further Approximation Techniques: Taylor polynomials, Newton's Method.
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