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To complete the studentís grasp of the techniques and skills of one-variable calculus. It proceeds largely in the same non-rigorous spirit as the Leaving Certificate course, with the emphasis on problem-solving techniques.
Some time will be spent as needed on prerequisites, including Differentiation, the Fundamental Theorem of Calculus, the Mean Value theorem, Riemann Sums, the notion of continuity and continuous functions. Certain limits will also be emphasised, in particular those involving trigonometric functions. Some applications of integration: volume by parallel cross-sections, volume by the shell method. Elementary transcendental functions. Logs, exponentials, trigonometric functions and their inverses. Techniques of Integration: Parts, partial fractions, powers and products of sines and cosines. Numerical integration. Improper integrals.