The course revises and extends Matriculation and STPM topics such as differentiation and integration towards hyperbolic and trigonometric inverses. Applications in computing arc length and area of surfaces of revolution are also included. Other topics covered are improper integrals, parametric equations, polar coordinates, and multivariable functions. This later topic serves as an introduction to three dimensional calculus which students will learn in Mathematical Methods II. The chapter will merely devoted to sketching surfaces and finding limits of two variable functions. It is hoped that upon completion of the course, students should have acquired some firm basic tools to pursue further mathematics.
- Convert polar coordinates to Cartesian and vice versa, convert parametric and polar equations to Cartesian and vice versa, and sketch parametric and polar equations.
- Sketch graphs of hyperbolic and trigonometric inverses, and prove some identities related to these functions.
- Find derivatives and anti-derivatives of hyperbolic, trigonometric inverses and combination of them using appropriate techniques.
- Find arc length and area of surfaces of revolutions via integration using the formula in Cartesian, parametric and polar form.
- Determine convergence and divergence of improper integrals by direct computation.
- Sketch graphs of two variable functions and determine continuity of two variable functions at a point via computation of limits.
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