To develop the student’s understanding of and problem solving skills in the areas of Pre-Calculus and Differential Calculus.

Syllabus

[Series] and tests for convergence. Real valued [functions] of a real variable, [limits, continuity and differentiation from first principles]. Physical and graphical interpretation of derivatives.
[Transcendental functions]: properties of trignometric, exponential, logarithmic and hyperbolic functions and their inverses.
[Vector Algebra]: coordinates, resolution of vectors, dot product and cross product. [Complex numbers]: Cartesian, polar and exponential forms. The algebra of complex numbers. The nth roots of unity.
[Differential Calculus: properties] of derivatives, product, quotient and chain rules. Derivatives of transcendental functions.
Applications of Differential Calculus to finding [maxima and minima, curve sketching, roots of equations] (Newton’s method), [undetermined forms] (L’Hopital’s Rule) and [Power Series] (Taylor and Maclaurin Series) of a univariate function.