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

[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.

Represent a given complex number in the Cartesian and polar forms; perform arithmetic operations with complex numbers. Given a real-valued function of a real variable, find its derivative from the definition and using tables combined with the product, quotient and chain rules. Given a real-valued function of a real variable, find its domain, maxima and minima, inflection points, sketch its curve, find the equation of the tangent line to its curve at a given point, evaluate its limit at a given point or at an infinity. Given a series, evaluate its sum or show that it diverges; given a power series, find its interval of convergence. Given a real-valued function of a real variable, find its Taylor and Maclaurin series. Perform arithmetic operations with vectors in 3-space and evaluate their dot products and cross products.

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Normal mathematics lectures. Students will have weekly homework (not for credit), a mid-term exam worth 30% and a final exam worth 70%.