GP115: Calculus I

Sets and their applications, real number system and its properties, method of mathematical induction, concept of a function, description and classification of functions.

Limits, indeterminate forms and L’Hospital’s rule, continuity and differentiability of real valued functions.

Intermediate value theorem, mean value theorem, leibnitz theorem, and tangent line approximation.

Local and global maximum and minimum, inflection points

Identify Riemann definition and find arc lengths, areas, volumes and moments using integration.

Partial derivatives and total differential, chain rule and higher order partial derivatives.

Curvature, radius and center of curvature.

Roots of unity and functions of complex variables, mapping of complex variables, derivatives of complex functions, Cauchy Reimann equation, holomorphic functions.

Vector equations of lines and planes in space, coplanar lines, shortest distance between a point (line, plane) and a line (plane), skew lines in the space, angels between planes and the equation of the intersection line, derivatives of vector valued function.

Define sequences and examples, monotonic sequence and bounded sequence, convergence, divergence and oscillation of a sequence.

Standard examples of infinite series, conditions for convergence, alternating series, absolute and conditional convergence.

Power series of function f(x); binomial expansion, radius and interval of convergence of power series, Maclaurin and Taylor series approximation.