EM 1010: Calculus I

Functions and Limits, Continuity and Differentiability of real valued functions, Intermediate value theorem, Rolle’s theorem, Mean value theorem, Leibnitz theorem, and tangent line approximation, extreme values, integration of single variable function.

Monotonic and bounded sequences, Convergence, divergence and oscillation of a sequence, Series and their convergence, Real power series and their convergence, Maclaurin and Taylor series approximation.

Differential Equations as a mathematical model and Classification, Separable, Linear, Exact, Reducible forms.

Vectors, Determinant, Vector equations of lines and planes and their geometry, Parametric representation of curves in planes, Curvature, radius and center of curvature, Derivatives of vector valued function in parametric form.

Limit and continuity of functions of two and three variables, Partial derivatives and total differential, Chain rule and higher order partial derivatives.

Roots of unity and functions of complex variables, Mapping of complex variables, Derivatives of complex functions, Cauchy Riemann equation, Holomorphic functions, Harmonic functions.