Representing function of one variables, Polynomial, Trigonometric, Exponential and Logarithmic functions, Range and domain of functions and their graphs.

Precise definition of Limits and Continuity, Limits at infinity, Continuity, Horizontal asymptotes, Vertical and Slant asymptotes.

Tangents and velocity, Rate of change, Review of Derivative, Differentiability of a function, Mean value theorem, Indeterminate forms and L-Hospital Rule.

Curve sketching, Review of maxima and minima of one variable, Optimization problems, Newton's method.

Review of Antiderivatives, Rectilinear motion, Indefinite integrals and Net change, Definite integral, The fundamental theorem of calculus, Improper integrals.

Areas between the curves, Volume of cylindrical cells, Approximate Integrations, Arc length, Area of surface of revolution.

Introduction, Introduction to first order equations separable equations, Linear equations, Second Order linear differential equations, Non homogenous linear equations, Method of undetermined coefficients.

Infinite Sequence and Series, Convergence tests and power series, Taylor's and Maclaurin's series.

Introduction, Applications, Dot product and cross Product, Equations of lines and Planes, Derivatives and integrals of vector functions, Arc length and curvature, Normal and binomial vectors, Motion in space.

Limit and Continuity, Partial Derivatives, Tangent planes, Maximum and minimum values, Multiple integrals.