Mathematics I (Calculus) Syllabus

Four ways of representing a function, Linear mathematical model, Polynomial, Rational,

Trigonometric, Exponential and Logarithmic functions, Combination of functions, Range and

domain of functions and their Graphs

Precise definition of Limit, 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, Volumes 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 homogeneous 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,

Derivative and integrals of vector functions, Arc length and curvature, Normal and binormal

vectors, Motion in space

Limit and continuity, Partial derivatives, Tangent planes, Maximum and minimum values,

Multiple integrals