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Function of One Variable

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

Limits and Continuity

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

Derivatives

Tangents and velocity Rate of change Review of derivative Differentiability of a function Mean value theorem Indeterminate forms and L’Hospital rule

Applications of Derivatives

Curve sketching Review of maxima and minima of one variable Optimization problems Newton’s method

Antiderivatives

Review of antiderivatives Rectilinear motion Indefinite integrals and Net change Definite integral The Fundamental theorem of calculus Improper integrals

Applications of Antiderivatives

Areas between the curves Volumes of cylindrical cells Approximate Integrations Arc length Area of surface of revolution

Ordinary Differential Equations

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

Infinite sequence and series Convergence tests and power series Taylor’s and Maclaurin’s series

Plane and Space Vectors

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

Partial Derivatives and Multiple Integrals

Limit and continuity Partial derivatives Tangent planes Maximum and minimum values Multiple integrals