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Unit - 1

Differential Calculus

Representation of Functions – Limit of a Function – Continuity – Derivatives – Differentiation Rules –Maxima and Minima of Functions of One Variable.

Unit - 2

Functions of Several Variables

Partial Differentiation – Homogeneous Functions and Euler’s Theorem – Total Derivative – Change of Variables – Jacobians – Partial Differentiation of Implicit Functions – Taylor’s Series for Functions of Two Variables – Maxima and Minima of Functions of Two Variables – Lagrange’s Method of Undetermined Multipliers.

Unit - 3

Integral Calculus

Definite and Indefinite Integrals – Substitution Rule – Techniques of Integration – Integration by Parts,

Trigonometric Integrals, Trigonometric Substitutions, Integration of Rational Functions by Partial Fraction,

Integration of Irrational Functions – Improper Integrals.

Unit - 4

Multiple Integrals

Double integrals – Change of Order of Integration – Double Integrals in Polar Coordinates – Area Enclosed by Plane Curves – Triple Integrals – Volume of Solids – Change of Variables in Double and Triple Integrals.

Unit - 5

Differential Equations

Higher Order Linear Differential Equations with Constant Coefficients – Method of Variation of Parameters – Homogeneous Equation of Euler’s and Legendre’s Type – System of Simultaneous Linear Differential Equations with Constant Coefficients – Method of Undetermined Coefficients.