UNIT I DIFFERENTIAL CALCULUS

1.1 Representation of functions - Limit of a function - Continuity

1.2 Derivatives

1.3 Differentiation rules - Maxima and Minima of functions of one variable

UNIT II FUNCTIONS OF SEVERAL VARIABLES

2.1 Partial differentiation

2.2 Homogeneous functions and Euler’s theorem

2.3 Total derivative - Change of variables

2.4 Jacobians - Partial differentiation of implicit functions

2.5 Taylor’s series for functions of two variables

2.6 Maxima and minima of functions of two variables - Lagrange’s method of undetermined multipliers

UNIT III INTEGRAL CALCULUS

3.1 Definite and Indefinite integrals - Substitution rule

3.2 Techniques of Integration - Integration by parts - Trigonometric integrals - Trigonometric substitutions - Integration of rational functions by partial fraction - Integration of irrational functions - Improper integrals

UNIT IV MULTIPLE INTEGRALS

4.1 Double integrals

4.2 Change of order of integration-Double integrals in polar coordinates

4.3 Area enclosed by plane curves

4.4 Triple integrals - Volume of solids

4.5 Change of variables in double and triple integrals

UNIT V DIFFERENTIAL EQUATIONS

5.1 Higher order linear differential equations with constant coefficients - Method of variation of parameters

5.2 Homogeneous equation of Euler’s and Legendre’s type - system of simultaneous linear differential equations with constant coefficients - Method of undetermined coefficients