Differential and Vector Calculus (Theory)

Definition of the limit of a function, Continuity, Types of discontinuities, Differentiability, Maxima and Minima.

Rolle ’s Theorem, Lagrange’s and Cauchy’s Mean Value Theorems, Taylor’s theorem (Lagrange’s form and Cauchy’s forms of remainder), Maclaurin’s theorem and expansions, Indeterminate forms.

Successive differentiation, nth derivatives of functions, Leibnitz theorem and its applications, Partial differentiation, First and higher order derivatives, Partial derivatives, Total derivative.

Differentiation of the homogeneous functions, Euler’s theorem, Taylor’s theorem for two variables, Maxima and Minima of functions of two variables, Lagrange’s multipliers for two variables

Vectors, Types of Vectors, Operations on Vectors, Addition of Vectors Properties of Operation of Addition, Subtraction, Properties of Operation of Subtraction Multiplication by a scalar, , Product of Two Vectors (Dot and Cross Product) & its properties.

Scalar and vector point function, Gradient, Directional derivatives, Divergence and curl of a vector point function.