Other university, Information Technology , Mathematics-III (Differential Calculus) Syllabus

BSC 301 Mathematics-III (Differential Calculus)

Module 1 Lecture: 6 hrs.
Successive Differentiation, Leibnitz’s Theorem. Limit, Continuity and Differentiability of function for one
variable.
Module 2 Lecture: 8 hrs.
Limit, Continuity and Differentiability of function for several variables. Partial Derivatives, Euler’s
Theorem for Homogeneous functions, Total derivatives, Change of Variables. Maxima and Minima of
Several Variables. Methods of Lagrange Multipliers. Taylor’s and Maclaurin’s Theorem with remainders
of several variables.
Module 3 Lecture: 8 hrs.
Vector Calculus: Gradient, Divergence and Curl of a Vector and their Physical Interpretations, Vector
Identities. Directional Derivatives. Line, Surface and Volume integrals, Application of Green’s, Stokes and
Gauss Divergence Theorem (Without Proof).
Module 4 Lecture: 6 hrs.
First Order Ordinary Differential Equations: Exact, Linear and Bernoulli’s Equations, Euler’s Equations,
Equations not of First Degree: Equations Solvable for P, Equations Solvable for Y, Equations Solvable
for X and Clairaut’s Type.
Module 5 Lecture: 8 hrs.
Ordinary Differential Equations of Higher Orders: Second Order Linear Differential Equations with
Variable Coefficients, Method of Variation of Parameters, Cauchy-Euler Equation; Power Series
Solutions; Legendre Polynomials, Bessel Functions of the First Kind and their properties.
Module 6 Lecture: 6 hrs.
Partial Differential Equations – First Order: First Order Partial Differential Equations, Solutions of
First Order Linear and Non-Linear PDEs.