Derivative of vector valued functions, Velocity, Acceleration and related
problems, Scalar and Vector point functions.Definition Gradient,
Divergence, Curl- problems . Solenoidal and Irrotational vector fields.
Vector identities - div ( F A), curl ( F A),curl (grad F ), div (curl A).
Reduction formulae ∫ sinnx dx ∫cosnx dx ∫sinnxcosmxdx,, (m and n are
positive integers), evaluation of these integrals with standard limits (0 to л/2)
Solution of first order and first degree differential equations – Exact,
reducible to exact and Bernoulli‟s differential equations. Applicationsorthogonal trajectories in Cartesian and polar forms. Simple problems on
Newton‟s law of cooling.
Linear Algebra Rank of a matrix by elementary transformations, solution of
system of linear equations - Gauss- elimination method, Gauss- Jordan
method and Gauss-Seidel method. Rayleigh‟s power method to find the
largest Eigen value and the corresponding Eigen vector. Linear
transformation, diagonalisation of a square matrix, Quadratic forms,
reduction to Canonical form
On completion of this course students are able to
Use partial derivatives to calculate rates of change of multivariate
Analyse position, velocity and acceleration in two or three dimensions
using the calculus of vector valued functions
Recognize and solve first order ordinary differential equations, Newton‟s
law of cooling
Use matrices techniques for solving systems of linear equations in the
different areas of linear algebra.
DEPT OF MATHS, SJBIT