Section 1: Engineering Mathematics

• Linear Algebra:
  • Vector space, basis, linear dependence and independence, matrix algebra, Eigen values and eigen vectors, rank, solution of linear equations- existence and uniqueness.
• Calculus:
  • Mean value theorems, theorems of integral calculus, evaluation of definite and improper integrals, partial derivatives, maxima and minima, multiple integrals, line, surface and volume integrals, Taylor series.
• Differential Equations:
  • First order equations (linear and nonlinear), higher order linear differential equations, Cauchy's and Euler's equations, methods of solution using a variation of parameters, complementary function and particular integral, partial differential equations, variable separable method, initial and boundary value problems.
• Vector Analysis:
  • Vectors in plane and space, vector operations, gradient, divergence and curl, Gauss's, Green's and Stokes' theorems.
• Numerical Ability: Numerical computation, estimation, reasoning, and data interpretation.