Linear Algebra

• Matrix algebra,
• Systems of linear equation,
• eigen values and eigen vectors.

Calculus

• Functions of single variable, limit, continuity and differentiability,
• Mean value theorems,
• Evaluation of definite and improper integral,
• Partial derivatives,
• Total derivatives,
• Maxima and minima,
• Gradient, divergence and curl,
• Vector identities,
• Directional derivatives, line, surface and volume integrals,
• Theorems of Stokes, Gauss and Green.

Differential calculus

• Frist order linear and nonlinear equations,
• Higher order linear ODEs with constant coefficients,
• Cauchy and Euler equations,
• Initial and boundary value problems,
• Laplace transforms.
• Partial differential equations and separation of variables methods.

Numerical Methods

• Numerical solution of linear and nonlinear algebraic equations,
• Integration by trapezoidal and Simpson rule,
• Single and Multi-step methods for differential equations.