How to study Numerical Methods — Semester IV, Pokhara University BECE
What it covers
Solving engineering problems with computers: roots of equations, interpolation, numerical differentiation and integration, systems of linear equations, and numerical solution of differential equations.
Topics worth extra time
- Errors, and solving non-linear equations (bisection, Newton–Raphson, secant)
- Interpolation: Newton’s and Lagrange’s methods
- Numerical differentiation and integration (trapezoidal and Simpson’s rules)
- Solving linear systems (Gauss elimination, Gauss–Seidel, LU decomposition)
- Numerical solutions of ordinary differential equations (Euler, Runge–Kutta)
How to study it
Solve each method by hand on a small problem, then write a short program for it; the lab and the theory support each other. Understand when each method converges or fails, not only the formula.
In the exam
Present iterations in a table with enough decimal places, and state the stopping condition. Algorithm or flowchart questions are common, so prepare clean versions for the main methods.