Scientific Computing

Master the fundamental numerical methods used in science, engineering, and applied mathematics. From error analysis to differential equations, build a solid foundation in computational mathematics.

Courses

90+

Practice Problems

50+

Algorithms

Free

Forever

SC-01

Error Analysis and Numerical Stability

Sources of error, absolute/relative error, significant digits, error propagation, machine precision, and numerical stability.

SC-02

Polynomial Interpolation

Lagrange interpolation, Newton's divided differences, Hermite interpolation, and error estimation.

SC-03

Spline Interpolation and Data Fitting

Cubic splines, piecewise interpolation, least squares fitting, and orthogonal polynomials.

SC-04

Numerical Integration

Newton-Cotes formulas, composite rules, Romberg integration, and Gaussian quadrature.

SC-05

Numerical Differentiation

Finite difference formulas, higher-order approximations, and interpolation-based methods.

SC-06

Direct Methods for Linear Systems

Gaussian elimination, LU decomposition, pivoting strategies, and condition numbers.

SC-07

Iterative Methods for Linear Systems

Jacobi, Gauss-Seidel, SOR methods, convergence analysis, and spectral radius.

SC-08

Eigenvalue Problems

Power method, inverse power method, Jacobi rotation, and Gershgorin circles.

SC-09

Nonlinear Equations and ODEs

Root-finding methods, Newton's method, Euler method, and Runge-Kutta methods.

Prerequisites

What you should know before starting

Single and multivariable calculus
Linear algebra basics (matrices, vectors)
Basic differential equations
Programming experience (any language)

Recommended Learning Path

Follow this sequence for optimal understanding

Error Analysis (SC-01) - Foundation for all numerical methods

Interpolation (SC-02, SC-03) - Approximating functions from data

Integration & Differentiation (SC-04, SC-05) - Numerical calculus

Linear Systems (SC-06, SC-07, SC-08) - Matrix computations

Nonlinear & ODEs (SC-09) - Advanced applications