An introduction to numerical methods for the solution of mechanical engineering problems. Topics of interest include: Introduction to mathematical modeling and the numerical solution of engineering problems,  Numerical errors: Computer representation of real numbers. Accuracy, precision, and round-off error, Taylor series and truncation error. Root finding: Bisection and Newton-Raphson methods. Convergence. Curve fitting: Least-squares regression, polynomial interpolation, piecewise cubic splines. Numerical integration: Trapezoidal rule and Simpson’s 1/3 rule. Order of convergence. Ordinary differential equations: Euler’s method, Runge-Kutta methods (second and fourth order). Order of convergence. Initial value problems. Boundary value problems. Applications of numerical methods to engineering problems using programming languages. Additional topics may be covered including introduction to optimization algorithms, introduction to scientific computing etc.