A basic introduction to optimization methods for engineering students which is often taught as part of an undergraduate-level engineering numerical methods class. The material covered here is at that level, and includes one-dimensional optimization using Newton's and golden-search methods, multi-dimensional unconstrained optimization using direct and gradient methods, and constrained optimization using Lagrange multipliers. Students should have basic computer programming skills using a language such as C, C++, Fortran90, MATLAB, or Python, and have a basic knowledge of multivariable calculus and linear algebra. Course notes and codes (written in Fortran90) are available for download.