The purpose of this course is to introduce a first year graduate level numerical methods course with an emphasis on applications in chemical engineering. The course will consist of three main topic areas relevant to chemical engineering, namely: 1) numerical integration, 2) optimization and 3) solution of partial differential equations. The skills developed for numerical integration are fundamental to many more complex problems in numerical methods relevant to chemical engineering. In this course, we will first focus on the solution of initial value problems (IVP) of ordinary differential equations (ODEs) as this is a building block for advanced numerical integration. Many chemical engineering problems require the solution of ODE-IVPs, most prominently, chemical reaction kinetics and simple fluid flow problems. Next, we will introduce basic concepts in numerical optimization. Numerical optimization is another fundamental tool utilized by numerical methods analysts and there are many chemical engineering problems that require the use of numerical optimization. Some examples include the prediction of the geometry of a molecule, optimization of plant processes and optimal control. Finally, we will explore numerical methods for solving PDEs. PDEs are fundamental to chemical engineering processes and in all but some very simple cases, numerical methods are required to arrive at approximate solutions. Classical examples in chemical engineering include fluid mechanics and heat and mass transfer.