This is a course on scientific computing for ordinary differential equations (ODEs) and partial differential equations (PDEs). It includes the construction, analysis and application of numerical methods for ODEs/PDEs. Objects of this course are:

• to motivate the need for efficient numerical methods for solving differential equations;
• to understand basic finite difference methods for partial differential equations;
• to analyze consistency, stability, and convergence of the finite difference methods;
• to solve system of linear equations numerically using direct and iterative methods;
• to implement numerical methods on the computer to solve partial differential equations arising from the sciences and engineering.