Special Topics: Numerical Computing Course ID 15669 Description Many problems in science, engineering, and computer graphics cannot be solved exactly. Numerical computing provides methods to approximate these solutions using computational techniques. It combines mathematics and programming to solve real-world problems such as simulations, optimization, and data analysis. The course begins with a review of key mathematical concepts like vector spaces, matrices, and calculus. We then explore how numbers are represented on computers, the types of errors that can occur, and strategies to handle them. Core topics include solving linear and nonlinear systems, eigenvalue problems, optimization, and techniques such as LU decomposition, QR factorization, and singular value decomposition (SVD). We will also cover iterative methods for large systems, interpolation, numerical differentiation, integration, and both ordinary and partial differential equations. Students will gain hands-on experience implementing algorithms and learn to balance accuracy, stability, and efficiency in computational solutions. Key Topics numerical representation; error analysis; interpolation; numerical differentiation; numerical integration; linear and nonlinear systems; matrix factorization; numerical optimization; numerical solution of ODEs and PDEs; Required Background Knowledge Strong Math and Programming Skills Course Relevance This course is for graduate students. Undergraduates should enroll in 15-369. Learning Resources https://people.csail.mit.edu/jsolomon/share/book/numerical_book.pdf Assessment Structure Bi-weekly assignments: 100% Extra Time Commitment No extra time commitments.
