MIT OpenCourseWare

Browse materialsMIT 18.335J · Spring 2019

Introduction to Numerical Methods

Subjects: Algebra · Linear Algebra · Mathematics

Art: Johannes Kepler, Konjukce Saturnu a Jupiteru Originál, 1596 · Public domain

Instructor: Prof. Steven G. Johnson
Term: Spring 2019
Level: Graduate
What's inside: 4 problem sets · 8 exams · 11 solutions · 27 other files · 17 web pages
Materials open: MIT OCW

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About this course

Source: MIT OpenCourseWare 18.335J Introduction to Numerical Methods, Spring 2019, Prof. Steven G. Johnson — original course page on ocw.mit.edu ↗. License: CC BY-NC-SA 4.0. Study order: MIT's own listing order, section by section. Taken from MIT's published course files, downloaded from ocw.mit.edu on September 23, 2026. How RedLectern is built.

Materials are grouped the way MIT organized them. A verified, course-wide order has not been established here.

Has MIT solutions 11 files in this course are named by MIT as solutions.

Before you start

Prerequisites are not listed here. Check MIT's own syllabus for this course.

This course’s cited books, in our reading lists: Nonlinear Programming · Numerical Linear Algebra

How this course was organized

What's here, and what isn't

MIT's own materials here did not support a verified, course-wide order, so they are grouped by section instead.

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MIT's page format for this item wasn't recognized clearly enough to place it safely. (100 items)
Referenced in a table, but without MIT's own verified order, so it isn't used to claim a sequence. (2 items)

Materials by section

Grouped by section, as MIT organized them. Not sequenced or ordered.

Week 1

Week 2

Week 3

18.335J (S19) Lecture 6 - Modern differential equations solver softwarePDF Download

Week 4

Week 5

18.335J (S19) Lecture 12 - Experiments with Cache-Oblivious Matrix MultiplicationPDF Download

Week 6

Week 7

Week 9

18 files

Week 10

18.335J (S19) Lecture 27 - Adjoint methods and sensitivity analysis for recurrence relationsPDF Download

Week 11

18.335J (S19) Lecture 30 - Quasi-Newton optimizationPDF Download

Week 12

Week 14

Resource Index

MIT OpenCourseWare, Prof. Steven G. Johnson, 18.335J Introduction to Numerical Methods, Spring 2019.

License: CC BY-NC-SA 4.0 · Edition: Spring 2019 · Open the original course on OCW ↗

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Introduction to Numerical Methods

Before you start

What's here, and what isn't

Not included here

Materials by section

Week 1

Week 2

Week 3

Week 4

Week 5

Week 6

Week 7

Week 9

Week 10

Week 11

Week 12

Week 14

Resource Index

Lecture 1: Course overview, Newton’s method for root-finding

Lecture 2: Floating-point arithmetic

Lecture 3: Floating-point summation and backwards stability

Lecture 4: Norms on vector spaces

Lecture 5: Condition numbers

Lecture 6: Numerical methods for ordinary differential equations

Lecture 7: The SVD, its applications, and condition numbers

Lecture 8: Linear regression and the generalized SVD

Lecture 9: Solving the normal equations by QR and Gram-Schmidt

Lecture 10: Modified Gram-Schmidt and Householder QR

Lecture 11: Matrix operations, caches, and blocking

Lecture 12: Cache-oblivious algorithms and spatial locality

Lecture 13: LU factorization and partial pivoting

Lecture 14: Cholesky factorization and other specialized solvers. Eigenproblems and Schur factorizations

Lecture 15: Eigensolver algorithms: Companion matrices, ill-conditioning, and Hessenberg factorization

Lecture 16: The power method and the QR algorithm

Lecture 17: Shifted QR and Rayleigh quotients

Lecture 18: Krylov methods and the Arnoldi algorithm

Lecture 19: Arnoldi and Lanczos with restarting

Lecture 20: The GMRES algorithm and convergence of GMRES and Arnoldi

Lecture 21: Preconditioning techniques. The conjugate-gradient method

Lecture 22: Convergence of conjugate gradient

Lecture 23: Biconjugate gradient algorithms

Lecture 24: Sparse-direct solvers

Lecture 25: Overview of optimization algorithms

Lecture 26: Adjoint methods

Lecture 27: Adjoint methods for eigenproblems and recurrence relations

Lecture 28: Trust-regions methods and the CCSA algorithm

Lecture 29: Lagrange dual problems

Lecture 30: Quasi-Newton methods and the BFGS algorithm

Lecture 31: Derivation of the BFGS update

Lecture 32: Derivative-free optimization by linear and quadratic approximations

Lecture 33: Numerical integration and the convergence of the trapezoidal rule

Lecture 34: Clenshaw-Curtis quadrature

Lecture 35: Chebyshev approximation

Lecture 36: Integration with weight functions, and Gaussian quadrature

Lecture 37: Adaptive and multidimensional quadrature

Lecture 38: The discrete Fourier transform (DFT) and FFT algorithms

Lecture 39: FFT algorithms and FFTW