MIT OpenCourseWare: Free Courses from the institute

MIT OpenCourseWare: Free Courses from the institute

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MIT OpenCourseWare: Free Courses from the institute episodes

  • Review for 18.100B Real Analysis Midterm

    MIT 18.100B Real Analysis, Spring 2025
    Instructor: Tobias Holck Colding
    View the complete course: https://ocw.mit.edu/courses/18-100b-real-analysis-spring-2025/
    YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP62Ie7F_tTAhhXoX5_Cl8meG

    Uploaded 02-09-25

    We review the content presented to date in preparation for the midterm exam.

    License: Creative Commons BY-NC-SA
    More information at https://ocw.mit.edu/terms
    More courses at https://ocw.mit.edu
    Support OCW at http://ow.ly/a1If50zVRlQ

    We encourage constructive comments and discussion on OCW’s YouTube and other social media channels. Personal attacks, hate speech, trolling, and inappropriate comments are not allowed and may be removed. More details at https://ocw.mit.edu/comments.



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    1 hr 24 min
  • Lecture 25: Habituation, Novelty Responses

    MIT 9.01 Neuroscience and Behavior, Fall 2003
    Instructor: Prof. Gerald E. Schneider
    View the complete course: http://ocw.mit.edu/courses/brain-and-cognitive-sciences/9-01-neuroscience-and-behavior-fall-2003
    YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP63U7FmbKD9KClb-94dyPJim

    Uploaded 16-05-22

    Habituation, Novelty Responses

    License: Creative Commons BY-NC-SA
    More information at https://ocw.mit.edu/terms
    More courses at https://ocw.mit.edu
    Support OCW at http://ow.ly/a1If50zVRlQ

    We encourage constructive comments and discussion on OCW’s YouTube and other social media channels. Personal attacks, hate speech, trolling, and inappropriate comments are not allowed and may be removed. More details at https://ocw.mit.edu/comments.

    Speakers: Prof. Gerald E. Schneider



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    54 min
  • Lecture 19: Fundamental Theorem of Calculus

    MIT 18.100B Real Analysis, Spring 2025
    Instructor: Tobias Holck Colding
    View the complete course: https://ocw.mit.edu/courses/18-100b-real-analysis-spring-2025/
    YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP62Ie7F_tTAhhXoX5_Cl8meG

    Uploaded 02-09-25

    We will show the key link between differentiation and integrals: the fundamental theorem of calculus. In fact, we give two versions of this key theorem. We will also discuss improper integrals as well as integrals of unbounded functions.

    License: Creative Commons BY-NC-SA
    More information at https://ocw.mit.edu/terms
    More courses at https://ocw.mit.edu
    Support OCW at http://ow.ly/a1If50zVRlQ

    We encourage constructive comments and discussion on OCW’s YouTube and other social media channels. Personal attacks, hate speech, trolling, and inappropriate comments are not allowed and may be removed. More details at https://ocw.mit.edu/comments.



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    1 hr 28 min
  • Lecture 19: Motor System, 1

    MIT 9.01 Neuroscience and Behavior, Fall 2003
    Instructor: Prof. Gerald E. Schneider
    View the complete course: http://ocw.mit.edu/courses/brain-and-cognitive-sciences/9-01-neuroscience-and-behavior-fall-2003
    YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP63U7FmbKD9KClb-94dyPJim

    Uploaded 16-05-22

    Motor System, 1

    License: Creative Commons BY-NC-SA
    More information at https://ocw.mit.edu/terms
    More courses at https://ocw.mit.edu
    Support OCW at http://ow.ly/a1If50zVRlQ

    We encourage constructive comments and discussion on OCW’s YouTube and other social media channels. Personal attacks, hate speech, trolling, and inappropriate comments are not allowed and may be removed. More details at https://ocw.mit.edu/comments.

    Speakers: Prof. Gerald E. Schneider



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    51 min
  • Lecture 16: Rolle’s Theorem; Mean Theorem; L’Hôpital’s Rule; Taylor Expansion

    MIT 18.100B Real Analysis, Spring 2025
    Instructor: Tobias Holck Colding
    View the complete course: https://ocw.mit.edu/courses/18-100b-real-analysis-spring-2025/
    YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP62Ie7F_tTAhhXoX5_Cl8meG

    Uploaded 02-09-25

    In the lecture we show a second, more elaborate mean value theorem that involves two functions. This is the Cauchy mean value theorem and we use it to the show the two versions of L'Hôpital's rule for limits of quotients as well as the important theorem about Taylor expansion.

    License: Creative Commons BY-NC-SA
    More information at https://ocw.mit.edu/terms
    More courses at https://ocw.mit.edu
    Support OCW at http://ow.ly/a1If50zVRlQ

    We encourage constructive comments and discussion on OCW’s YouTube and other social media channels. Personal attacks, hate speech, trolling, and inappropriate comments are not allowed and may be removed. More details at https://ocw.mit.edu/comments.



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    1 hr 25 min
  • Lecture 23: Rhythms of Activity; Sleep and Waking

    MIT 9.01 Neuroscience and Behavior, Fall 2003
    Instructor: Prof. Gerald E. Schneider
    View the complete course: http://ocw.mit.edu/courses/brain-and-cognitive-sciences/9-01-neuroscience-and-behavior-fall-2003
    YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP63U7FmbKD9KClb-94dyPJim

    Uploaded 16-05-22

    Rhythms of Activity; Sleep and Waking

    License: Creative Commons BY-NC-SA
    More information at https://ocw.mit.edu/terms
    More courses at https://ocw.mit.edu
    Support OCW at http://ow.ly/a1If50zVRlQ

    We encourage constructive comments and discussion on OCW’s YouTube and other social media channels. Personal attacks, hate speech, trolling, and inappropriate comments are not allowed and may be removed. More details at https://ocw.mit.edu/comments.

    Speakers: Prof. Gerald E. Schneider



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    52 min
  • Lecture 12: Convergence in Metric Spaces; Operations on Sets

    MIT 18.100B Real Analysis, Spring 2025
    Instructor: Tobias Holck Colding
    View the complete course: https://ocw.mit.edu/courses/18-100b-real-analysis-spring-2025/
    YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP62Ie7F_tTAhhXoX5_Cl8meG

    Uploaded 02-09-25

    We continue our discussion of metric spaces and see that even more concepts that we have studied on the real line have counterparts in metric spaces. Those include, in addition to, sequences, convergence and Cauchy sequence also a ball, a bounded set, as well as open and closed subsets.

    License: Creative Commons BY-NC-SA
    More information at https://ocw.mit.edu/terms
    More courses at https://ocw.mit.edu
    Support OCW at http://ow.ly/a1If50zVRlQ

    We encourage constructive comments and discussion on OCW’s YouTube and other social media channels. Personal attacks, hate speech, trolling, and inappropriate comments are not allowed and may be removed. More details at https://ocw.mit.edu/comments.



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    1 hr 29 min
  • Lecture 14: Midbrain and Forebrain

    MIT 9.01 Neuroscience and Behavior, Fall 2003
    Instructor: Prof. Gerald E. Schneider
    View the complete course: http://ocw.mit.edu/courses/brain-and-cognitive-sciences/9-01-neuroscience-and-behavior-fall-2003
    YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP63U7FmbKD9KClb-94dyPJim

    Uploaded 16-05-22

    Midbrain and Forebrain

    License: Creative Commons BY-NC-SA
    More information at https://ocw.mit.edu/terms
    More courses at https://ocw.mit.edu
    Support OCW at http://ow.ly/a1If50zVRlQ

    We encourage constructive comments and discussion on OCW’s YouTube and other social media channels. Personal attacks, hate speech, trolling, and inappropriate comments are not allowed and may be removed. More details at https://ocw.mit.edu/comments.

    Speakers: Prof. Gerald E. Schneider



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    42 min
  • Lecture 14: Sequential Compactness; Bolzano–Weierstrass Theorem in a Metric Space

    MIT 18.100B Real Analysis, Spring 2025
    Instructor: Tobias Holck Colding
    View the complete course: https://ocw.mit.edu/courses/18-100b-real-analysis-spring-2025/
    YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP62Ie7F_tTAhhXoX5_Cl8meG

    Uploaded 02-09-25

    We show the Bolzano-Weierstrass theorem in a metric space. This theorem states that for a metric space, a sequence contained in a compact subset has a convergent subsequence.

    License: Creative Commons BY-NC-SA
    More information at https://ocw.mit.edu/terms
    More courses at https://ocw.mit.edu
    Support OCW at http://ow.ly/a1If50zVRlQ

    We encourage constructive comments and discussion on OCW’s YouTube and other social media channels. Personal attacks, hate speech, trolling, and inappropriate comments are not allowed and may be removed. More details at https://ocw.mit.edu/comments.



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    1 hr 31 min
  • Lecture 15: Development of CNS, Introduction

    MIT 9.01 Neuroscience and Behavior, Fall 2003
    Instructor: Prof. Gerald E. Schneider
    View the complete course: http://ocw.mit.edu/courses/brain-and-cognitive-sciences/9-01-neuroscience-and-behavior-fall-2003
    YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP63U7FmbKD9KClb-94dyPJim

    Uploaded 16-05-22

    Development of CNS, Introduction

    License: Creative Commons BY-NC-SA
    More information at https://ocw.mit.edu/terms
    More courses at https://ocw.mit.edu
    Support OCW at http://ow.ly/a1If50zVRlQ

    We encourage constructive comments and discussion on OCW’s YouTube and other social media channels. Personal attacks, hate speech, trolling, and inappropriate comments are not allowed and may be removed. More details at https://ocw.mit.edu/comments.

    Speakers: Prof. Gerald E. Schneider



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    38 min

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A free and open online publication of educational material from thousands of MIT courses, covering the entire MIT curriculum, ranging from introductory to the most advanced graduate courses. On the…