Finding Derivatives Using the Limit Definition
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From playlist Differentiation
Epsilon delta limit (Example 3): Infinite limit at a point
This is the continuation of the epsilon-delta series! You can find Examples 1 and 2 on blackpenredpen's channel. Here I use an epsilon-delta argument to calculate an infinite limit, and at the same time I'm showing you how to calculate a right-hand-side limit. Enjoy!
From playlist Calculus
Calculus 3.03f - Derivative Example 6
Another of example of finding a derivative using the definition of the derivative.
From playlist Calculus Ch 3 - Derivatives
Delta-Star is a polyhedral object which I invented in 1996. The type of Delta-Star corresponds to Deltahedrons. It expands and shrinks.
From playlist Handmade geometric toys
Math 131 111416 Sequences of Functions: Pointwise and Uniform Convergence
Definition of pointwise convergence. Examples, nonexamples. Pointwise convergence does not preserve continuity, differentiability, or integrability, or commute with differentiation or integration. Uniform convergence. Cauchy criterion for uniform convergence. Weierstrass M-test to imp
From playlist Course 7: (Rudin's) Principles of Mathematical Analysis
Calculus 3.03g - Derivative Example 7
Another example of finding a derivative.
From playlist Calculus Ch 3 - Derivatives
Lecture: Higher-order Accuracy Schemes for Differentiation and Integration
The accuracy of the differentiation approximations is considered and new schemes are developed to lower the error. Integration is also introduced as a numerical algorithm.
From playlist Beginning Scientific Computing
Calculus - Find the limit of a function using epsilon and delta
This video shows how to use epsilon and delta to prove that the limit of a function is a certain value. This particular video uses a linear function to highlight the process and make it easier to understand. Later videos take care of more complicated functions and using epsilon and delta
From playlist Calculus
PHYS 201 | Young's Double Slit 5, the Delta
The physics of an interference problem (paths, reflections) shows up in delta, which we treat in more detail here.
From playlist PHYS 201 | Interference
Lecture 14: Limits of Functions in Terms of Sequences and Continuity
MIT 18.100A Real Analysis, Fall 2020 Instructor: Dr. Casey Rodriguez View the complete course: http://ocw.mit.edu/courses/18-100a-real-analysis-fall-2020/ YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP61O7HkcF7UImpM0cR_L2gSw How are limits of functions and limits of s
From playlist MIT 18.100A Real Analysis, Fall 2020
Math 131 Fall 2018 120318 Equicontinuity and Uniform Convergence
Review of previous results. Equicontinuity. Exercise: finite set of uniformly continuous functions is equicontinuous. A uniformly convergent sequence of continuous functions on a compact set is equicontinuous. Theorem of Ascoli-Arzela: a pointwise bounded sequence of equicontinuous fun
From playlist Course 7: (Rudin's) Principles of Mathematical Analysis (Fall 2018)
Lecture 25: Power Series and the Weierstrass Approximation Theorem
MIT 18.100A Real Analysis, Fall 2020 Instructor: Dr. Casey Rodriguez View the complete course: http://ocw.mit.edu/courses/18-100a-real-analysis-fall-2020/ YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP61O7HkcF7UImpM0cR_L2gSw We return to the study of power series as w
From playlist MIT 18.100A Real Analysis, Fall 2020
Lecture 15: The Continuity of Sine and Cosine and the Many Discontinuities of Dirichlet's Function
MIT 18.100A Real Analysis, Fall 2020 Instructor: Dr. Casey Rodriguez View the complete course: http://ocw.mit.edu/courses/18-100a-real-analysis-fall-2020/ YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP61O7HkcF7UImpM0cR_L2gSw We wrap up our discussion of cluster points
From playlist MIT 18.100A Real Analysis, Fall 2020
Lecture 13: Limits of Functions
MIT 18.100A Real Analysis, Fall 2020 Instructor: Dr. Casey Rodriguez View the complete course: http://ocw.mit.edu/courses/18-100a-real-analysis-fall-2020/ YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP61O7HkcF7UImpM0cR_L2gSw We begin to discuss limits of functions, in
From playlist MIT 18.100A Real Analysis, Fall 2020
Math 131 113016 Heading Towards Ascoli-Arzela
Pointwise bounded sequence of functions on a countable set has a pointwise convergent subsequence (sketch). Remark: uniformly bounded, pointwise convergent sequence on a compact set does not imply existence of a uniformly convergent subsequence. Equicontinuity. Remark: finite collection
From playlist Course 7: (Rudin's) Principles of Mathematical Analysis
Math 101 Fall 2017 111517 Continuity Part 2
Recall: two definitions of continuity at a point (sequence definition, epsilon-delta definition). Theorem: the definitions are equivalent. Example of showing that a (quadratic) function is continuous, using both definitions.
From playlist Course 6: Introduction to Analysis (Fall 2017)
Math 131 Spring 2022 042522 Stone Weierstrass Theorem. Introduction to analytic functions.
Stone-Weierstrass theorem. Statement. Strategy of proof: use of "approximation of the identity." Proof: construction of the approximation of the identity. Construction of the sequence of polynomials. Demonstrating that the polynomials converge uniformly to the original function. New
From playlist Math 131 Spring 2022 Principles of Mathematical Analysis (Rudin)
Connecting Function Limits and Sequence Limits | Real Analysis
We prove the limit of a function f as x approaches c is L if and only if the sequence of images of a_n converges to L for all sequences a_n in the domain of f where each a_n is not equal to c. Our bidirectional proof will begin with a direct proof, using the epsilon delta definition of the
From playlist Real Analysis
Lec 10 | MIT Finite Element Procedures for Solids and Structures, Nonlinear Analysis
Lecture 10: Solution of Nonlinear Static FE Equations I Instructor: Klaus-Jürgen Bathe View the complete course: http://ocw.mit.edu/RES2-002S10 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu
From playlist MIT Nonlinear Finite Element Analysis
Delta-Star is a polyhedral object which I invented in 1996. The type of Delta-Star corresponds to Deltahedrons. It expands and shrinks. Especially highly symmetric tetrahedron,octahedron,icosahedron types and hexahedron,decahedron types can transform smoothly.
From playlist Handmade geometric toys