Nonstandard analysis | Infinity | Calculus
In mathematics, nonstandard calculus is the modern application of infinitesimals, in the sense of nonstandard analysis, to infinitesimal calculus. It provides a rigorous justification for some arguments in calculus that were previously considered merely heuristic. Non-rigorous calculations with infinitesimals were widely used before Karl Weierstrass sought to replace them with the (ε, δ)-definition of limit starting in the 1870s. (See history of calculus.) For almost one hundred years thereafter, mathematicians such as Richard Courant viewed infinitesimals as being naive and vague or meaningless. Contrary to such views, Abraham Robinson showed in 1960 that infinitesimals are precise, clear, and meaningful, building upon work by Edwin Hewitt and Jerzy Łoś. According to Howard Keisler, "Robinson solved a three hundred year old problem by giving a precise treatment of infinitesimals. Robinson's achievement will probably rank as one of the major mathematical advances of the twentieth century." (Wikipedia).
Pre-Calculus - The vocabulary of linear functions and equations
This video will introduce you to a few of the terms that are commonly used with linear functions and equations. Pay close attention to how you can tell the difference between linear and non-linear functions. For more videos please visit http://www.mysecretmathtutor.com
From playlist Pre-Calculus
Euler's method for solving non-separable differential equation by approximation.
From playlist Advanced Calculus / Multivariable Calculus
Differentiating a Continued Fraction
More resources available at www.misterwootube.com
From playlist Differential Calculus (related content)
Transformation matrix with respect to a basis | Linear Algebra | Khan Academy
Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/linear-algebra/alternate-bases/change-of-basis/v/lin-alg-transformation-matrix-with-respect-to-a-basis Finding the transformation matrix with respect to a non-stan
From playlist Alternate coordinate systems (bases) | Linear Algebra | Khan Academy
Infinite Limits With Equal Exponents (Calculus)
#Calculus #Math #Engineering #tiktok #NicholasGKK #shorts
From playlist Calculus
Alternate basis transformation matrix example | Linear Algebra | Khan Academy
Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/linear-algebra/alternate-bases/change-of-basis/v/lin-alg-alternate-basis-tranformation-matrix-example Example of finding the transformation matrix for an alternate
From playlist Alternate coordinate systems (bases) | Linear Algebra | Khan Academy
Two Nonstandard Infinite Geometric Series (visual proof)
My previous wordless Wednesday video showing the sum of the powers of 1/7 generated some interesting questions about using the same technique for nonstandard geometric series. Here we include a short, animated visual proof demonstrating the infinite sum of the powers of 2/7 and 3/11; from
From playlist Geometric Sums
Pre-Calculus - Where is a function continuous
This video covers how you can tell if a function is continuous or not using an informal definition for continuity. Later in the video, we look at a function that is not continuous for all values, but is continuous for certain intervals. For more videos visit http://www.mysecretmathtutor.
From playlist Pre-Calculus
Changing Between Two Bases | Derivation + Example
We previously saw the "Change of Basis" formula between a nonstandard basis and the standard basis. In this video, we look at how to change between two different nonstandard bases. Indeed, we derive a single matrix, called the Change of Basis Matrix, that is simply the product of two other
From playlist Linear Algebra (Full Course)
Definition of a Surjective Function and a Function that is NOT Surjective
We define what it means for a function to be surjective and explain the intuition behind the definition. We then do an example where we show a function is not surjective. Surjective functions are also called onto functions. Useful Math Supplies https://amzn.to/3Y5TGcv My Recording Gear ht
From playlist Injective, Surjective, and Bijective Functions
Nernst equation | Redox reactions and electrochemistry | Chemistry | Khan Academy
Deriving a few different forms of the Nernst equation, the relationship between Gibbs free energy and reaction quotient Q. Watch the next lesson: https://www.khanacademy.org/science/chemistry/oxidation-reduction/cell-potentials-under-nonstandard-conditions/v/using-the-nernst-equation?utm
From playlist Redox reactions and electrochemistry | Chemistry | Khan Academy
Using the Nernst equation | Redox reactions and electrochemistry | Chemistry | Khan Academy
Using the Nernst equation to calculate the cell potential when concentrations are not standard conditions. Watch the next lesson: https://www.khanacademy.org/science/chemistry/oxidation-reduction/cell-potentials-under-nonstandard-conditions/v/concentration-cell?utm_source=YT&utm_medium=D
From playlist Redox reactions and electrochemistry | Chemistry | Khan Academy
Standard and Nonstandard Comparisons of Relative Trace Formulas - Yiannis Sakellaridis
Yiannis Sakellaridis Rutgers, The State University of New Jersey March 1, 2013 The trace formula has been the most powerful and mainstream tool in automorphic forms for proving instances of Langlands functoriality, including character relations. Its generalization, the relative trace formu
From playlist Mathematics
11_3_6 Continuity and Differentiablility
Prerequisites for continuity. What criteria need to be fulfilled to call a multivariable function continuous.
From playlist Advanced Calculus / Multivariable Calculus
A Nonstandard Geometric Series (visual proof)
This is a short, animated visual proof showing the sum of the infinite geometric series with first term 1/8 and ratio 1/2. #manim #math #mathshorts #mathvideo #trisect #trisectangle #impossible #geometry #chords #mtbos #manim #animation #theorem #pww #proofwithoutwords #visualpr
From playlist Proofs Without Words
Euler's method for estimating solution to non-separable first-order differential equations.
From playlist Advanced Calculus / Multivariable Calculus
Calculus - Continuous functions
This video will describe how calculus defines a continuous function using limits. Some examples are used to find where a function is continuous, and where it is not continuous. Remember to check that the value at c and the limit as x approaches c exist, and agree. For more videos please
From playlist Calculus
Find a Polynomial Given B-coordinates and a Nonstandard Basis
This video explains how to determine a polynomial given the B-coordinates and a nonstandard basis.
From playlist Transformations of General Vector Spaces
Continuity vs Partial Derivatives vs Differentiability | My Favorite Multivariable Function
In single variable calculus, a differentiable function is necessarily continuous (and thus conversely a discontinuous function is not differentiable). In multivariable calculus, you might expect a similar relationship with partial derivatives and continuity, but it turns out this is not th
Find the B-coordinates of a Vector Given Coordinates Relative to Standard Basis (R3)
This video explains how to find the standard basis coordinates of a vector given a nonstandard basis and nonstandard coordinates. https://mathispower4u.com
From playlist Vectors: Change of Basis