3Blue1Brown
Vectors, What Even Are They? | Essence of Linear Algebra, Chapter 1
Take a look at vectors as geometric objects and then as an algebraic concept. The second video in a series of 15 introduces the vector using three perspectives: the physics, computer science, and mathematical. The resource shows the...
3Blue1Brown
Snell's Law Proof Using Springs
Does light always travel in a straight line? The narrator of a short video discusses the path light travels when going between different mediums and points out that light will want to travel on the path that minimizes the travel time....
3Blue1Brown
Higher Order Derivatives | Footnote, Essence of Calculus
Take the derivative. Then repeat. Scholars learn about higher order derivatives in the 10th video of an 11-part series. They see how the second derivative connects to physics concepts such as acceleration.
3Blue1Brown
Integration and the Fundamental Theorem of Calculus | Essence of Calculus, Chapter 8
Integrate a great resource into your lesson plans. The eighth video in an 11-part series explains integration and the relationship between derivatives and integrals. The relationship between a car's velocity and its travel distance...
3Blue1Brown
Limits | Essence of Calculus, Chapter 7
There's no limit on the importance of the limit in calculus. Scholars learn the formal definition of derivative and the epsilon-delta definition of limit by watching a video. They also listen to an explanation of l'Hospital's Rule.
3Blue1Brown
Derivatives of Exponentials | Essence of Calculus, Chapter 5
See why exponential functions are special. Viewers learn how the derivatives of exponential functions are proportional to their original functions. They see that e^x is a special case where the constant of proportionality is one.
3Blue1Brown
Derivative Formulas Through Geometry | Essence of Calculus, Chapter 3
Geometry to the rescue. By watching a video, scholars see how geometric concepts help explain derivative formulas: areas of rectangles and volumes of rectangular prisms for the Power Rule and similarity and trig ratios for the Sine Rule.
3Blue1Brown
Essence of Calculus, Chapter 1
Dive into the essence of calculus. The first installment of an 11-part playlist introduces the video series by looking at the area of a circle and the area under curves. The narrator explains how to look at calculus as taking a hard...
3Blue1Brown
Taylor Series | Essence of Calculus, Chapter 10
Sometimes close enough is just perfect. The last video in a series of 11 explores the Taylor series and its connection to derivatives. It shows the process for finding Taylor series approximations for y = sin x and for y = e^x.
3Blue1Brown
What Does Area Have to Do with Slope? | Essence of Calculus, Chapter 9
It seems like area and slope wouldn't have any connection. Here is a video that explains how to find the average value of a function over an interval. It connects the area under a curve to the slope of the antiderivative curve.
3Blue1Brown
Implicit Differentiation, What's Going on Here? | Essence of Calculus, Chapter 6
Teach implicit differentiation explicitly. An engaging video explains implicit differentiation to viewers. It describes how small changes in x and y can be thought of as contributing to the derivative dy/dx. This is the sixth video in a...
3Blue1Brown
Visualizing the Chain Rule and Product Rule | Essence of Calculus, Chapter 4
Take a look at the product rule and chain rule through the eyes of geometry. The fourth video in an 11-part series continues to explore derivative rules using geometry. An area model and a set of number lines help viewers...
3Blue1Brown
The Paradox of the Derivative | Essence of Calculus, Chapter 2
It turns out that "instantaneous rate of change" isn't an accurate representation of the derivative. Viewers of the second video in a series of 11 learn about the concept of the derivative, from the limit of a difference quotient to the...
3Blue1Brown
Cross Products | Essence of Linear Algebra, Chapter 8
Equate the area of a parallelogram with the magnitude. The 11th installment in a 15-video series introduces the concept of the cross product of two vectors. The presentation makes the geometric connection between the cross product, the...
3Blue1Brown
Dot Products and Duality | Essence of Linear Algebra, Chapter 7
The dot product of two matrices is a number on the number line, its transformation. The resource presents the dot product as a linear transformation from two dimensions to one dimension. The video uses the numerical and graphical...
3Blue1Brown
Nonsquare Matrices as Transformations Between Dimensions | Essence of Linear Algebra, Footnote
But what happens if the matrix is not square? The ninth video in a series of 15 serves as a footnote to discuss non-square matrices. The resource presents them as transformations between two and three dimensions. The presentation...
3Blue1Brown
Inverse Matrices, Column Space and Null Space | Essence of Linear Algebra, Chapter 6
Determine the geometric representation to the solution of a system of linear equations. The resource shows how scholars can represent a system of linear equations as a linear transformation. The video discusses using an inverse...
3Blue1Brown
The Determinant | Essence of Linear Algebra, Chapter 5
Determine how much a linear transformation alters area. The seventh segment in a series of 15 makes the connection between the determinant and the scale factor of areas during a linear transformation. The video goes on to explain the...
3Blue1Brown
Three-dimensional Linear Transformations | Essence of Linear Algebra, Footnote
Bring it all to three dimensions. The short video points out that the discussion in the previous presentations in two dimensions also holds true for three dimensions. The sixth video in the series of 15 specifically makes the...
3Blue1Brown
Matrix Multiplication as Composition | Essence of Linear Algebra, Chapter 4
Take a different view at matrix multiplication. Based on vector transformations, the video presents matrix multiplication as the result of the composition of multiple linear transformations. The presentation explains the numerical...
3Blue1Brown
Linear Transformations and Matrices | Essence of Linear Algebra, Chapter 3
Are all transformations of the plane linear transformations? The video provides examples of transformations of the plane and provides the definition of linear transformations. The resource begins the discussion of using matrix...
3Blue1Brown
Essence of Linear Algebra Preview
Make connections with linear algebra. The video introduces the concept of linear algebra and its geometric underpinnings. The resource makes the case that a complete understanding of linear algebra topics should include geometric...
3Blue1Brown
A Curious Pattern Indeed
1, 2, 4, 8, 16, 31 ... hold it, that does not seem right. The resource presents the pattern of the number of sections created in a circle by connecting ever-increasing numbers of points on the circle. The video points out that the...
3Blue1Brown
Tattoos on Math
How is the cosecant function like a tattoo? Pupils learn about the geometric representations on a unit circle of all six trigonometric functions through a video. They also learn why secant, cosecant, and cotangent ended up affixed in...