- 144
- 4 606
Math Simplified
Приєднався 21 кві 2024
Math lecture videos with examples ranging from Elementary Algebra through Calculus.
Example - Area of Region Outside Circle & Inside Cardioid
Use a double integral in polar coordinates to find the area of the region that is outside of a circle and inside a cardioid. This example explains the reason for choosing to integrate with respect to r first. It also shows in detail all of the steps used to calculate the integral.
Переглядів: 46
Відео
Example - Find Area of 2D Region using Double Integral in Polar Coordinates
Переглядів 537 годин тому
Use a double integral to find the area of the region enclosed by 2 circles. This video includes a discussion on why we choose to integrate with respect to r first instead of integrating with respect to theta first. There is also a discussion on why we can use symmetry to help with the calculations.
Example - Evaluate Double Integral by converting to Polar Coordinates
Переглядів 397 годин тому
Example - Graph the domain region in 2D. The convert the domain region and the integral to polar coordinates. Evaluate the double integral.
Derive Conversion Formula for Double Integrals over Polar Regions
Переглядів 487 годин тому
A derivation of the formula that is used to convert a double integral in rectangular form to a double integral using polar coordinates. Also a discussion on the limits of integration and deciding when to integrate with respect to r first, or when to integrate with respect to theta first
Double Integral to find Area of Domain Region
Переглядів 369 годин тому
Use a double integral to find the area of a 2D domain region in the xy-plane. This video contains an explanation for why we use f(x,y) = 1 as the integrand.
Volume of Solid bounded by a Cylinder and Planes
Переглядів 249 годин тому
Find the volume of the solid bounded by a cylinder and the planes x=2y, x=0, and z=0. Video contains concept drawings to illustrate the bounded region and discusses the reasons for choosing to integrate with respect to x first.
Double Integral over General Region - Set up 2 ways
Переглядів 209 годин тому
Set up, but do not evaluate, the double integral over a triangular regions. First set up to integrate with respect to y and then with respect to x. Second set up is to integrate with respect to x and then with respect to y. When integrating with respect to x first, it's necessary to split the domain into two separate regions, each with its own double integral, and then add them together.
Double Integral over General Region - Example wrt Y first
Переглядів 139 годин тому
Evaluate the double integral over a general domain region that is not rectangular. Graph the 2D domain to determine the order of integration. This example shows integration with respect to y first, and with respect to x second.
Double Integrals over General Regions - Introduction
Переглядів 3712 годин тому
An introduction to the theory behind choosing the order of integration for a double integral over a general region that is not rectangular.
Double Integral Special Case Rectangular Region
Переглядів 1812 годин тому
An example of evaluating a double integral over a rectangular region where the integrand can be factored into unique functions of x and y. This special case can be evaluated using a formula that is proved in the video.
Introduction to Iterated Integrals with Example
Переглядів 5114 годин тому
An introduction to iterated integrals and how to evaluate them. An example of calculating an iterated integral over a rectangular region.
Midpoint Rule to Approximate Volume Between Surface and Domain Region
Переглядів 2814 годин тому
Use the midpoint rule to approximate the double integral by using volumes of 4 rectangular cylinders. This is used to estimate the volume between a surface function and a rectangular region in the xy-plane.
Evaluate Double Integral using Geometry
Переглядів 2014 годин тому
Evaluate a double integral using geometry and the fact that the double integral yields the volume between a surface and the xy-plane. The surface function in this example is a plane and the region in the xy-plane is a rectangle.
Derive Double Reimann Sum to Approximate Volume over Rectangular Region
Переглядів 8016 годин тому
A derivation of the Double Reimann Sum used to approximate the volume between a surface and a rectangular domain region in the xy-plane.
Find Extrema on Surface over Closed and Bounded Domain Region
Переглядів 39День тому
Find Extrema on Surface over Closed and Bounded Domain Region
Find Rel Max, Rel Min, Saddle Point Example
Переглядів 15День тому
Find Rel Max, Rel Min, Saddle Point Example
Intro to 3D Second Derivative Test for Relative Extrema
Переглядів 29День тому
Intro to 3D Second Derivative Test for Relative Extrema
Proof - Gradient Vector is Perpendicular to Tangent Plane
Переглядів 7114 днів тому
Proof - Gradient Vector is Perpendicular to Tangent Plane
Use the Gradient to findTangent Plane to Surface at Point
Переглядів 9914 днів тому
Use the Gradient to findTangent Plane to Surface at Point
Find Points to make Gradient Vector in direction of i + j
Переглядів 3414 днів тому
Find Points to make Gradient Vector in direction of i j
Maximum Value Directional Derivative - Example
Переглядів 2314 днів тому
Maximum Value Directional Derivative - Example
Gradient Vector & Maximum Value of Directional Derivative
Переглядів 8814 днів тому
Gradient Vector & Maximum Value of Directional Derivative
Calculate the Directional Derivative Example
Переглядів 2214 днів тому
Calculate the Directional Derivative Example
Intro to Directional Derivative and its Formula
Переглядів 7014 днів тому
Intro to Directional Derivative and its Formula
Chain Rule Application Example - Bug on Hot Plate
Переглядів 3814 днів тому
Chain Rule Application Example - Bug on Hot Plate
Implicit Function Theorem More Variables Example
Переглядів 1914 днів тому
Implicit Function Theorem More Variables Example
Inverse Secant & Inverse Cotangent - Example
Переглядів 2614 днів тому
Inverse Secant & Inverse Cotangent - Example
How did it "formalize" at -6xyz? Shouldn't it be +6xyz?
...at approximately 40 seconds
You are right! It should be +6xyz! I'll fix it soon and post the correction. Thanks for brining that to my attention.
Just double-checking for the YZ plane it would be (3,0) and (-3,0) instead of (2,0) and (-2,0)
The trace curve in the yz-plane (x = 0 plane) is a hyperbola opening in the direction of y with vertices at the (y, z) points (2,0) and (-2,0). This is because the value under the y^2 term in the general form of the hyperboloid of one sheet is 4, and the square root of 4 is 2. This section starts at around 5:13 in the video. I hope that helps.
Amazing content. I love it
Thank you for the feedback! I'm glad it's working for you.
You have the most amazing pleasant voice with crystal clear dictions. Joy to my ear. Makes Calculus painless and unbelievably digestible with ease. Thank you. Please upload more 🙏
Glad you like them!