In calculus, it’s fascinating that the disk and shell methods both yield the same volume for a solid of revolution. Yet in practice, one can make your work smooth and elegant—while the other can make …
Understanding Dimensions and Finding the Center of Mass of a Spheroid
When we study geometry and physics, we often hear about one-dimensional (1D), two-dimensional (2D), and three-dimensional (3D) objects. Understanding these dimensions helps us determine how to locate …
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Disk vs Shell Methods — Explained with Diagrams, Math, and Examples
When a 2-D region is revolved around an axis, it creates a 3-D solid. To find the volume of such a solid, we slice it into many thin pieces, find the volume of each slice, and then integrate (add up) …
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What is an ODE?
An ordinary differential equation (ODE) relates a function y(x) to its derivatives. For example: $latex \frac{dy}{dx}=x$ This equation says the slope of the function y(x) at every point equals …
🌍Practical Applications of Differential Equations in Physical Science and Business Mathematics
Differential equations are one of the most powerful tools in applied mathematics because they describe how quantities change with respect to time or space. From predicting how a hot cup of tea cools …
Schoolhouse.world: Free Certifications in Calculus and More
When it comes to free online learning, most of us know platforms like Khan Academy, Coursera, edX, or Alison. They all offer high-quality courses, but there’s usually a catch: while learning is free, …
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