#calculus

Five hour deep-dive into 7 advanced math problems on vector functions. Buckle up!

In this video, I calculate the height covered by a coil of cable of known length around a spool, counting only the portion of the height that includes a full loop. Notes - 3Speak #math #calculus #physics

Deep dive into deriving an equation for the height covered by a cable wound around a spool, for any given cable thickness or spool radius.

In this video, I show that firing a projectile has a maximum total distance traveled in the air when the launch angle is approximately 56°. This is 11° higher than the 45° angle needed to maximize the

Extensive tutorial on deriving the launch angle to maximize the total distance, not just horizontal distance, that a projectile travels in the air.

In this video, I show how to obtain the curvature of parametric equations that involve integrals, by first utilizing the fundamental theorem of calculus to obtain the derivative of the position vector

The curvature of a space curve is obtained when given its parametric equations as integrals for the x and y components.

In this video, I go over the physics of a ball rolling off a table and determine how far it falls, the angle and speed it bounces with, and the distance it travels for a second bounce after losing 80%

The physics of a ball rolling off of a table is explained via vector functions and vector calculus.

In this video, I go over projectile motion along an inclined plane and show that the launch angle that gives the maximum range upwards or downwards is half the angle between the plane and the vertical.

Firing a projectile up or down an inclined plane goes the furthest when the launch angle is half the angle between the plane and the vertical!

In this video, I show that firing a projectile while aiming at a distance target downrange and dropping it at the same time will always cause the projectile to hit the target, provided that the projectile

The math checks out: aiming at a distant target and then firing a projectile at the same time as dropping the target will always hit!

In this video, I examine projectile motion launched from the origin and show that the projectile will always lie within a parabola defined by launching a projectile from the maximum height horizontally

Analyzing projectile motion of an object launched from the origin and analyzing its maximum height, flight path, and ability to hit distant targets.

In this video, I go over the end-of-chapter Problems Plus questions and solve 7 very advanced problems on vector functions. Three of the questions involve launching a projectile either on a flat, inclined,

Livestream discussion on electromotive force (emf) and electromagnetism in general.

In this video, I show that modifying our earlier Theorem 2 remainder estimate by adding the partial sum to both sides of the inequality provides a much better approximation than simply using the partial

Tutorial on approximating the sum of infinite series by using an interval via the remainder estimation theorem rather than just the partial sum.

Remainder Estimate for the Integral Test + Example & In this video, I approximate the accuracy of the partial sums of a series that converges via the Integral Test by estimating the size of the remainder.