A negative instantaneous acceleration means the velocity is decreasing. If it is positive, our velocity is increasing. Using Calculus to Find Acceleration Acceleration is measured as the change in velocity over change in time (ΔV/Δt), where Δ is shorthand for “change in”. For example, le...
In calculus we use the terms instantaneous acceleration and instantaneous velocity to talk about very accurate measurements of acceleration and velocity. Acceleration is still defined as the rate of change of velocity, but these measurements refer to motion at an instant instead of over a period of ...
If you’d like to find out why in the example above the ball ended up traveling at 0.88c instead of something else, or what would happen if Walter “The Big Train” Johnson had thrown the ball sideways off of the train, you’ll find ...
To determine the differential change in momentum per unit time, Newton developed a new type of math — differential calculus. His original equation looked something like this: F = (m)(Δv/Δt) where the delta symbols signify change. Because acceleration is defined as the instantaneous change ...
All functions have certain properties, or distinct features, which can be very useful when trying to analyze them. The following common properties of functions describe how a graph is shaped, what happens as x-values increase, and whether the functions can be further analyzed with calculus: ...
…I began to honestly enjoy learning all the new applications for the calculus concepts I had been learning alongside physics, previously unaware of just how intertwined they were. The relationship between position, velocity, and acceleration through derivatives and integrals tied everything together in...
15.1 Introduction to Differential Calculus: Rates of Change 15.2 Limits 15.2.1 Introduction to Limits 15.2.2 Definition 15.2.3 Big O Notation 15.2.4 Change of Variable 15.2.5 One-sided Limits 15.3 Differentiation (permaquestions: 15.3.26 15.3.27) 15.3.1 Instantaneous Rate of Change 15.3.2 Deri...
s been a while since I’ve posted anything on this blog. My life has been in flux of late, as I’ve been moving to Princeton, NJ, changing jobs, and having a baby all at the same time. Now that things are starting to settle, it should be a lot easier for me to find time to...
Suppose that we want to findthe probabilistic law that is most likely given the observed data?That is, solve the MAP estimation problem. The solution to the MAP estimation problem is quite fascinating. When you work out the mathematics of MAP estimation, it turns out that in the init...
II. The velocity of the motion being continually given; to find the length of the Space describ’d at any time propos’d (Whiteside, p. 50). References Kitcher, P. Fluxions, Limits, and Infinite Littlenesse: A Study of Newton’s Presentation of the Calculus. Isis. Vol. 64, No. 1...