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a. In order to use differential equations, we must have equations with functions that not only are continuous, but also are differentiable. Name one natural process that is not differentiable everywhere. b. Consider the classic two-dimensional model for projectile motion in physics: X: = xo + vot cos 0 and y; = yo + vot sin 0 – gt². As you know, the ordered pairs (x¡, Y¡) (parametrized in time) trace a perfect parabola. No one questions whether this model is useful (even if we wish it included air resistance). However, this model is false. Why? Because it assumes that the earth is c. Sabine Hossenfelder said, "I find it hard to think of anything that's more relevant for understanding how the world works than " She goes on to say that these are fundamentally useful for understanding pandemics, the expansion of the universe, climate, financial markets, and quantum mechanics.

a. In order to use differential equations, we must have equations with functions that not only are continuous, but also are differentiable. Name one natural process that is not differentiable everywhere. b. Consider the classic two-dimensional model for projectile motion in physics: X: = xo + vot cos 0 and y; = yo + vot sin 0 – gt². As you know, the ordered pairs (x¡, Y¡) (parametrized in time) trace a perfect parabola. No one questions whether this model is useful (even if we wish it included air resistance). However, this model is false. Why? Because it assumes that the earth is c. Sabine Hossenfelder said, "I find it hard to think of anything that's more relevant for understanding how the world works than " She goes on to say that these are fundamentally useful for understanding pandemics, the expansion of the universe, climate, financial markets, and quantum mechanics.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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a. In order to use differential equations, we must have equations with functions that not only are continuous, but also are differentiable. Name one natural process that is not differentiable everywhere. b. Consider the classic two-dimensional model for projectile motion in physics: Xt = Xo + vot cos 0 and y; = yo + vot sin 0 – gt². As you know, the ordered pairs (x¡, Y¡) (parametrized in time) trace a perfect parabola. No one questions whether this model is useful (even if we wish it included air resistance). However, this model is false. Why? Because it assumes that the earth is c. Sabine Hossenfelder said, "I find it hard to think of anything that's more relevant for understanding how the world works than " She goes on to say that these are fundamentally useful for understanding pandemics, the expansion of the universe, climate, financial markets, and quantum mechanics. d. We are told that the universe is 12 to 13 (or so) billions years old to the Big Bang. If we had the right differential equations to model the universe, and we plugged is something corresponding to 15 or so billion years ago, what could expect to find?
Transcribed Image Text:a. In order to use differential equations, we must have equations with functions that not only are continuous, but also are differentiable. Name one natural process that is not differentiable everywhere. b. Consider the classic two-dimensional model for projectile motion in physics: Xt = Xo + vot cos 0 and y; = yo + vot sin 0 – gt². As you know, the ordered pairs (x¡, Y¡) (parametrized in time) trace a perfect parabola. No one questions whether this model is useful (even if we wish it included air resistance). However, this model is false. Why? Because it assumes that the earth is c. Sabine Hossenfelder said, "I find it hard to think of anything that's more relevant for understanding how the world works than " She goes on to say that these are fundamentally useful for understanding pandemics, the expansion of the universe, climate, financial markets, and quantum mechanics. d. We are told that the universe is 12 to 13 (or so) billions years old to the Big Bang. If we had the right differential equations to model the universe, and we plugged is something corresponding to 15 or so billion years ago, what could expect to find?
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