# Will I Use Differential Equations in My Computer Science Career?

• BicycleTree
In summary: Differential equations are about deriving information about a phenomenon, from a knowledge of the way it changes. For example, knowing that falling objects speed up at a constant rate due to the pull of gravity enabled Galileo to compute the exact speed and distance traveled by any falling object after any amout of time. Knowing more precisely the inverse square law for gravity of bodies that are further apart enabled Newton to predict the orbits of planets. Knowing the rate of population growth can enable you to predict the population of the Earth in the future, and knowing the interest rate and inflation rate of money can enable you to predict how much wealth you will have at old age, or what retirement savings
BicycleTree
I've had high school AP calculus and took the AB and BC exams, which my college decided, this September, covered my Calculus I and II requirements. So I took a two-semester calculus-based statistics course, and I had to learn some stuff on the fly, but I got through it with good grades. Now, next year, I am thinking of taking Differential Equations. I signed up for it, actualy, but now I'm not so sure I want to take it.

Mainly, I only want to take courses that I directly see the use of. I'm a computer science major at the moment. Logic, discrete math, any computer science course, and linear algebra are some of these that I really see the use of and want to take (and am taking). I do not _have_ to take Differential Equations; my main reason for signing up for it was that I'd seen other people on these forums doing differential equations and I wanted to know what it's about.

But now I'm thinking, will I ever use differential equations outside of the course? So my question here is, what is the relevance of calculus with differential equations to other types of math? For example, topology. I'm trying to absorb as much computer-related math as I can, and I don't want to bother taking something that won't be useful later. Anyway, if I don't see it as important then there's an off chance that I might not do well in it. Are differential equations mainly a tool for physicists and physical engineers, or do they have broader scope?

are you kidding me?

what kinda institution doesn't require Diff Eq for Comp Sci?!

If I was an employer, I won't ever hire a CS major without a course in Diff EQ!@#\$

That is single most important class for a CS major - you don't even need so much Calculus as you would need to substitute that with Numerical Methods

well as a general rule, you can use anything you understand.

but more concretely:

differential equations are about deriving information about a phenomenon, from a knowledge of the way it changes.

for example, knowing that falling objects speed up at a constant rate due toi the pull of gravity enabled galileo to compute the exact speed and distance traveled by any falling object after any amoiunt of time.

knwoing more precisely the inverse square law for gravity of bodies that are further apart enabled Newton to predict the orbits of planets.

knowing the rate of population growth can ebnable you to rpedict the population of the Earth in the future, and knowing the interest rate and inflkation rate of moneyu can enable you to predict how much wealth you will have at old age, or what retirement savings you will need. it eanbles you to see the lies in the ads for lottery payoffs of huge sums, that conveniently omit such factors as the time value of money.

I have a friend in forestry who used integral calculus to estimate the dollar value and "btu's" of fallen trees over a large area.

I have another friend who uses differential geometry to design cardboard test models to measure the aerodynamics of automobiles of various shapes at a car company.

cronxeh said:
what kinda institution doesn't require Diff Eq for Comp Sci?!

What are some of the universities that require a course in DEs for competion of a pure computer science degree?

i think diff eq is really useful for physics, but all the engineers take it too, so it must be useful for them. I really like diff eq as well. i didn't think it was too hard. i thought it was an even more practical application of calculus. you also use lots and lots of various math stuff in it, so it was a good review of everything I've learned thus far. i'd say you ought take it. its pretty straight forward, and i think if you're a smart fella, it should likely be an easy A. well... not a terribly difficult A at least...

That's kinda strange about having to do differential equations in comp sci. Here, most of the maths you get taught is discrete/set theory/logic/linear algebra in CS courses.

BicycleTree said:
But now I'm thinking, will I ever use differential equations outside of the course?

Hello Bicycle. You know, so many people live their lives in a sort of haze about why things happen around them the way they do. They don't have a clue and it causes grief in their lives. I believe differential equations answer many questions about the world, why things happen the way they do, not just in physics, but biology, life, and society. Now I'm not saying differential equations is the answer to everything, but you know what, I use to wonder why about a lot of things. I don't anymore.

saltydog said:
. I believe differential equations answer many questions about the world, why things happen the way they do, not just in physics, but biology, life, and society. Now I'm not saying differential equations is the answer to everything,...
But that's obvious, saltydog; that would have made every solution of diff.eqs equal to the constant function 42.
(Congrats with the new medal, BTW)

arildno said:
But that's obvious, saltydog; that would have made every solution of diff.eqs equal to the constant function 42.

What does that mean? You know sometimes I think the entire universe is a single equation. That's right. The parts we use have the coefficients on the other variables set to zero.

As far as the medals, I told you guys I know less than 1% of Mathematics. Homework helper? I need help too.

Eeh, you HAVE read "The Hitch-hiker's Guide to the Galaxy", haven't you?

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arildno said:
Eeh, you HAVE read "The Hitch-hiker's Guide to the Galaxy", have you not?

No. What's up with that?

Then you would know what the ultimate answer to life, the universe and everything is.
(I won't disclose that, however I will disclose that it doesn't really help us, because we don't know what the ultimate question is (to which the ultimate answer is the answer)..)

arildno said:
Then you would know what the ultimate answer to life, the universe and everything is.
(I won't disclose that, however I will disclose that it doesn't really help us, because we don't know what the ultimate question is (to which the ultimate answer is the answer)..)

I once read an article about magnifying the Mandelbrot Set to world-record extents. They were trying to find the fine filigree which connected the child sets to the main set. However, the more they magnified it, the smaller the filigree would become . . . like that burried treasure story: the deeper they dug, the deeper it would sink.

I think the Universe is a lot like that. Infinite regression punctuated every so often with singularities which changes the rules and makes our concepts on one side, no longer relevant on the other side. Swimming in ice is my favorite analogy.

See, see Bicycle. See what differential equations will do to you.

Well, thanks for your replies. I think I will take differential equations, because it will increase my mathematical experience and it will be useful if I want to do neural networks.

Why calc? One word: Money. And, if you integrate that one word, you get this large area known as the Stock Market.

I wonder, how many stock signals are derived from calc equations? Too many for one person to know (I bet). Think of it this way: if the stock market is a collection of continuous processes (where each stock is one processes of its own), then what tools do we have to measure the movement? Of course, the answer is, in part, our subject at hand.

As for Neural Nets: the summation formula for a back-prop neural net is rooted in e!

I remember in my CS degree thinking of the algorithm as an end in-and-of itself (rather like art). After all, CS is a fantastic thing all by itself. But, eventually, I got hungry. Using my degree to make money seemed like a cheapening of the pure algorithm, but eventually, theory has to turn into cash or we don't eat. Not to belie the art of our trade, but using the computer to apply math to make money is what it is all about -- and calc is part of that equation.

If that’s not good enough, then I speak in the name of my professor, Dr. Scott Sigman, as he would tell us -- in essence -- that knowledge is worth having for its own sake, and sometimes it’s just worth it to be educated! The ubiquitous plea for applicability may say more about us than about the "intangible" subject -- this last part is me, but I think it gets at Scott’s point.

SR

Unfortunately, there are always interesting classes to take, and sometimes you need to make difficult choices about what you have time for. If you have a more specific plan about what you want to do after you graduate, that will help.

There's also the option of learning it later on, independently of a university class. Learning doesn't have to end once you stop going to school. Independent study is especially important for grad students, since classroom learning can only go so far.

One needs to master differential equations and integral calculus before one attempts numerical analysis. In my organization, we develop complex models of large and small structures with which we perform predictive analysis using nonlinear finite element analysis (FEA).

We start with the basic linear and partial differential, and integral equations for phenomenon like heat transfer, mass (fluid or gas) flow and stress-strain (constitutive models), both steady-state and time dependent.

Do we use calculus? Oh, yeah. We have a theory manual which is devoted to descriptions of the basic differential and integral equations which are the basis of our FEA models.

CrankFan said:
What are some of the universities that require a course in DEs for completion of a pure computer science degree?

MIT is one.

Waterloo is another...any cs that emphasize math or simulations modelling.

I wrote:

"What are some of the universities that require a course in DEs for completion of a pure computer science degree?"

To which dfan responded:

dfan said:
MIT is one.

Are you talking about a pure Computer Science degree or something that includes Electrical engineering or Engineering? Of course anything that includes engineering is likely going to have a course in DEs.

Regarding Waterloo, I don't see any requirements or any mention of a course in DEs in the link below.

I'm not saying a course in differential equations isn't useful, I'm probably going to take one myself at some point. It just seems to me to be a bit rude for someone to exclaim "what kind of institution doesn't require a course in DEs for comp sci majors?!" in response to the OP, when in fact that vast majority of universities -- perhaps even all, don't.

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CrankFan said:
It just seems to me to be a bit rude for someone to exclaim "what kind of institution doesn't require a course in DEs for comp sci majors?!" in response to the OP, when in fact that vast majority of universities -- perhaps even all, don't.

I will backup my original statement with even more emphasis on DE. Any University that doesn't require, no, demand a course in DE from a Comp SCIENCE major is NOT a good University.

cronxeh said:
I will backup my original statement with even more emphasis on DE. Any University that doesn't require, no, demand a course in DE from a Comp SCIENCE major is NOT a good University.

Well then, name one that does?

Carnegie Melon University

cronxeh said:
Carnegie Melon University

http://www.csd.cs.cmu.edu/education/bscs/currreq.html

Where on that list is a course in differential equations (even by a different name) *required* for completion of a degree?

21-120 Differential & Integral Calculus
21-122 Integration, Differential Equations, and Approximation

Based on the catalogue, 21-120 seems to be standard "science" calc I and 21-122 seems to be mostly standard "science" calc II stuff.

What does everyone else think? This is the course listing:

"21-122 Integration, Differential Equations, and Approximation
All Semesters: 10 units
Integration by trigonometric substitution and partial fractions;
arclength; improper integrals; Simpson’s and Trapezoidal Rules for
numerical integration; separable differential equations, first order
linear differential equations, homogeneous second order linear
differential equations with constant coefficients, series solution,
Newton’s method, Taylor’s Theorem including a discussion of the
remainder, sequences, series, power series. 3 hrs lec., 2 hrs. rec.
Prerequisites: 21112 or 21120 or 21121"

CMU offers the course: 21-260 Differential Equations. This is the class I am talking about when I say a course in DEs.
(This course is NOT required for a CS degree).

All Semesters: 9 units
Ordinary differential equations: first and second order equations,
applications, Laplace transforms; partial differential equations: partial
derivatives, separation of variables, Fourier series; systems of
ordinary differential equations; applications. 3 hrs. lec., 1 hr. rec.
Prerequisites: 21118 or 21122 or 21123 or 21132

A catalogue can be found here: http://www.cmu.edu/esg-cat/

EDIT: It occurred to me that maybe you're thinking along the lines that any course that gives some instruction in differential equations is a course in DEs, and if that's what you mean then I'd agree that Calc I and II are of fundamental importance. However, I think that when most people say they are taking a course in DEs, it's understood to be something along the lines of 21-260 rather than a calc I, II or III course. I am objecting to the claim that a school that doesn't require a course (wholly dedicated) to differential equations of its CS students is a bad school. If that were the case then clearly CMU would be a bad school :(

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CS majors will be taught numerical methods for solving DE and PDE, but aside from that a knowledge of an analytical solution must exist.

cronxeh said:
CS majors will be taught numerical methods for solving DE and PDE, but aside from that a knowledge of an analytical solution must exist.

When the OP said the following it seems that he had in mind something like CMU's 21-260 course:

"I've had high school AP calculus and took the AB and BC exams, which my college decided, this September, covered my Calculus I and II requirements [...] Now, next year, I am thinking of taking Differential Equations."

That people might get some instruction about DEs from other courses isn't relevant, because he is obviously talking about a course wholly dedicated to the subject. For you to shoot back that a school is bad for not requiring a course in differential equations for that major is just plain ignorant.

Moreover, your profile indicates that you're undergrad physics, just how recently did you switch to a Computer Science major, if at all?

cronxeh said:
CS majors will be taught numerical methods for solving DE and PDE, but aside from that a knowledge of an analytical solution must exist.

i think he meant 21-122 course.

cronxeh, think before you type.

what is it the two of you fail to understand?
"Comp Sci majors without a course in DE is a useless major" -cronxeh (c) 2005.

And I started as a CS major and switched to Physics - but this isn't about me. The OP got his answer from me when I first posted, and then you come in here arguing about something that you don't even understanding remotely

I thought I had posted a response, but apparently not. Ah well.

One of the more useful things I got out of DiffEq (from the computer science perspective) is the techniques for solving them. Many of them carry over directly to solving difference equations, which are important. Differential equations tend to behave much better than difference equations, making it an easier setting to learn the techniques!

Now, analysis in general is quite valuable in computer science. Continuous approximations to discrete phenomena are often much easier to manipulate. Algorithmic analysis is based upon asymptotic behavior. Numerical methods have already been mentioned.

cronxeh said:
what is it the two of you fail to understand?
"Comp Sci majors without a course in DE is a useless major" -cronxeh (c) 2005.

And I started as a CS major and switched to Physics - but this isn't about me. The OP got his answer from me when I first posted, and then you come in here arguing about something that you don't even understanding remotely

why is it useless?

Where is calculus used?

It's good for picking up chicks.

## 1. What is calculus used for?

Calculus is used to study and analyze change and motion in various fields such as physics, engineering, economics, and statistics. It helps to understand and predict how quantities change over time.

## 2. Where is calculus used in physics?

Calculus is used in physics to describe and analyze motion, forces, and energy. It is used to solve problems related to acceleration, velocity, and position of objects in both classical mechanics and quantum mechanics.

## 3. How is calculus used in engineering?

Calculus is used in engineering to design and optimize structures and systems. It is used to solve problems related to rates of change, optimization, and differential equations in fields such as civil engineering, mechanical engineering, and electrical engineering.

## 4. Where is calculus used in economics?

Calculus is used in economics to analyze and model economic systems and behaviors. It is used to study and predict how variables such as supply, demand, and prices change over time. It is also used in game theory and optimization problems in economics.

## 5. How is calculus used in statistics?

Calculus is used in statistics to calculate and analyze probabilities and distributions. It is used to find the derivative and integral of probability functions, which are used to calculate important values such as mean, variance, and standard deviation in statistical analysis.

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