Which easier probabilty or differential equations?

In summary, the conversation revolves around choosing between differential equations and probability as an elective for an engineering student. While differential equations may be more relevant to the field of engineering, probability can also be useful and may pop up frequently in various forms. However, the level of difficulty for each course varies and some students may find one easier than the other. Ultimately, it is important to have a strong understanding and conceptual understanding of both subjects.
  • #1
mohamadh95
45
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I'm an engineering student, and in my next semester I want to take one of these 2 courses, differential equations or probability. I'm good in math but I'm taking some hard engineering courses and that's why I'm willing to choose the easiest of these 2 courses. Thank you for your advice.
 
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  • #2
mohamadh95 said:
I'm an engineering student, and in my next semester I want to take one of these 2 courses, differential equations or probability. I'm good in math but I'm taking some hard engineering courses and that's why I'm willing to choose the easiest of these 2 courses. Thank you for your advice.

The obvious choice for engineering is DE. Choose the most appropriate course, not the easiest one.
 
  • #3
Differential equations is an elective?
 
  • #4
Well it's true that DE is more appropriate for my field of studies but I would really like to know which is easiest.
And about this question:
Turion said:
Differential equations is an elective?
Both courses are required, they are not electives.
 
  • #5
For the first half semester, I suspect DE would be easier. For the second half, probability would be easier, IMHO.
 
  • #6
I'd say differential equations is easier overall.
 
  • #7
It really depends on what level. The first term of DE is pretty standard, but probability classes vary more in difficulty.
 
  • #8
I thought ODE is the hardest of all the math class including PDE. All the other students in the thought that too. We might had a hard class as it's a 4 units. But I compare to the EM class in terms of difficulty. We all agree ODE is so much harder that Cal II and III combined.

I never study probability in college, but we studied in HS, it's easy.
 
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  • #9
Take differential equations. Not only is it highly important for your engineering courses like heat transfer and fluid dynamics its not all that difficult. I mean how good are you in calculus 2? If you can integrate and understand what a derivative is and it's applications you will be fine. To me differential equations was actually easier than calculus 2 because I didn't have the lab component nor did I have to learn integration techniques or series and convergence theorems. Once you get to differential equations you should already know these things, and you can model pretty interesting and practical things like radioactive decay and population growth. Take DE, stats is boring and involves long drawn out formulas. I struggled with statistics, not even sure how I managed to stay focus enough to get an A.
 
  • #10
yungman said:
I thought ODE is the hardest of all the math class including PDE. All the other students in the thought that too. We might had a hard class as it's a 4 units. But I compare to the EM class in terms of difficulty. We all agree ODE is so much harder that Cal II and III combined.

I never study probability in college, but we studied in HS, it's easy.

No. Just no. I took statistical methods and engineering statistics and they were both far more involved and difficult then the statistics course I took in high school. I should upload some of my notes and coursework for you.
 
  • #11
LCKurtz said:
The obvious choice for engineering is DE.

Not necessarily. As an engineer you're also definitely never going to see a differential equation outside of school but probability is something that can pop up very frequently in one form or another, and something that engineers are typically quite weak at, with little focus having been given to it during school.
 
  • #12
caldweab said:
No. Just no. I took statistical methods and engineering statistics and they were both far more involved and difficult then the statistics course I took in high school. I should upload some of my notes and coursework for you.

He's talking about probability, not statistics. Often the two are included together in introductory classes, but there is a difference.
 
  • #13
yungman said:
I never study probability in college, but we studied in HS, it's easy.
In the U.S., the level of difficulty with what's covered in high school and what's covered in college is vastly different. In my experience, many students really struggle with probability the first time they encounter it in college.
 
  • #14
Probability can be highly unintuitive, diff eq is straightforward.
 
  • #15
Shaun_W said:
Not necessarily. As an engineer you're also definitely never going to see a differential equation outside of school but probability is something that can pop up very frequently in one form or another, and something that engineers are typically quite weak at, with little focus having been given to it during school.

I don't know about that claim. Some engineers see DEs all the time. Some even see PDEs, which are quite common in mechanics and hydrodynamics.
 
  • #16
Shaun_W said:
As an engineer you're also definitely never going to see a differential equation outside of school

SteamKing said:
I don't know about that claim. Some engineers see DEs all the time. Some even see PDEs, which are quite common in mechanics and hydrodynamics.

I would agree you are probably never going to have to produce an closed form solution to the simple types of DE you meet in a BEng course - unless your employer wants your reports written with a quill pen instead of a word processor.

But some conceptual understanding of (for example) how the difference between elliptic, parabolic, and hyperbolic, DEs relates to the physics of what they are modelling, or the relationship between DEs and Laplace transforms (and Z transforms if you are using DSP) is a different issue, and you have to learn to walk before you can run - which is why college courses in DEs start from where they do.

As Hamming said, the purpose of computation (either on paper or with a software package) is not numbers, but insight.
 
  • #17
If I were to give a fast and simplified answer I would say that probabilities/combinatorics is harder conceptually but simpler to calculate, whereas DE's/PDE's are the opposite, easier conceptually but often hard to calculate.
 
  • #18
ModusPwnd said:
It really depends on what level. The first term of DE is pretty standard, but probability classes vary more in difficulty.

This is very true. At my school, the EE's take a pretty difficult probability class and we don't take it until our third year. Because of that, our probability class is significantly harder than the DE class we take in our second year. People going into stuff like communications and signal processing I guess need that solid background in probability theory. On the flip side, some people in other majors take a probability class in their first year, which I imagine is probably easier than DE.
 
  • #19
honestly, and I'm not trying to be offensive, but if you do not currently know diff eq, how difficult could an engineering course really be? that being said, and this coming from a math major and grad-student in mechanical engineering, take diff eq!
 
  • #20
mohamadh95,

I think you will get more reliable answers by asking other students and perhaps faculty at your university. I also recommend speaking with your advisor on what course would make the most sense for you. You may be taking courses very soon that will be much easier going if you know differential equations, even though it isn't an official prerequisite. Likewise for probability.

jason
 
  • #21
If anyone is interested I took both and I found that probability was easy, but differential equations are really hard, harder than all the calculus courses.
 
  • #22
Sounds likely that diff eq was a much more valuable course to take then.
 

1. What is the difference between probability and differential equations?

Probability is a mathematical concept used to measure the likelihood of events occurring. It deals with uncertainty and randomness, and is often used in fields such as statistics and finance. On the other hand, differential equations are mathematical equations used to describe the relationship between a function and its derivatives. They are commonly used in physics and engineering to model systems and predict future behavior.

2. Which one is easier to learn, probability or differential equations?

This is a subjective question and the answer may vary depending on the individual's background and interests. However, in general, probability is considered to be easier to learn as it involves basic concepts such as counting, permutations, and combinations. Differential equations, on the other hand, require a strong understanding of calculus and can be more challenging for some individuals.

3. Are there any real-world applications for probability and differential equations?

Both probability and differential equations have numerous real-world applications. Probability is commonly used in fields such as insurance, risk management, and gambling to make predictions and inform decision making. Differential equations are used in physics, engineering, and economics to model complex systems and make predictions about their behavior over time.

4. Do I need to know probability to understand differential equations?

While a basic understanding of probability can be helpful in understanding some concepts in differential equations, it is not a prerequisite. The two fields are separate and do not rely on each other. However, some applications of differential equations may involve probability and statistics, so knowledge in these areas can be beneficial.

5. What are the common misconceptions about probability and differential equations?

One common misconception about probability is that it is all about luck or chance. In reality, probability involves understanding and quantifying uncertainty and can be used to make informed decisions. As for differential equations, some people may think that they are only used in theoretical or abstract contexts. However, they have numerous practical applications in various fields and are essential for understanding complex systems.

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