Can you study differential equations without finishing integral calcul

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Discussion Overview

The discussion revolves around the question of whether one can study differential equations without having completed integral calculus. Participants explore the relationship between differential calculus and integral calculus in the context of understanding differential equations.

Discussion Character

  • Debate/contested
  • Conceptual clarification

Main Points Raised

  • Some participants propose that understanding integrals is essential for studying differential equations, as the simplest differential equations require integration to solve.
  • Others argue that having a background in differential calculus may provide some foundational knowledge, but it is not sufficient on its own for rigorously studying differential equations.
  • A participant highlights a specific example of a basic differential equation that involves integration, emphasizing the necessity of this mathematical operation in solving such equations.

Areas of Agreement / Disagreement

Participants generally disagree on the sufficiency of differential calculus alone for studying differential equations, with some asserting that integral calculus is necessary while others believe that differential calculus can provide some assistance.

Contextual Notes

There is an implicit assumption that a solid understanding of both differential and integral calculus is beneficial for tackling differential equations, but the exact nature of this relationship remains unresolved.

thedailyshoe
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I mean is it possible? would it be a problem?
 
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Yes. The most basic differential equations are the ones which you can just integrate to get the answer. If you didn't finish integral calculus, it will be very hard for you to understand those calculations.

As integration is the inverse of differentiation, there's really no way to rigorously study differential equations without understanding integrals.
 
Matterwave said:
Yes. The most basic differential equations are the ones which you can just integrate to get the answer. If you didn't finish integral calculus, it will be very hard for you to understand those calculations.

As integration is the inverse of differentiation, there's really no way to rigorously study differential equations without understanding integrals.

hey but i already finished differential calculus last sem and my grades were beautiful.. can't it help with differential equations? i mean both are "differential" so arent they similar?
 
thedailyshoe said:
hey but i already finished differential calculus last sem and my grades were beautiful.. can't it help with differential equations? i mean both are "differential" so arent they similar?

Sure it "helps", but it's not sufficient. Literally the easiest differential equation is this one, which involves an integral:

$$\frac{df}{dx}=f$$

You solve this by basically splitting up the differential and integrating (slight abuse of notation):

$$\int \frac{df}{f} = \int dx$$

Giving you:

$$\ln(f)=x+C$$
$$f(x)=Ae^x$$

Solving differential equations very often involves integrating because integrating is the "inverse" so-to-speak of differentiation.
 

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