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Differential equations vs linear algebra

If you are interested to know the difference between differential equations and linear algebra this is the right post for you.

 in this post, we’re going to discover the differences between differential equations and linear algebra and also respond to some famous questions asked by students about this topic.

The difference between differential equations and linear algebra

Differential equations is a subject that’s based on calculus and precalculus courses that students take in college, in the second year for stem majors(engineers, mathematicians, and physicists). In other words, it requires preparation by studying topics like limits, continuity, derivatives, integrals, and multi-variable functions.

 For this reason, we find a lot of students taking differential equations as the last calculus topics to study after taking all the courses including:

 Differential equations are one of the most difficult calculus courses. it requires an interesting maturity in mathematics to succeed. In the differential equations topic you will be studying theses following principal subjects:

  1. First-order differential equations
  2. Second-order linear equations
  3. Laplace transform

Having a weak foundation in the previous calculus courses we mentioned, will guarantee you to fail in differential equations. especially for students who still struggle with derivatives and integrals. the differential equations will be like hell in this case.

Linear algebra is also an interesting subject students take in college, in the second or third year. It is based hugely on all college algebra topics especially focusing on vectors, matrices, and basic algebraic topics like equations systems and polynomials.

Linear algebra is one of the most difficult algebra courses you will take in your first 4 years in college especially if you are studying engineering physics or mathematics. it’s a topic that a lot of people struggle with because they require some having the solid basics in geometry and other topics we mention in this article.

In a linear algebra  class you’ll be taking the following principal subject: 

Having a bad foundation of vectors and spaces that you should be taking in pre-calculus and previews High School courses like geometry, is enough to make you suffer in linear algebra courses.

Because in linear algebra there are obnoxious applications of vectors and the graphic representation in spaces.

In addtion, the critical thing that makes also students sufferring or not do well in linear algebra is having weak foundations with matrices and systems as we explained in detail in this following article.

why linear algebra is hard.

Differential equations is a subject that tends to be more practical and less abstract than linear algebra.  In other words, there is a lot of proofing and abstraction in differential equations than in linear algebra. 

Are differential equations harder than linear algebra?

Both of these courses are similar in terms of difficulty, some students find differential equations difficult while others say the contrast. But you have to understand that differential equations require a little bit more memorization than linear algebra based on proofs.

If you love to deal with vectors and play with numbers and matrices, linear algebra would be easier and more fun for you. But you have to know that is more abstract and less applied compared to differential equations.

  If you haven’t taken a multivariable calculus course or at least a calculus 2 course in this case linear algebra would be much harder than differential equations.

But at the same time differential equations remains difficult, especially for students who have not done well in precalculus and calculus 1 course.

Should I take differential equations or linear algebra first?

Is better to take linear algebra before differential equations because it is more helpful for instance you will discover some interesting topics in linear algebra like systems that would be helpful to solving first-degree equations and all linear systems in differential equations.

It is not necessary to take linear algebra first, but it is interesting and useful to prepare in linear algebra courses to take differential equations topics with more confidence and ease. 

In addition, if you haven’t yet taken a multivariable calculus course is better to avoid taking differential equations. So the best choice to do is to take linear algebra then multivariable calculus and finally differential equations.

 because differential equations require some basics of linear algebra in addtion to multivariable caluclus.

you could read more in this related article: multivariable calculus vs differential equations.

 but anyway if you are a stem major you would be required to complete them both. but it’s better, to begin with, linear algebra first then differential equations.

Can I take differential equations and linear algebra at the same time?

You can take both differential equations and linear algebra but it is not recommended because it will be tough and heavy. As a result, risk decreasing your focus and finally not doing well in both courses.

 unless you are confident in yourself by doing well in math. You can take this adventure but it doesn’t worth it or have any profit advantage to take this risk.

The best thing is to focus first on linear algebra and then take differential equations later as we described in the previous paragraph.

 but if you love a challenge and your University or School allows you to do that go for it.

Which is harder integral or differential calculus

Integral is just a part of a subject required to have knowledge about to study differential calculus. so it is hard to make a differentiation between integral and differential calculus because finally, you would be employing all integral applications in differential calculus.

 Typically students take integral calculus in previous calculus courses like Calculus 1 and calculus 2  to be prepared for studying differential calculus or multivariate calculus.

So the best thing is to focus on  Calculus 1 and calculus 2 where you’ll be studying integrals Then taking finally differential calculus.