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multivariable calculus vs differential equations

if you’re asking about the difference between multivariable calculus and differential equations, in this post you will discover the all details.

In additon we will be responding to the following questions:

  • Multivariable calculus or differential equations first?
  • Is multivariable calculus harder than differential equations?
  • Is differential equations the same as multivariable calculus?
  • Do you need multivariable calculus for differential equations?

difference between multivariable calculus vs differential equations

multivariable calculus is a course students take after calculus 2 or calculus 3 depending on their personal choice and preparation. Some studnet take multivariable calculus before differential equations while others take differential equations before multivariable calculus.

differential equations subjects have 3 main topics:

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

while multivariable calculus is wider and more complex than differential equations it comprises:

  1. Derivatives of multivariable functions
  2. Applications of multivariable derivatives
  3. Integrating multivariable functions
  4. Green’s, Stokes’, and the divergence theorems

differential equations and multivariable calculus have a lot of similar subejcts like partial derivative, derivative and integral of mutiple functions. 

differential equations require having a solid background in previous calculus courses, especially calculus 1 and calculus 2 where studnet discover the basics and application of derivatives and integrals.

Derivatives and integrals are the main subjects students should focus on either studying multivariable calculus or differential equations.

Typically, in calculus 1 and 2 courses students study a single variable of derivative or integrals which are functions like the example below.

theses functions are easier compared to what students will study in multivariable or differential equations.

In multivariable students operate on complex math subjects that have multivariable like this example below :

So as you can see this function has 3 variables which makes it so complicated to make a derivative or find an integral compared to a single value function in the previous example students study in calculus 1 and 2 courses.

Multivariable calculus or differential equations first

you can take multivariable calculus first or differential equations, both are possible. in addtion, there is another opportunity for students who are confident in themselves or love to challenge themselves to take honors calculus classes where they should complete multivariable calculus and differential equations at the same time.

but it will be difficult and not a good option for anyone. For this reason, we mention people who have studied honors classes like honors calculus, and who are used to absorbing and studying heavy and condensed programs in short deadlines.

However, the best option we recommend is to take multivariable calculus first then differential equations, because there are a lot of subjects students study in multivariable calculus that is based on differential equations including partial derivatives, multivariable functions, etc.

So it will be more efficient to discover these subjects earlier in multivariable calculus courses than be confronted directly with the differential equations.

Is multivariable calculus harder than differential equations?

Multivariable calculus is harder than differential equations because it covers many topics than differential equations. In addtion, multivariable and differential equations courses have the same duration. As a result, makes multivariable calculus harder to complete or absorb in a time like differential equations.

Moreover, differential equations are relatively easier because they focus more on memorization than critical skills students must deploy in multivariable calculus.

But differential equations remain a little bit harder when it comes to solving second-order equations or applying the Laplace transform. the rest of the topics are easier and anyone can understand. 

Is differential equations the same as multivariable calculus

differential equations are not the same as multivariable calculus, they are separate courses. Studnet can take differential equations first then multivariable calculus or vice versa. Or taking them together at the same time because differential equations and multivariable calculus have some overlaps allowing them to have the possibility of being taught together.

To explain more we’re going to give a timeline of when students can study differential equations and where is not possible.

after finishing both courses calculus 1 and calculus 2 students get the choice to study differential equations or multivariable.

Or even study them together if they are very good at math and smart or fast learners.

Most people choose the safe road which is studying multivariable calculus then taking differential equations because some differential equations topics are based on multivariable courses.

 you could go back to the previous paragraph “ differential equations or multivariable calculus first ”  where we talked in detail about this subject.

so finally they take differential equation courses with previous knowledge courses.

Do you need multivariable calculus for differential equations?

It is not definitely required to study multivariable calculus for differential equations you could take differential equations directly without any background in multivariable calculus, but you will be required to learn some multivariable calculus topics like partial derivatives, muti variables derivatives, and integrals.

So, students who don’t take multivariable calculus before differential equations, have to study some subjects in differential equations courses before they go directly and focus on differential equations.

If you are a fast learner there is no problem you can take differential equations directly after you finish calculus 2 courses. But you must do well in calculus and integrals before you make this decision. 

In addtion, it will be good to have some linear algebra background, particularly material on eigenvalues. it is so helpful for solving systems of equations, especially for second-order differential equations.

Conclusion

Differential equations are an important subject that students used in engineering and physics classes. It is so interesting for studnet who study based physics calculus one of the hardest calculus subjects.

The famous example where differential equations are widespread is in thermodynamics. If you majoring in physics there are a lot of differential equations to use. So the key you should focus on is to have good preparation by deploying enough effort in practice.