If you ask what is the difference between calculus 2 and differential equations in this post you will find a full response.
The difference between calculus 2 and differential equations
Differential equations is a more advanced course than calculus 2, typically students take calculus 1 and calculus 2 courses before they can apply or take differential equations. Because differential equations are totally based on calculus 1 and 2 courses especially derivatives, integrals, and series.
In addition differential equations is a course that many students take after completing calculus 3 or multivariable which is considered the most complicated course in bachelors or the first 4-year degree for stem majors.
In the next paragraph, we’ll discover the main differences between calculus 2 and differential equations by exposing what students study in calculus 2 and what they will be studying after in differential equations.
what do students study in calculus 2?
In calculus 2 courses studnet study these 4 main subejcts:
1 – Integrals
Integrals are the first topic students study in calculus 2, integral are a mathematical technic used to solve complex equations especially dedicated to determining the areas, surfaces, and volumes of objects.
For instance, if you have a bottle of water and you need to determine how much water volume require to fill in this case engineers use integrals. All the basics rule of geometry like how to determine the surface or square or rectangle are determined using integrals.
Integrals are an essential subject students need in differential equations. But before calculus 2, students must have solid basics of calculus 1, especially derivatives, which are everting in integrals.
If you haven’t studied yet calculus 2, we recommend hugely focusing on derivatives a subject taught in calculus 1.
Simply because in calculus 2 you will find integral functions all these subjects are based on derivatives. So it is impossible to study integrals with derivatives.
2 differential equations
in some calculus 2 courses, students take some basic courses about differential equations, in other words, they prepare for differential courses by studying some topics and basic stuff about the subject to take an official differential course easily.
In calculus 2 you might be studying some introductory topics of differential equations like:
- Differential equations introduction
- Verifying solutions for differential equations
- Sketching slope fields
- Reasoning using slope fields
- Separation of variables
- Particular solutions to differential equations
- Exponential models
- Logistic models
These topics in the calculus 2 course are good and useful preparation to discover these topics earlier and be prepared well for the official differential equations course.
3 – Series
series are interesting subejcts studnet study in calculus 2 and remain a good preparation for the differential equations course.
In other words, series are used in finding solutions to differential equations and are important applications in Laplace transform one of the main subjects students will study in differential equations.
you could find all the details in this link about the topics student take or must complete in the calculus 2 courses.
what do students study in differential equations?
In differential equations students study 3 main topics:
1 – First order differential equations
the first subject students are required to complete in differential equations, is solving first-degree equations meaning equations in like the form below.
typically first degree or order differential equations are not tough to complete, especially for students who have been doing well in calculus 2 and have solid basics in algebra including equations and inequalities. You should normally be taking the algebra 2 courses.
you could read this relead article: For those who can’t pass calculus 2
2 – second order differential equations
second-degree equations are more emphasized and difficult to solve than first-degree, in general, second-degree equations are written like the form below.
theses types of equations require using different technics like:
3 – Series, Laplace Transforms & Systems
Laplace transform and series are the most difficult subject you will be studying in differential equations. This subject requires having a solid background in integrals and a series of the topics we mentioned in calculus 2 courses.
In addtion it requires using some multivariable functions that students take at calculus 3, so for this reason we find a lot of people asking if they should take differential equations or calculus 3 first.
Differential equations course is an advanced calculus course that students have to prepare for. The good preparation to do is you must have good foundations or basics in calculus 2 courses especially integrals, derivatives, and series.
Struggling in these topics automatically means increasing the odds of failing in this course.
Is calculus 2 harder than differential equations?
Differential equations are harder than calculus 2, they are more complex and advanced. The proof is students can’t take differential equations without taking calculus 2 courses. Because they must study some introductory topics like integrals and series in calculus 2 before taking a differential equations course that is based on.
if you are not doing well in calculus 2, it means that you won’t be too at differential equations. one of the reasons that make differential equations hard is their dependency on the previous calculus courses calculus 1 and calculus 2.
In other words, you can’t take differential equations if you don’t have solid foundations in precalculus, calculus 1, and calculus .2
Do you need calc 2 for differential equations?
you need to take calculus 2 for, before differential equations, it is impossible to study differential equations without taking calculus 2. Calculus 2 prepares studnet to study or take differential equations by studying integrals, derivatives, and functions As the main subjects to study and succeed in the differential equations course.