If you are asking about the difference between linear algebra and calculus 2, this is the right post for you.
In this post, we’ll discover the main differences between linear algebra and calculus 2. In addtion discover which is the hardest one, linear algebra or calculus 2.
so have fun and keep reading till the end to take the complete picture.
The difference between linear algebra and calculus 2
Linear algebra and calculus are two completely different subjects, In linear algebra student-focused on Vector spaces that are based on abstract algebra. The linear algebra topics require a lot of proof than calculus 2.
While calculus 2 is more applied math where students solve a lot of equations and functions that relate to change like the derivatives and integrals to calculate surfaces and volumes.
1 – The principal topics students study in linear algebra
In linear algebra students focus on these 4 main topics:
- vectors
- mattresses
- systems
- spaces
1- vectors
If you are going to study linear algebra the first thing you will be required to have is a good knowledge of vector basics. In other words, you need to know how to manipulate vectors and represent them in spaces.
The most famous applications of vectors that students do in linear algebra include:
- Adding vectors
- subtracting vectors
- multiplier vectors
This operation requires solid basics in the previous algebra course, especially precalculus where students prepare for these kinds of applications. In addtion, you need to have good Foundations in trigonometry not to face any problems with vectors.
2 matrices
The second interesting topic does follow vectors is matrices. linear algebra is a topic that requires a lot of space representation. For this reason, you’ll be needing to use a lot of matrices to make transformations of vectors or even spaces.
matrice subject it’s always taught in every calculus course that you should generally have an idea about if you want to take a linear algebra course. because taking a linear algebra course without precalculus remains complex and not a good idea to opt for.
you will be applying matrices rules like this one example.
matrices Represent 90% of linear algebra context it’s used almost in all linear algebra problems. for instance, you will be using matrices to:
- make a linear combination between vectors
- make a transformation of spaces
- explain the relationship between spaces and subspaces,etc
Having problems with matrices means that you would surely struggle in linear algebra. So this is the number 1 topic that you should focus on if you want to succeed in a linear algebra course.
3 systems
Systems are also important and related to matrices, In many cases, linear algebra students are required to solve systems.
5x +y =10
y+1=0
Systems required to have solid Basics and equations and inequalities that you should normally be taking in high school Algebra 1 and Algebra 2 courses. In addtion to polynomials, students study in precalculus courses.
4 spaces and systems
the last thing that you should focus on in a linear algebra course is spaces and systems. In this subject, you will apply a lot of geometry-inducing projection and basis changes. It will be your favorite subject if you like geometry.
In addtion, there are some complicated notions called eigenvectors and eigenvalues, which remain the most difficult subejcts to deal with in this part and even linear algebra course.
2 – The principal topics students study in calculus 2
In calculus students focus on these 3 main topics:
- derivatives
- integrals
1- derivative
if you have taken a calculus 1 course, you already know what are derivatives.
So in calculus 2, you will not find any difference except in the calculus course, a derivative is just more complex and difficult than calculus 2.
If you haven’t yet taken calculus 1, derivatives are just a kind of mathematical function used to study differences and changes. For instance to calculus a speed of a car we use the derivative equation of speed which is:
v= dx/dt
v is a speed
dx/dt is the distance crossed in a certain time
for instance if a cross the distance of 60 km at 1 hour, the equation will be :
v = 60 / 1 = 60 km/h
dx/dt = 60 /1 = v =60
this was a simple example for beginners, just to understand where derivatives are used.
In calculus 2 you will be solving more difficult derivative problems that also require precalculus basics.
2 – integrals
The second subject that students focus on in calculus, is integrals which is a topic based on derivatives. to explain more derivatives are inverse functions of integrals.
In other words, if you made a derivative of a given function it will give you the integral. In derivative we will take this example below:
let’s say we have :
f(x) = x²
the derivative or df(x)/dx = 2x
the integral of ∫ 2x dx = ½ 2x² =x²
so it is like a loop you can begin from a derivative and go to the integral or vice versa.
integrals are useful to calculate volume and areas of complex subejcts. This topic is so useful for physicists, engineers, and mathematicians.
The only bad thing about integrals, is you have to study before derivatives, so you can take afterward integrals. Without derivatives is impossible to understand integrals.
Is linear algebra harder than calculus 2
linear algebra topic is easier than calculus 2, linear algebra is more abstract but not condensed into complex topics like derivatives, limits and continuity, and integrals. The majority of studnet take linear algebra before calculus courses, especially calculus 2.
but linear algebra can be difficult for students who are not good at geometry like vectors and spaces. So it finally depends on each one point of view and math comfort zone.
If you like more applied math calculus 2 will be easier and good for you.
If you like more abstract math linear algebra will be easier and good for you.