In this post, we’ll respond to the most famous questions asked about linear algebra and calculus. So keep reading to know all the details.
Does linear algebra require calculus?
Linear algebra doesn’t require too much calculus, it is still possible to study linear algebra without calculus. But is a better decision to finish calculus classes before you take linear at least take a precalculus course or even better calculus 1. Because linear algebra subject requires some maturity and logical aspects you get studying in calculus.
linear-algebra you study these main 3 following components:
1 vector and spaces
the first subject you should train yourself on is vectors and spaces, in other words, you will be learning how to deal with and represent vector components in the space like the example below in the image.
vector and spaces are very crucial to any enthusiast who want to begin to learn linear algebra. having trouble understanding vectors or how to apply them in space will affect hugely your understanding of the next more complex subject that we will talk about.
2 Matrix transformations
For students who haven’t heard before about matrices, matrices are mathematics operations that are so useful for space transformation and other useful applications of linear algebra. In other words, matrices are written in the form below.
if you ask what is the unique topics you should focus on in linear algebra? : we would say matrices.
In all parts of college linear algbear courses, you employ or need to use matrices. So you have to study and understand well how to implement and use matrices.
3 coordinate systems
linear algebra is a topic that bases on graphics and vector representation. To represent or draw a function or vector you need to learn about spaces or subspaces. The most simple space that you will already be aware of is the orthogonal space.
In addtion, you learn how to project vectors and change basis using all the previous chapters or topics knowledge we mentioned vectors and matrices.
So studying these 3 components will guarantee your success in linear algebra, but you must have a solid foundation in an elementary course like:
- algebra 1
- algebra 2 and precalculus
is linear algebra after or before calculus
In most cases linear algebra is taken after a calculus course, meaning most students study linear algebra after getting their foot into college. But when we talk about math majors they can study linea algebra in high school at the 12th grade which is not always the case for all high schools.
So the noraml phase that most stem students go through is at the 11th grade they take Algebra 2 courses, then at the 12th study or take precalculus course to prepare for a college calculus and linear algebra.
because the math in college is more advanced and complicated. For instance, if take engineering classes students take in their first year they must complete calculus and algebra courses as:
so most stem colleges put ahead calculus and then linear algebra followed. but regarding that, students don’t use calculus in their linear algebra courses except in fewer cases.
Is linear algebra more important than calculus
linear algebra and calculus are more important for stem majors, meaning students who study engineering, physics, and math majors. Calculus is important according to its high use in engineering and manufacturing like building plans, and cars.
while linear algebra is also interesting in computer programming and sociology. In addtion, there are many applications of linear algebra mathematicians to solve calculus equations like differential equations.
but calculus is more widespread than linear algebra because it is mainly used in engineering and physics applications more than linear algebra.
how calculus is important In engineering
Engineering is based almost 100% on calculus in its activities. Engineers use calculus to:
there are unlimited applications of calculus in engineering, but we will try to give one simple example.
when you drive your car at a certain speed, your monitor speed car will show you the speed you’re running. These specific devices use calculus equations every minutes the speed value by using this famous derivative relation.
how calculus is important in physics
physicists use all their day calculus in their research about different topics like:
To give a simple example in the use of how physicist’s calculus. Physicists apply some complex calculus equaiton to determine enough quantity need a spaceship to cross the atmosphere.
This operation is not easy because the speed of aerospace or rocket is not constant meaning the amount of fuel consumed is variable. So calculus is the only tool to use to solve this issue and predict the right answer.
linear-algebra has also some interesting applications, especially in computer science and space exploration, for instance, linear algebra can:
But what makes calculus more famous and important, especially in the united state is the amount of interest a country give to engineering fields that finally to related to many reasons.
you could read this related article talking about the historical reasons why calculus is important in the US.
So if you want to become an engineer or physics you will need a lot of calculus and focus on it more than linear algebra. But finally, you will need to study linear algebra because it is also applied in engineering, physics, and even calculus itself.