I find that math can be intimidating for some, particularly regarding the two most common advanced math classes: differential equations and linear algebra. They both often require students to have a deep understanding of mathematical concepts and the ability to think logically and analytically.
But are differential equations really harder than linear algebra? Generally, most students find linear algebra easier than differential equations; however, each difficulty level depends on the teacher/professor, the student’s abilities, and their commitment to learning.
Read on to explore more about differential equations and linear algebra and their difficulty levels so that you can make an informed decision when choosing either of these classes.
If, like most students, you wonder whether linear algebra is harder than calculus. I encourage you to read this article to find out!
What Are Differential Equations?
Differential equations involve derivatives, terms describing the rates of change of continuously varying quantities (they can be either ordinary derivatives or partial derivatives) (Source: Paul Dawkins). They are generally used to model physical phenomena such as velocity, acceleration, and other aspects of motion. Because of this focus on physical applications, this course often requires more than just mathematical understanding; knowledge in related fields such as physics is also necessary.
You can use Differential Equations to describe how populations change, how heat moves, and how radioactive material decays.
As a result, many students often find differential equations difficult because they require a combination of math skills plus knowledge from other subject areas.
Differential equations are generally used in science, engineering, and many other fields of quantitative study because of what we can directly observe and measure as these systems change.
If you are interested in learning differential equations, I encourage you to watch this video from Khan Academy.
What Is Linear Algebra?
Linear algebra is a branch of mathematics that explores systems of linear equations and the properties of matrices. The concepts you will learn in linear algebra are extremely helpful in physics, social sciences, economics, natural sciences, and engineering (Source: Massachusetts Institute of Technology (MIT))
In other words, linear algebra is the study of vectors and matrices. It involves manipulating equations with multiple variables and solving systems of linear equations. Unlike differential equations, linear algebra does not generally require any knowledge from outside sources; all you need is a solid understanding of mathematics to succeed in this class.
Many of my students find linear algebra difficult because it requires abstract thinking and problem-solving skills in order to arrive at solutions.
If you are interested in learning linear algebra, I suggest checking out Khan Academy free course.
If you wonder why you should learn linear algebra, I encourage you to watch the video below.
Differential Equations Vs. Linear Algebra: Key Differences And Similarities
Studying differential equations and linear algebra is excellent because they are essential to building a good math education. Regardless of their differences, differential equations and linear algebra will give you a great advantage when it comes time for exams and career prospects.
Here are the key differences and similarities between differential equations and linear algebra:
1- Differences in Content
On the surface level, one major difference between differential equations and linear algebra is the content covered in each subject.
Here is the general focus of each class:
- Differential equations involve solving calculus-related problems, such as finding derivatives and integrals of functions.
- Linear algebra involves working with vectors and matrices to solve systems of linear equations.
Knowing which subject covers which content can help you decide which topic is more suitable for your particular interests or needs.
2- Differences in Complexity
Another difference between differential equations and linear algebra is their levels of complexity. I found that the complexity of each subject depends on the teacher or professor and the student’s abilities and willingness to work harder.
Here are the main differences between differential equations and linear algebra in terms of complexity:
- Differential equations are considered more complex than linear algebra because they involve more advanced mathematics, such as higher-order derivatives, partial derivatives, and vector calculus.
- Linear algebra is considered less complex because it requires solving simpler systems of equations using basic mathematical operations like addition, subtraction, multiplication, and division.
3- Similarities in Application
Despite their differences in content and complexity, there are some similarities between differential equations and linear algebra when it comes to application.
Both differential equations and linear algebra will require you to use problem-solving techniques like trial-and-error methods or guess-and-check approaches that can be used to find solutions for problems involving derivatives or matrices, respectively.
Additionally, both subjects have wide applications in various areas, such as engineering, economics, science, physics, or finance, where their concepts are used regularly to create models or solve problems related to those fields.
Are Differential Equations Same As Linear Algebra?
Differential equations are both complex objects at a mathematical level and essential in many ways for engineers. In addition, linear algebra methods are an integral part of the methodology typically used to solve differential equations systems (Source: Purdue University Department of Mathematics)
Keep in mind that most linear differential equations are solvable as systems of linear equations.
Should You Learn Linear Algebra Or Differential Equations First?
It is generally recommended to complete at least an introductory linear algebra before seriously considering studying differential equations.
I suggest you take linear algebra first because when you take an ordinary differential equations (ODEs) course, you will ultimately encounter systems of ordinary differential equations. And taking linear algebra class first will prove to be very useful to you.
Which Is Harder, Linear Algebra Or Differential Equations?
Linear Algebra requires different types of thinking from your regular math class and takes some effort to understand its abstract concepts. On the other hand, Differential Equations require you to memorize formulas, use calculus knowledge and learn methods for solving problems. Both Differential Equations and Linear Algebra are relatively easy to understand if you work harder and put in the effort.
If you have a good understanding of calculus and want to challenge yourself with more complex problems, then you might find differential equations much easier; however, if you prefer working with simpler systems, then linear algebra may be better suited for you instead.
What to read next:
- Can You Do A Level Maths In 1 Year? (And How to Ace A Level Math in a Year!)
- 9 Hardest Calculus Problems Ever You’ll Ever Encounter.
- Are Differential Equations Hard? (And helpful tips to succeed in this class!)
- Is the Casio FX-CG50 Graphing Calculator Worth It?
So, are differential equations harder than linear algebra? Generally, most students find differential equations to be harder than linear algebra, depending on the students’ skills and willingness to work harder.
I believe that both differential equations and linear algebra will require mathematical skills as well as problem-solving abilities in order to succeed. However, depending on their strengths and weaknesses, different students may find one course easier.
If you are more into analytical thinking involving multiple variables and abstract concepts, then linear algebra may be the better choice for them; conversely, if you want an application-based approach with a focus on physical phenomena may prefer taking differential equations instead.