A differential equation is simply defined as an equation that relates one or more functions and their derivatives. Differential equations can be used to describe how populations change, how heat moves, how springs vibrate, how radioactive material decays, and much more.
In this article, we will be going over the difficulty of differential equations in general, how hard a differential equation course typically is, and other questions that you may have around the topic.
Are Differential Equations Hard?
Differential equations are quite hard. There is no unified way of solving differential equations. Instead, you will have to critically analyze the problem, use your past experience, and devise an algorithm to solve the question. These factors together make differential equations difficult.
Generally speaking, students in the mathematics, computer science, physics, and engineering departments tend to study differential equations. Differential equations usually refer to the basic version i.e. ordinary differential equations. Partial differential equations are considered the more advanced form of it.
Students find differential equations hard because it is unlike most other intermediate levels of maths since it requires a lot of critical analysis. Instead of simply plugging in the values and computing the answer, you will have to think and find the best way to approach the question in differential equations.
Moreover, differential equations are both abstract and applied at the same time. This makes them harder than most other forms of math. Not only do examiners expect you to understand something difficult to comprehend but also demand that you apply that knowledge in practical contexts.
To solve differential equations you need to have a good grasp of differentiation, integration, algebraic manipulation, pattern recognition, and applying algorithms to different kinds of problems.
Why are differential equations so hard?
Solving differential equations is hard but forming them is even more challenging. Forming a differential equation requires appropriate situational and subject knowledge.
Practicing a lot of questions can help with understanding the trend of usual questions but examiners can always stump you with a new kind of problem.
Is Differential Equations a Difficult Course?
Differential equations is a difficult course. Differential equations require a strong understanding of prior concepts such as differentiation, integration, and algebraic manipulation. Differential equations are not easy because you are expected to apply your acquired knowledge in both familiar and unfamiliar contexts.
Differential equations are one of those courses where there is no unified way of approaching a problem. Instead, you will need to study a wide range of methods and applications so that you reach a level of competence where you would be able to determine which method would be the most suitable for a given question without solving it entirely.
Hence you will need to be good at two very different skills to master a differential equations course:
- memorizing formulas and methods and
- visual problem solving and abstract thinking.
The reputation of your institute and the department you do your course from plays a big role in the difficulty of the course. For instance, higher-ranked universities tend to make their courses harder to avoid grade inflation and push their students to higher levels.
Math departments often have a harder version of differential equations compared to the one taught by engineering or computer science departments. Math faculties have a propensity of making their courses proof-heavy which adds to the overall difficulty.
To give you an idea of the complexity and approaches used to solve differential equations take a look at the following steps:
- Identify the type of differential eqaution
- Apply an algorithmic-like approach to solve the differential equation
- Handle special cases and anamolies
- Apply integration, differentation, algebra, and arithmetic where appopraite
It is crucial to have a strong understanding of the underlying principles of differentiation and integration to fully grasp why a differential equation is solved in a certain manner.
A differential equation course is one of the most advanced forms of mathematics most STEM majors will encounter (barring math and physics majors) which explains why there are a lot of students online claiming it to be amongst the toughest courses they have taken in their entire engineering or computer science degree.
What level of math are differential equations?
Differential equations are considered an intermediate form of mathematics. It is considered more advanced than courses like calculus 1, calculus 2, trigonometry, discrete math, and linear algebra but less advanced than classes such as abstract algebra, topology, and complex analysis.
Is Differential Equations Harder than Calculus?
Differential equations are equally difficult as calculus courses in general. Differential equations are harder than calculus courses such as calculus I and calculus II but easier than calculus III and calculus IV. Differential equations are considered an important topic in calculus and are taught separately as a result.
Differential equations are actually a subset of calculus itself. The reason differential equations are taught separately is due to the fact that they have a large number of real-life applications and are of many different types.
Addressing and learning the techniques for solving different kinds of differential equations makes sense to create a separate course for it. The numerous practical use of differential equations makes even more sense to dedicate an entire course for it.
Do you need Calculus 3 before Differential Equations?
Most universities do not require you to study calculus 3 before differential equations since the prerequisites for the course will be covered by taking calculus 1 and 2. Calculus 3 is usually taken in the same year as differential equations and they have similar requirements.
Is Differential Equations Harder than Linear Algebra?
Differential equations and linear algebra are equally hard. They are often taught during the second year of most STEM majors and have nearly the same pre-requisites. These factors explain why students and professors alike rank them similarly in terms of difficulty.
Are Differential Equations Useful?
Differential equations are extremely useful such that colleges design an entire course around them. Differential equations are central to several fields including mathematics, computer science, engineering, and physics.
Differential equations have a large number of real life applications. Here is a list of a few of them:
- Creating a mathematical model of a physical system
- Numerical Analysis
- Predict Population changes and trends
- Vibration of Springs
- Decay of Radioactive Material
- Simple Harmonic Motion
- Compound Interest
- Celestial Motion
- Bridge Design
- Interaction Between Neurons
- Propogation of Light and Sound in the Atmosphere
- Wave and Heat Eqautions
Differential equations have the power of connecting different things and providing a means of calculating their relationships with a particular focus on their relationship with time.
Conclusion
Differential equations are hard but easily manageable with sufficient practice and understanding. Differential equations are quite different from most basic and intermediate forms of math since there is no unified way of solving them. Part of the challenge in solving differential equations is identifying the type of equation before you can carry out the mechanics as efficiently as possible.
Differential equations is not an advanced form of mathematics and student from the math department will attest to this. However, for most STEM majors this is the most complex math course they study in the entirety of their degree which explains where it has gotten its notorious reputation of being extremely difficult.
