Students find hardships in differential equations because the subject requires strong mathematical skills, a deep understanding of calculus, and the ability to visualize and manipulate abstract concepts. Additionally, the complexity and variety of problems encountered in differential equations can present significant challenges.
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Differential equations are notorious for being a challenging subject for students because of their fundamental complexity and practical applications. As stated previously, this requires strong mathematical skills, a deep understanding of calculus, and the ability to visualize and manipulate abstract concepts. However, the challenges of differential equations go beyond these technical requirements.
As Stephen Hawking once famously said, “It is not enough to be able to solve problems. One must also know which problems to solve.” This applies directly to differential equations, as students must not only understand the mathematics behind the subject but also how to apply it to real-world problems. Moreover, the variety of problems encountered in differential equations can present significant challenges, as there are countless ways to approach a single problem.
Here are some interesting facts about differential equations:
Differential equations have been used to model everything from chemical reactions to financial markets.
Differential equations are closely related to analytic geometry, and both subjects rely heavily on calculus.
The study of differential equations has led to numerous advances in engineering, physics, and computer science, among other fields.
Many famous mathematicians have contributed to the field of differential equations, including Isaac Newton, Leonhard Euler, and Bernhard Riemann.
To help illustrate the complexity and importance of differential equations, here is an example of a table that shows some common types of differential equations and their applications:
In conclusion, differential equations are a challenging subject that requires a deep understanding of mathematics and real-world applications. By understanding the broader significance of this subject, students can better navigate the complexity and develop the necessary skills to excel.
On the Internet, there are additional viewpoints
I’d say it’s because people don’t really study and memorize the methods and techniques to solving Ordinary Differential Equations and therefore, when it comes to a quiz or an exam they struggle to figure out how to approach solving the differential equation. Now, if we’re talking Partial Differential Equations then people struggle because it’s just flat out hard as hell just by itself, P.D.E.’s can be extremely complex and tedious due to the amount of independent variables involved which in turn requires more in-depth understanding of differentiation techniques specifically partial differentiation, and a lot of times the equations don’t even have general solutions, and it’s because of this that P.D.E.’s are so difficult.
Answer in the video
In this video, the speaker emphasizes the importance of learning the five methods for solving differential equations, using the example of a simple harmonic oscillator. The five methods include making a guess and checking, using energy conservation, using series expansion, using Laplace transforms, and visualizing the behavior of the solution as a flow on face space using Hamilton’s equations. The speaker provides examples and thorough explanations for each of the methods, and notes that these tools become invaluable as physicists encounter more complex differential equations. The video creator also thanks their supporters on Patreon and highlights the use of the manim programming library for math animations.
More interesting on the topic
What are the real life problems involving differential equations?
Ordinary differential equations applications in real life are used to calculate the movement or flow of electricity, motion of an object to and fro like a pendulum, to explain thermodynamics concepts. Also, in medical terms, they are used to check the growth of diseases in graphical representation.
What are the factors affecting problem solving ability in differential equations?
Response to this: Therefore, in the present study, major contribution of these four factors, epistemological belief, usefulness, goal orientation and self-regulated learning strategies on the differential equation problem solving were discussed.
What are the disadvantages of differential equations?
Some differential equations are not as well-behaved, and show singularities due to a failure to model the problem correctly, or a limitation of the model that was not apparent. Some DE’s can be solved analytically in closed-form, but most have to be approximated by numerical procedures, which can be unstable.
What is the main problem of differential calculus deals with?
differential calculus, Branch of mathematical analysis, devised by Isaac Newton and G.W. Leibniz, and concerned with the problem of finding the rate of change of a function with respect to the variable on which it depends.
Why do students struggle in differential equations?
Answer will be: The problem with students who struggle in differential equations is the gaps or knowledge holes they build up or expand over the years through missing or not understating foundational topics. In other words, they miss the basics they take in high school and also in college, especially algebra.
Is differential equations hard?
As a response to this: Homework Helper. Differential equations as a theory is *hard*. Differential equations as a mathmatics class is *easy*, since you will only be given questions for which you have the tools required. So, learn the tools and do it.
What skills do you need to solve differential equations?
Differential equations include a lot of different functions and techniques like solving equations and inequalities students should always be good at. For instance, to solve a first differential equations degree you must have a solid foundation and good background to solve systems and matrices.
What is a solution to a differential equation?
Response: A differential equation is an equation involving an unknown function y = f(x) and one or more of its derivatives. A solution to a differential equation is a function y = f(x) that satisfies the differential equation when f and its derivatives are substituted into the equation. Go to this website to explore more on this topic.
Why do students struggle in differential equations?
The problem with students who struggle in differential equations is the gaps or knowledge holes they build up or expand over the years through missing or not understating foundational topics. In other words, they miss the basics they take in high school and also in college, especially algebra.
How do upper-division physics students solve partial differential equations?
Answer: Upper-division physics students solve partial differential equations in various contexts in quantum mechanics courses. Separation of variables is a standard technique to solve these equations. We investigated students’ solutions to midterm exam questions and utilized think-aloud interviews.
Is it hard to proof a differential equation?
Compared to a class like real analysis, the proofs in differential equations are not as difficult but they can still be hard. If you are taking differential equations in high school, it is unlikely that you will be asked for proofs, but it is possible in college and it depends largely on the professor.
What skills do you need to solve differential equations?
The reply will be: Differential equations include a lot of different functions and techniques like solving equations and inequalities students should always be good at. For instance, to solve a first differential equations degree you must have a solid foundation and good background to solve systems and matrices.
