# Is Linear Algebra More Important Than Calculus in Physics?

• Winzer
In summary, the conversation discusses the importance of linear algebra and calculus in physics. While some may argue that one is more important than the other, the reality is that they work together to create powerful results. Algebra forms the primary base of both trigonometry and calculus, and while it may be ignored for a while, it is still necessary for final proof of theories. The conversation also touches on the idea that some assume the problem lies in calculus, when in fact it may have originated in algebra. Ultimately, having an open and patient mind is crucial in understanding the complex concepts in physics.
Winzer
Some physics major told me:
"Linear Algebra is much more important then calculus"
Can anyone give weight to these words?

Hmmm. That sounds a bit like saying, "I'm already comfortable with calculus, and linear algebra is novel and interesting to me, so it must be more important."

Or perhaps, "Linear algebra feels more relevant to quantum mechanics, and since that's the course I'm taking right now, it must be more important than calculus."

It's simply not true.

In physics, linear algebra and calculus work together quite often to create some rather powerful results. They're both extremely important and without either of them, you could do very little. If one wanted to be particular, though, you can get through first year physics without touching linear algebra, but try getting through any first year physics course without calculus.

Even in quantum mechanics, linear algebra and calculus play equally important roles. (Heck, you can't even comprehend L^2 without linear algebra or calculus, and that's where everything in QM is derived from.)

... yes, just like physics majors think physics is much more important than math (ask them).

The logical mind knows that Algebra forms the "primary" base of both Trig and Calculus; therefore - an UNBREAKABLE permanent relationship is always present in ALL SCIENCES.

Now, the wise mind knows that because Algebra is ALWAYS in there, it can be "ignored" for a "while".

Now, the ordered mind reminds itself that specific "Algebra only" calculations, must be "performed" as "final proof", of any proposed theory.

The practical mind knows most "hold ups" in prooving "theories" is structure; so "Algebra" is on the back bunner for a while.

The experimental mind gradually matures to an assumption, that because every possible "math" issue that "appears" to be in the Calculus always gets "solved" independantly: it has to be somewhere else.

The precise mind finds the "problem" to have been in the Algebra all along; causing "errors" in the Trig and Calculus when their base "rules" were set up in the first place; and "finds" a SINGLE assuption that "caused" the mess.

The patient mind is one with the cosmos; therefore, evolves into a "pure black" mental state, which is the foundation of the open mind.

AUMathTutor said:
... yes, just like physics majors think physics is much more important than math (ask them).
How silly of them!

## 1. What is the difference between Linear Algebra and Calculus?

Linear Algebra is a branch of mathematics that deals with linear equations, vectors, and matrices. It is primarily concerned with solving systems of linear equations and studying their properties. Calculus, on the other hand, is a branch of mathematics that deals with rates of change and accumulation. It includes topics such as derivatives, integrals, and limits.

## 2. How are Linear Algebra and Calculus related?

Linear Algebra and Calculus are closely related as many concepts in Calculus involve operations on vectors and matrices, which are fundamental concepts in Linear Algebra. For example, derivatives of multivariable functions involve calculating partial derivatives, which can be represented using matrices. Additionally, the study of optimization problems in Calculus also relies heavily on linear algebra concepts.

## 3. What are the applications of Linear Algebra in Calculus?

Linear Algebra has many applications in Calculus, including solving systems of differential equations, finding critical points and inflection points of multivariable functions, and performing optimization in multiple dimensions. It is also used in the study of curves and surfaces in space, which are essential topics in Calculus.

## 4. Can Linear Algebra and Calculus be applied in other fields?

Yes, both Linear Algebra and Calculus have numerous applications in various fields, including physics, engineering, computer science, and economics. For example, in physics, Calculus is used to study the motion of objects, while Linear Algebra is used in quantum mechanics and electromagnetism. In computer science, both disciplines are used in machine learning and data analysis.

## 5. How can one improve their understanding of Linear Algebra and Calculus?

To improve your understanding of Linear Algebra and Calculus, it is essential to practice solving problems and working through examples. It is also helpful to review the fundamental concepts regularly and seek help from a tutor or professor if needed. Additionally, exploring real-life applications of these subjects can also deepen your understanding and appreciation for them.

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