Mastering Derivation: Techniques for Simplifying Formulas in Physics and Math

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In summary: If they are not the same, it might be because one side is in terms of mass or time, and the other side is in terms of distance or energy. In that case, you might need to convert one to the other. In summary, this trick lets you solve equations easier by replacing one of the unknowns with a variable that is automatically the same in both equations.
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DDS
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I just have a quick question. I know that in physics and any other math, you can short cut your way if you know various relationships and thus you can derive various forumlas from a few simple ones. Is there any trick to doing this or an easier way, because i have never really been exceptionally well at it but i could always squeeze by.

If anyone knows any methods or tricks is it possible to let me know
 
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There are some notions about what formulae for certain types of relationships look like - proportional, inversely proportional, geometric, and so on. The general problem of translating a relationship into a nice expression is very difficult. It eventually does lead to very complicated formulae for things like QM.
 
  • #3
DDS said:
If anyone knows any methods or tricks is it possible to let me know
Try here for converting units (which is sort of the same think. You do have to construct the equation yourself). For other thinks it takes understanding of what you are doing and quiet a bit of maths. e.g trapiezum rule in maths needs the knowledge of calculus so that you can see how to use the area of a trapiezum to work out the rule with different 'heights'.

What sort of relationships/forumulae are you on about?

The Bob (2004 ©)
 
  • #4
One trick I teach my students:
Often you will have two formulas with a common variable. If you solve both formulas for that variable, and then set them equal to each other, then that variable goes away. This is handy if you trying to figure out a problem where one seemingly important variable is always unknown.
 
  • #5
I suppose dimensional analysis helps here too.

The units of both sides of your equation (when expressed in their basic terms) should always be the same. You can often use this as a guide.
 

1. What is derivation and why is it important in physics and math?

Derivation is the process of finding a formula or equation that describes a relationship between different variables. It is important in physics and math because it allows us to understand the fundamental principles and laws that govern the natural world. Derivation also helps simplify complex formulas and make them more manageable for solving problems.

2. How do I know which techniques to use when deriving a formula?

The specific techniques used for deriving a formula will depend on the specific problem and the variables involved. Generally, it is important to understand the fundamental principles and laws of physics and math, as well as knowing the properties and relationships between different variables. Practice and experience also play a key role in knowing which techniques to use.

3. Can I use the same techniques for deriving formulas in both physics and math?

While some techniques for deriving formulas may be applicable to both physics and math, there are also specific techniques that are more commonly used in one discipline over the other. For example, the use of calculus is more prevalent in deriving formulas in physics, while algebraic manipulation is often used in math. It is important to have a strong understanding of both disciplines in order to effectively derive formulas in each.

4. How can I check if I have correctly derived a formula?

One way to check if you have correctly derived a formula is to plug in known values for the variables and see if the resulting equation makes sense in the context of the problem. You can also compare your derived formula to existing formulas or equations that describe similar relationships. It is also helpful to have someone else review your work to catch any mistakes or oversights.

5. Are there any shortcuts or tips for mastering derivation?

One helpful tip for mastering derivation is to first understand the fundamental principles and laws that govern the problem at hand. This will provide a solid foundation for applying the appropriate techniques and simplifying the formula. It is also important to practice regularly and seek help or guidance when needed. Additionally, having a strong understanding of algebra and calculus can greatly aid in mastering derivation.

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