- #1

Yashbhatt

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I am not sure whether I should first study the math rigorously or just concentrate on applications. Any advice is welcome.

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- Thread starter Yashbhatt
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In summary: You should definitely learn number theory. It will help you understand the underlying concepts in physics and engineering. There are many introductory books on number theory, but I would recommend "An Introduction to Number Theory" by Timothy Gowers and Philippa Jones.

- #1

Yashbhatt

- 348

- 13

I am not sure whether I should first study the math rigorously or just concentrate on applications. Any advice is welcome.

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- #2

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I am not sure whether I should first study the math rigorously or just concentrate on applications. Any advice is welcome.

You shuold definitely not study the math very rigorously. But don't completely ignore the rigorous details either! For example, you can safely ignore the ##\varepsilon-\delta## stuff, but some proofs (such as the derivative rules) would be important.

- #3

QuantumCurt

Education Advisor

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For first year physics, it's most important to have a solid foundation in algebra and trigonometry. The only calculus that's really needed right away in physics are the basic rules of differentiation and integration.

More specifically -

Algebra - Basic algebraic manipulations, properties of exponents, solving systems of equations, some familiarity with matrices

Trigonometry - Right triangle trigonometry for finding angles, heights, lengths, etc., and familiarity with basic trig identities

Differentiation - specifically the power rule, product rule, chain rule (or extended power rule as some call it), and basic knowledge (or memorization) of the derivatives of the basic trigonometric functions

Integration - antiderivatives and definite integration by the power rule, integration by U-substitution, and basic knowledge (or memorization) of the antiderivatives of the basic trigonometric functions

If your main goal is to be prepared for a first year calculus based physics course, then having a solid foundation in algebra and trig, and at least some familiarity with the other topics listed should put a student in a good place to do well. However, familiarity with calculus isn't always assumed, and may not be necessary. That said, it would certainly be of benefit. Things like 1 and 2 dimensional kinematics problems are often introduced algebraically without using any calculus to derive them. This isn't necessarily a problem because as one learns calculus, these same equations will be developed more formally. However, having some prior knowledge of calculus will give a student a much better understanding of how things like position, velocity, and acceleration are related to one another.

- #4

Yashbhatt

- 348

- 13

Algebra, Trigonometry, Geometry. I know basics of what limits, derivatives, integrals are but I am not very good at calculating them.What is your current math knowledge.

micromass said:What courses exactly do you mean with "first year physics"?

Slightly above the level of Halliday Resnick/University Physics. (Some of Irodov too).

You shuold definitely not study the math very rigorously. But don't completely ignore the rigorous details either! For example, you can safely ignore the ε−δ stuff, but some proofs (such as the derivative rules) would be important.

I was actually having problems calculating limits with that stuff. So, I tried to ignore it but then I could not understand how the limit rules were derived.

- #5

neosoul

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It is a rigorous book in the sense that it proves most of the results, including the limit rules. But it is much easier because it does not use the ##\varepsilon-\delta##-formalism. It uses a formalism of infintiesimals which are much more suited for physics (and mathematically rigorous). It doesn cover limits, so you won't miss anything.

- #7

Yashbhatt

- 348

- 13

Thanks.micromass said:

It is a rigorous book in the sense that it proves most of the results, including the limit rules. But it is much easier because it does not use the ##\varepsilon-\delta##-formalism. It uses a formalism of infintiesimals which are much more suited for physics (and mathematically rigorous). It doesn cover limits, so you won't miss anything.

- #8

akki31

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Number theory will not be relevant at all to a physicist.

- #10

akki31

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thanxmicromass said:Number theory will not be relevant at all to a physicist.

- #11

Student100

Education Advisor

Gold Member

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neosoul said:

Mathematical methods courses are either graduate or sophomore/junior classes. There is no course for students who haven't even completed the basic core mathematic classes yet.

i have already started spivak for calculus,undoubtedly book is really good,exercises are quite challenging.i know spivak will definitely help me for calculus background i need for learning physics and my respective field in engineering (Microwave and RF)...

You might end up disappointed. If you've already taken a calculus course your background is likely sufficient.

Hello, I need some book which covers all the essential mathematics(especially calculus) required for first year Physics.

QuantumCurt has great advice, I just wanted to stress trig. It's probably the most important mathematics for a first course in mechanics. It's absolutely essential to understanding vectors, which is in turn absolutely essential for solving many mechanic problems.

Towards the end of an intro course you might get introduced to some math you've never seen; such as, the Taylor series. It's normally developed pretty well because there's an assumption that the majority of students haven't seen it before. If the course has a concurrent lab session you might get introduced to some statistics and partial derivatives- which may seem archaic at first- but are pretty intuitive once you've done a few labs.

Obviously this kind of stuff depends on the professor and the course, but QC's advice is universal.

- #12

akki31

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- #13

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The most Calculus intensive 1st year physics courses have Calculus as a pre-requisite, depend heavily on it, and use a considerable part of the Calculus curriculum throughout the year, including some optimization problems.

Less Calculus intensive 1st year physics problems require knowledge of Calculus for less than 10% of the possible points over the course, meaning students can earn an A without knowing any Calculus at all.

Calculus is used in physics to study rates of change, such as velocity and acceleration, and to calculate areas and volumes of irregular shapes. It is an essential tool for understanding and solving many physical problems.

The key concepts of calculus that are important for physics include derivatives, which represent rates of change, and integrals, which represent the accumulation of a quantity over a given interval. Other important concepts include limits, optimization, and related rates.

Calculus is closely related to algebra, geometry, and trigonometry, which are all used in physics. In particular, calculus is used to solve equations and to describe the behavior of continuous systems, which are common in physics.

While a strong background in calculus is not necessary to understand basic physics concepts, it is essential for more advanced topics. It is recommended to have a solid understanding of calculus before delving into more complex physics problems.

Yes, calculus is used in many real-world examples in physics. For instance, it is used to calculate the velocity and acceleration of objects in motion, to determine the force of gravity between two objects, and to calculate the rate of change of temperature in a system.

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