Math for Physics: Essential Calculus for 1st Year Physicists

[Yashbhatt]

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

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

 

[micromass]

What is your current math knowledge. What courses exactly do you mean with "first year physics"?

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.

 

[QuantumCurt]

A first year physics course will often assume that the students have no previous knowledge of calculus, and will further assume that students are taking calculus 1 at the same time as Physics I. Some schools will require calculus 1 as a prerequisite for physics I, but this isn't universal.

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.

 

[Yashbhatt]

What is your current math knowledge.

Algebra, Trigonometry, Geometry. I know basics of what limits, derivatives, integrals are but I am not very good at calculating them.

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.

 

[neosoul]

Usually, undergraduate physics programs offer a course in Mathematical Methods for physics. I would recommend Mary Boas. Still, don't focus so much on mathematics that you don't understand why it is useful in physics.

 

[micromass]

I highly recommend the book by Keisler: https://www.math.wisc.edu/~keisler/calc.html
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.

 

[Yashbhatt]

I highly recommend the book by Keisler: https://www.math.wisc.edu/~keisler/calc.html
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.

Thanks.

 

[akki31]

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),but my real interest is in physics(specifically in electromagnetism and gravity) and for that my mathematical foundation should be good and i am doing it completely independently ,so my question is should i also learn number theory or it is only for pure mathematicians ,and if i need to then what are the best introductory books on number theory,the real reason behind this is that the thought of having strong mathematical foundation for physics sometimes take the physics completely out of equation and makes me worried about mathematics only which i don't want it to happen.i hope anyone who is already in field of physics will understand my concern..please help

 

[micromass]

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

 

[akki31]

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

thanx

 

[Student100]

Usually, undergraduate physics programs offer a course in Mathematical Methods for physics. I would recommend Mary Boas. Still, don't focus so much on mathematics that you don't understand why it is useful in physics.

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.

 

[akki31]

so the conclusion is, i don't have to worry about pure mathematics instead i need to concentrate more on applied mathematics..

 

[Dr. Courtney]

Not all "Calc-based Physics" courses use the same parts or depend on knowning the same parts from Calculus.

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.