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# How much of this calculus book do I need to work through to understand classical physics?

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I have a introductory Calculus book called 'Thomas' Calculus 14th edition'. I want to learn classical/undergrad physics through the book "University Physics with Modern Physics 15th edition".

Based on the contents of Thomas' Calculus, how much of it do I need to know to understand the Physics textbook I have?

1. Functions
2. Limits and Continuity
3. Derivatives
4. Applications of Derivatives
5. Integrals
6. Applications of Definite Integrals
7. Transcendental Functions
8. Techniques of Integration
9. First-Order Differential Equations
10. Infinite Sequences and Series
11. Parametric Equations and Polar Coordinates
12. Vectors and the Geometry of Space
13. Vector-valued functions and motion in space
14. Partial derivatives
15. Multiple integrals
16. Integrals and vector fields

Contents of "University Physics with Modern Physics 15th edition":

1. Mechanics

2. Waves/Acoustics

3. Thermodynamics

4. Electromagnetism

5. Optics

6. Modern Physics

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It depends on the kind of classical physics and the complexity. If you want to understand basic toy kinematics and dynamics at the high school level, you could get away with going up to the first order differential equations.

You'll be doing stuff like taking the derivative of a displacement equation to get a velocity equation.

If you want to understand more complex problems with more modern paradigms, then you'll need multivariable calculus.

You'll be doing things like solving the Euler-Lagrange equations and integrating Lagrangians to find the least action.

With waves, electromagnetism, and "Modern Physics", that table of contents specifically tells me you'll likely need the multivariable parts of the calculus text as well.

But it might be simplified for like an introductory course. You'll have to look at the physics book. If it has $\partial$ or an upside-down triangle,you know you'll need the multivariable parts.

TL;DR:

That physics book's topics suggest you'll need the entirety of the calculus book

Edit:

!

Moderator Note

Topic moved from Lounge to Classical Physics

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9 hours ago, Parkour said:

I have a introductory Calculus book called 'Thomas' Calculus 14th edition'. I want to learn classical/undergrad physics through the book "University Physics with Modern Physics 15th edition".

Based on the contents of Thomas' Calculus, how much of it do I need to know to understand the Physics textbook I have?

1. Functions
2. Limits and Continuity
3. Derivatives
4. Applications of Derivatives
5. Integrals
6. Applications of Definite Integrals
7. Transcendental Functions
8. Techniques of Integration
9. First-Order Differential Equations
10. Infinite Sequences and Series
11. Parametric Equations and Polar Coordinates
12. Vectors and the Geometry of Space
13. Vector-valued functions and motion in space
14. Partial derivatives
15. Multiple integrals
16. Integrals and vector fields

Contents of "University Physics with Modern Physics 15th edition":

1. Mechanics

2. Waves/Acoustics

3. Thermodynamics

4. Electromagnetism

5. Optics

6. Modern Physics

First let me say what a well presented question you have asked.

Keep this standard up and you will go far.

+1

Now the books.

First the Physics.

The original editions of this book were written by Professors Sears and Zemansky in 1949.

So you see that it has a very long history and pedigree and is very well respected.

Young and later Freedman joined the team and the task of keeping it up to date.

The material is aimed at high school and on into first year university level and offers a geat deal of excellent explanation and promotes understanding rather than clever mathematics.

Yes understanding classical calculus is necessary to get the most out of this book, but not to the level of speciality you will find in Thomas.

Having said that, Thomas is also a very good book (see below).

But remember that students generally learn both the physics and Mathematics in tandem.

So you will lear some Physics then some Mathematics, which will enable you to learn some more Physics ... and so on.

Now the Mathematics.

I have already praised Thomas.
It contains a thorough introduction to 'the calculus' for students but to a depth and facility greater than is required for Physics as it really is a Mathematics book.
So you will only need to learn it all if you are going to do further Mathematics.
It will, however, provide the understanding you need to follow the Physics in Young etc.
It should also serve well as a reference to go back to as you

But it is not a pure Mathematics book and would not be of much use (except as background) in a formal University course in Analysis (The posh part of maths that includes calculus).
But then formal university Analysis books are not much use in Physics either.

Better than that it provides an elementary introduction to some more advanced mathematical topics, used in more modern Physics.
For instance it provides a useful introduction to topics such as differential forms which you might require when going from first degree Phyics into postgrad.

So both excellent choices that will last you a long time to come.

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I remember having gone through Young/Freedman many years ago, an older edition. From what I remember, you will only really need (1)-(5), as well as (8) and (9) of the topics in your maths text. I would recommend going through the whole thing though!

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In my experience, undergrad intro physics classes require knowledge up through derivatives and integrals. You might see differential equations in derivations of the equations that you use, but you would not be asked to solve them, as such. You might use infinite series, parametric equations and/or polar coordinates, depending on what's covered.

Diff Eq's was something learned for later, more in-depth courses in the topics covered in the intro course.

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The mathematics topics that caught me under-prepared as a new undergrad (nearly 50 years ago!) were set theory and matrix algebra which weren't in our school curriculum.

On the calculus side, the major missing item appears to be Numerical Solutions to ODEs, but as stated by several previously, such advanced topics will be covered during your course.

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Much appreciated guys, thanks for the helpful answers!

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