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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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In Autumn, (note spelling) actually they don't 'turn' yellow, red etc. What actually happens is that the plant stops producing chlorophyl, which give plants their green colour and masks the colouring of any other chemicals. As the chlorophyl dissipates the green fades away leaving tthe base colour. Then the residual chemicals start to form darker sugars which make the leaves darken from yellow through orange, red and brown.

Have a look this US Forestry Service article: https://www.fs.usda.gov/visit/fall-colors/science-of-fall-colors

Read this (1962 edition) from Einsteins's friend ,nobel Physicist, Max Born. Sorry it's all words. No Pictures.

Sounds like a job for…a search engine!

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.

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 [math]\partial[/math] 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

Too much of anything is always bad. The difficult part is agreeing on the right mix. As for J Peterson, his ideas are certainly well thought out, and the fact that he has a large following, from all parts of the political spectrum, allows certain people to bring up his large RW following as proof that he is evil/incompetent/opinionated/etc. He is not just another opinionated guy with a YouTube channel, he is actually a tenured profesor at the University of Toronto in the field of Psychology. He is not right wing at all, as a matter of fact, his notoriety began when he opposed a law that would have forced Canadians to use people's preferred pronouns, which is totally absurd. In your own fantasy, and sometimes demented mind, you can use any pronoun you wish, but forcing others to do so , and live in your reality is something not even G Orwell considered. If I should want to be referred to as, "His exalted royal highness", should people be jailed if they don't do so ?? He has no problem complying with requests to use preferred pronouns, and has often done so in interviews and debates; he has a problem with being forced by law to do so. I suggest getting less information from YouTube.

I agree with both you and swansont, however I was holding off infinity until we had determined other definitions since CE is mixing up physics and maths, as several people have now commented. It should also be pointed out that there is more than one type of infinity (or meaning to the word) which makes things more complicated. I have already pointed out the easier question that we need CE's definition of natural numbers. So thank you for this @Conscious Energy OK so you wish to include 0 in the natural numbers. That is fine. Some Mathematicians include zero some do not. Personally I prefer to start at 1 because it makes the philosophy of numbers easier and more elegant. Either way we can state the following axioms to obtain all the natural numbers. 1) 0 is the first number. 2) Every number has a successor number, obtained by incrementing that number by 1. It follows from these two axioms that 0 is the smallest natural number but there is no largest natural number. This leads directly on to one type of infinity as a non terminating process.

That's a somewhat spectacular return ydoaPs +1