Need help getting started on my path to University

[Juicydog1]

Hello everyone I hope this is an appropriate place to post. It will be two years until I can attend university and I have some questions. I have developed a love for math and more recently physics and am sure this is the path that I want to take at university. To give you an idea of what I mean, I enjoy studying the two subjects in my spare time.

I am currently working through a calculus textbook and am nearly up to integration, I was wondering if anyone would have an idea as to what physics books I should start to work through simultaneously with my maths work. Or at that, should I even start until I have finished calc (1,2,3) (I believe that is the terminology for calculus in America). If this helps I am considering a double major in physics (priority) and mathematics, with postgraduate physics work after. Obviously any opinion I form now is from a place of naivety and could easily change in the future, but I think I will tend towards the more theoretical side of physics as I have an aptitude for/enjoy mathematics and learning how things work. Any feedback would be greatly appreciated, have a nice day.

(As for my level right now, at school the entire syllabus is non calc based and I am aware this is nothing like higher physics, we have only really covered basic kinematics, so I practically have no prior knowledge)

 

[Mondayman]

I would obtain a copy of one of these textbooks:

Physics for Scientists and Engineers by Serway/Jewett.
Fundamentals of Physics by Halliday/Resnick/Walker.
University Physics by Young/Freedman.

Also worth looking at: Fundamentals of Physics I and II by Shankar, and the accompanying lectures on Open Yale Courses.

Work through one of these books or using the lectures and supplementing them with the text. Take your time and learn it well, its important to have a firm grounding in the basics. There's tons of problems and a lot of material to cover.

I would put a lot of emphasis on learning the mathematics. Learn these topics:

Single Variable Calculus
Multivariable Calculus
Linear Algebra
Differential Equations

If you can get these areas down cold, you are pretty well set for the mathematics requirements for the first two years of university. By third year most students take a math methods course, so obtaining a copy of Mathematical Methods in the Physical Sciences by Mary Boas is a good idea. You can use it to supplement the above topics. If you know all the mathematics in that book, you are pretty good for undergraduate physics.

Two years is a lot of time to prepare. You are in a good position. Just make sure you don't work too fast. Focus on understanding, and take time to review topics once you've moved past them as well.

 

[Juicydog1]

I would obtain a copy of one of these textbooks:

Physics for Scientists and Engineers by Serway/Jewett.
Fundamentals of Physics by Halliday/Resnick/Walker.
University Physics by Young/Freedman.

Also worth looking at: Fundamentals of Physics I and II by Shankar, and the accompanying lectures on Open Yale Courses.

Work through one of these books or using the lectures and supplementing them with the text. Take your time and learn it well, its important to have a firm grounding in the basics. There's tons of problems and a lot of material to cover.

I would put a lot of emphasis on learning the mathematics. Learn these topics:

Single Variable Calculus
Multivariable Calculus
Linear Algebra
Differential Equations

If you can get these areas down cold, you are pretty well set for the mathematics requirements for the first two years of university. By third year most students take a math methods course, so obtaining a copy of Mathematical Methods in the Physical Sciences by Mary Boas is a good idea. You can use it to supplement the above topics. If you know all the mathematics in that book, you are pretty good for undergraduate physics.

Two years is a lot of time to prepare. You are in a good position. Just make sure you don't work too fast. Focus on understanding, and take time to review topics once you've moved past them as well.

Thanks for the help

 

[gmax137]

Or at that, should I even start until I have finished calc (1,2,3) (I believe that is the terminology for calculus in America).

No, you don't have to wait to start on the physics. The normal path is to work simultaneously on the math and the physics. They each shed light on the other.

Just make sure you don't work too fast. Focus on understanding, and take time to review topics once you've moved past them as well.

This is very good advice.

 

[jtbell]

"Calculus-based" introductory physics textbooks at the level of the ones listed by Mondayman don't actually use much calculus.

For the classical mechanics part, it's enough to be familiar with the basic concepts of derivatives and integrals, and how to evaluate them for simple functions like polynomials, exponential functions, and trigonometric functions (especially sine and cosine). You will not encounter complicated functions like the ones calculus textbooks give you for the more challenging exercises. You should definitely be familiar with the geometric interpretation of a derivative as the slope of the tangent-line to a graph at a point; and of an integral as the area underneath a graph of a function.

The electromagnetism part will probably introduce you to Gauss's Law using surface integrals and Ampere's Law using line integrals, which are Calculus III topics (multivariable calculus). However, you will probably use surface and line integrals mainly conceptually. You will actually apply them only to simple, highly symmetric situations in which you can evaluate the integral as a simple product, by inspecting a diagram. (In class, I sometimes called them "Geico integrals"... so easy a caveman can do them. )

The details of the math become more challenging in courses that follow the introductory ones, e.g. an E&M course using Griffiths' widely used textbook.

 

[Mondayman]

I think the biggest thing is to focus on the foundations, and it particular the mathematics. You won't find too much calculus in your first-year physics. But I find the sequence of calculus I-II-III-IV, linear algebra, and differential equations much easier to self-study competently than physics. If you can nail down the math before you start university, you'll hopefully get easy A's in your math courses and be able to focus on the physics.

Also, look ahead at your universities physics program and see if you can find out what courses you take in your first two years. I don't think you'll get through all that math and one of the physics texts in two years, but I like to plan ahead and become acquainted with texts my school usually uses. I bought my mechanics text (Fowles) and modern physics text (Taylor) two years before I took the classes, for only twenty bucks. They cost like $175 each brand new!

 

[Vanadium 50]

What is your plan? To try and get through college faster? I might suggest the better strategy is to focus on getting into the college of your choice.

 

[Mondayman]

I missed that the OP is in class still, I thought he/she just had two years to kill before starting university.

 

[Juicydog1]

I missed that the OP is in class still, I thought he/she just had two years to kill before starting university.

No I’m still in high school, I’m not necessarily looking to skip classes in the future I just want to learn as much as I can. Also thanks for the help

 

[Juicydog1]

What is your plan? To try and get through college faster? I might suggest the better strategy is to focus on getting into the college of your choice.

My plan is just to learn as much as I can, skipping university classes probably isn’t a good idea in case I have gaps in my knowledge. As far as getting into a school, I could be wrong but I believe the process in Australia isn’t as big of a deal as getting into a prestigious college is in the US. I always hear talk about how certain schools are more prestigious than others in the states, but haven’t heard that culture so much here. Thanks for the help

 

[Juicydog1]

"Calculus-based" introductory physics textbooks at the level of the ones listed by Mondayman don't actually use much calculus.

For the classical mechanics part, it's enough to be familiar with the basic concepts of derivatives and integrals, and how to evaluate them for simple functions like polynomials, exponential functions, and trigonometric functions (especially sine and cosine). You will not encounter complicated functions like the ones calculus textbooks give you for the more challenging exercises. You should definitely be familiar with the geometric interpretation of a derivative as the slope of the tangent-line to a graph at a point; and of an integral as the area underneath a graph of a function.

The electromagnetism part will probably introduce you to Gauss's Law using surface integrals and Ampere's Law using line integrals, which are Calculus III topics (multivariable calculus). However, you will probably use surface and line integrals mainly conceptually. You will actually apply them only to simple, highly symmetric situations in which you can evaluate the integral as a simple product, by inspecting a diagram. (In class, I sometimes called them "Geico integrals"... so easy a caveman can do them. )

The details of the math become more challenging in courses that follow the introductory ones, e.g. an E&M course using Griffiths' widely used textbook.

thanks for the help