cscott Posted June 21, 2005 Share Posted June 21, 2005 How much calculus is needed for this book? Link to comment Share on other sites More sharing options...
DQW Posted June 21, 2005 Share Posted June 21, 2005 I speak from knowledge of an old edition, but I don't think it's changed very much since. Just very basic differentiation and integration (definite and indefinite). No knowledge of differential equations, special functions, etc. is required. The only functions you will encounter are polynomials, exponents/logarithms, and trigonometric functions. Link to comment Share on other sites More sharing options...
cscott Posted June 22, 2005 Author Share Posted June 22, 2005 I speak from knowledge of an old edition' date=' but I don't think it's changed very much since. Just very basic differentiation and integration (definite and indefinite). No knowledge of differential equations, special functions, etc. is required. The only functions you will encounter are polynomials, exponents/logarithms, and trigonometric functions.[/quote'] So I should be able to get buy without having a formal class on calculus? I'm just reading an intro to the subject written by my grandfather but it does seem to cover what you mentioned. What I'm basically asking is how "hard" the calculus is for the first 9 chapters or so. From what I understand it's not too demanding. In addition, I've covered the subjects in chapters 1 through 9 in my Physics 111 course, which didn't utilize calculus at all. What does calculus bring to these same topics? Please excuse my ignorance Thanks in advance! Link to comment Share on other sites More sharing options...
swansont Posted June 22, 2005 Share Posted June 22, 2005 In addition, I've covered the subjects in chapters 1 through 9 in my Physics 111 course, which didn't utilize calculus at all. What does calculus bring to these same topics? Calculus lets you derive many of the equations that are given without proof in a non-calculus-based course. e.g. all of kinematics can be derived from the defintions of position, velocity and acceleration, and some calculus. Link to comment Share on other sites More sharing options...
DQW Posted June 22, 2005 Share Posted June 22, 2005 Please excuse my ignorance The First Golden Rule of Forum Life : Make no apology for asking honest questions. There is no shame in wanting to know more. (and do remind me of this if I err the same way) So I should be able to get buy without having a formal class on calculus? I'm just reading an intro to the subject written by my grandfather but it does seem to cover what you mentioned. Since you're persistent (which I respect) I shall put in more effort than I did the first time. <digs through the rubble for dust-covered tome titled : "Physics, Part I; Robert Resnick, David Halliday"> Okay, here goes : My copy is a 1960 edition !! These are the first 9 chapters according to my book (make sure they roughly agree with yours) 1. Measurement, 2. Vectors, 3. Motion in One Dimension, 4. Motion in a Plane, 5. Particle Dynamics - I, 6. Particle Dynamics - II, 7. Work and Energy, 8. The Conservation of Energy, 9. Conservation of Linear Momentum Next, I shall list what are the important things to be gained from each chapter, and the math preparation required (of course, going by what's in my book). The pre-requisite for any chapter is all of the preceeding chapters. Do not skip a chapter, ever ! Link to comment Share on other sites More sharing options...
DQW Posted June 22, 2005 Share Posted June 22, 2005 The Chapters : 1. MEASUREMENT : Reference frames, and units. R&H does not have a section on dimensional analysis, which I consider essential to this part of your learning. Find another source for this (or ask me). Math required : basic arithmetic. 2. VECTORS : This chapter teaches you basic vector algebra, and is a pre-requisite to everything that follows in the book (and in physics, in general). Do not go to the next chapter until you can solve all the problems in this one (at least all but the last few, which are exercises in mathematical muscle-building). Math prep : very basic trig (the definitions of sin, cos, tan and the knowledge that sin2(x) + cos2(x) = 1 is minimum), a prior knowledge of vector algebra will make this chapter a breeze, but that only means you can get to the problems sooner ! 3. MOTION IN ONE DIMENSION : This chapter teaches you how to use the equations of (linear) motion, under constant acceleration (and otherwise). An important special case is the free-fall problem. It rigorously teaches you what velocity and acceleration are, and in the process, develops the concept of a derivative and its application to finding rates or slopes of functions. Learn how to draw the graphs - that's essential. Math prep : You will need know how to find derivatives of (or to differentiate) polynomials. While you're at it, learn how to do this for other functions as well : trig functions, logs and exponentials should do. 4. MOTION IN A PLANE : Here, the concepts taught in the previous chapter are extended to motion in 2-dimensions, by means of the previously developed tachniques of vector algebra. Important special cases are projectile motion and circular motion. You will also learn the valuable technique of using relative velocities and accelerations. Math prep : nothing new - more vector resolution, addition and subtraction. Also, you must understand how a 2D vector equation is nothing but a pair of scalar equations. 5. PARTICLE DYNAMICS - I : Here, you learn how forces affect dynamics (motion), through the framework of Newton's Laws. Be perfectly clear about what the Third Law teaches. You will also learn the vital (and I can not stress this too much) technique of drawing free-body diagrams, and using them to solve static and dynamic problems. No new math here (but you get more practice writing vactor equations as pairs of scalar equations in the x- and y-directions). <more follows> Link to comment Share on other sites More sharing options...
Tom Mattson Posted June 22, 2005 Share Posted June 22, 2005 So I should be able to get buy without having a formal class on calculus? Honestly' date=' I think that you would be ill-advised to attempt this. I taught physics out of Halliday and Resnick for 4 years, and you really should have a course in calculus if you are to really know what you are doing. There are questions such as, "The position of a particle as a function of time is given by [b']r[/b]=(4t-2t2)i+(-3+2t)j. What is the y-coordinate when the x-coordinate is a minimum?" To answer that question you need to understand differential calculus. Yes, you can be taught a quickie lesson wherein you learn to parrot the formal rules of differentiation so that you can "get the answer". But that's not the goal. The goal is understanding, and you aren't going to get that without having studied calculus. Link to comment Share on other sites More sharing options...
Fortuna Posted June 22, 2005 Share Posted June 22, 2005 Wow, Halliday & Resnick, that book really takes me back ! This was used in my very first UG collegiate physics class (Physics 101), back in the late 1970s. I remember that most of us already had a decent grasp of basic calculus at the time (what might now be called high school AP Calculus). However I remember that I and the others in that class was at the same time taking Calc I and II. These parallel Calc classes were the real hardcore Calc I and II, (not business calculus or the watered down versions for business majors, MBA programs and other non-science majors). I agree with the other poster, you do need a good grasp of the general concepts of differentiation and integration, but as I remember the problems are really not all that difficult mechanically. What you need is a good grasp of the concepts to really understand the derivations in order to learn how to apply these in a more general way. This enables you to solve a variety of specific problems for that particular topic. I thoroughly enjoyed my first year UG physics class. The first semester of this class also served more or less as the elimination round for the physics program. We started the first semester with about 40 students in the class (most of them top notch sci students from their respective high schools), and at the start of the second semester the class had only 6 persons remaining. No worries though, almost all of those who dropped out changed their majors to Engineering (most of them to the EE program ehich was popular at that time) Anyway good luck to you, and hang in there ! Fortuna Link to comment Share on other sites More sharing options...
DQW Posted June 22, 2005 Share Posted June 22, 2005 I partially agree with Tom. When you learn calculus, you want to learn it right - from first principles and definitions up to applications. But I do think that (with a focused effort) you can learn this from a good text, by yourself, in no more than a couple of weeks. The test of your understanding is simply your ability to solve problems. If you can work the exercises at the end of each chapter (of a calculus text), you are good to go. I'm not sure about your grandfather's introuductory text though (no insult here, and I speak from no knowledge of what he's written, but you are certainly not a judge of that either) - I would get a good book from a library. We can recommend a few perhaps. Link to comment Share on other sites More sharing options...
DQW Posted June 22, 2005 Share Posted June 22, 2005 <continuation> 6. PARTICLE DYNAMICS - II : In this chapter, there's more of the same stuff that went into the previous chapter, but in addition, you learn about friction and centripetal forces. No new math here. 7. WORK AND ENERGY - Here's where you will first need integral calculus - to deal with the work done by a variable force. You will also learn how to use the work energy theorem and how to understand power. Math prep : integral calculus. 8. THE CONSERVATION OF ENERGY : Here you are taught important concepts of conservative and non-conservative forces and potential energy, and the powerful technique of energy conservation. There's also a little section on relativistic mass which you could easily skip and not hurt yourself. It's best to learn relativity separately, as a coherent package. 9. CONSERVATION OF LINEAR MOMENTUM : First you will learn about the center of mass and its frame of reference. Then you will learn to apply momentum conservation to open and closed systems. No new math here. Link to comment Share on other sites More sharing options...
cscott Posted June 22, 2005 Author Share Posted June 22, 2005 My grandfather did say his book was merely an introduction and is no substitute for a good textbook, so I think I'll end up picking one up. As it's summer and I have plenty of time on my hands I think I'm going to make the attempt at learning the calculus and working through the physics. Even getting a small picture of what I'll be doing next year would be nice. I can fill in any gaps when I get a formal education on these topics. Thanks for the time invested in your replies! P.S. Oh, and any ideas on a good intro text on calculus? I've heard good thinks about Spivak's book but I don't know its level... P.P.S I forgot to mention that with the link I gave in my OP you can click on the picture of the book and get the table of contents. Sorry about that! Your book matches closely though, so it's np. Link to comment Share on other sites More sharing options...
Tom Mattson Posted June 22, 2005 Share Posted June 22, 2005 P.S. Oh' date=' and any ideas on a good intro text on calculus? I've heard good thinks about Spivak's book but I don't know its level... [/quote'] Spivak's book is good, but it is very difficult for a beginning calculus student. The idea behind his book is that a first course in calculus should be a first exposure to "real math", not just a prelude to it. And it is not without its problems (for instance it tries to give a taste of real analysis, but it doesn't cover set theory at all). I would recommend Stewart for an intro to calculus. Link to comment Share on other sites More sharing options...
cscott Posted June 26, 2005 Author Share Posted June 26, 2005 Calculus lets you derive many of the equations that are given without proof in a non-calculus-based course. e.g. all of kinematics can be derived from the defintions of position, velocity and acceleration, and some calculus. It it safe to assume a physicist should be able to derive all of kinematics from those definitions once one has adequate understanding? Link to comment Share on other sites More sharing options...
swansont Posted June 26, 2005 Share Posted June 26, 2005 It it safe to assume a physicist should be able to derive all of kinematics from those definitions once one has adequate understanding? Yes. Link to comment Share on other sites More sharing options...
cscott Posted June 27, 2005 Author Share Posted June 27, 2005 Yes. Sounds fun . I have one more question (I think): How easy will it be to relate what I've learned with calculus to the same concepts except with pure algebra? If I'm not mistaking my next years Physics course includes very little calculus. Thanks in advance Link to comment Share on other sites More sharing options...
swansont Posted June 27, 2005 Share Posted June 27, 2005 Sounds fun . I have one more question (I think): How easy will it be to relate what I've learned with calculus to the same concepts except with pure algebra? If I'm not mistaking my next years Physics course includes very little calculus. Thanks in advance Algebra-based physics is a little easier because the math is not as difficult (assuming you agree that calculus is more difficult than geometry). The concepts are the same, but you restrict yourself to the problems that can be solved with the relevant math skills. If you have a handle on the calculus, you won't have to worry as much about memorizing equations. You can derive them, and understanding where they came from (as well as using them a lot) tends to make it easier to remember them. Link to comment Share on other sites More sharing options...
cscott Posted June 27, 2005 Author Share Posted June 27, 2005 Sounds good to me. Thanks again! Link to comment Share on other sites More sharing options...
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