Should I learn calculus before physics?
Calculus is necessary to understand physics and to solve virtually any realistic physics problem. Let's take Newton's second law, the famous F = ma.What's a? It's acceleration, a concept that can only be defined via calculus except when it is constant — which is not realistic.What's F? Force is an undefined concept in basic physics until you learn that it's the negative gradient of potential energy. Gradient is another calculus concept, and it can only be computed without calculus when the force is constant: the same unrealistic situation.What about the second law the way Newton actually stated it: F = dp/dt? There's a derivative right in there, and it's not the kind that can be easily guesstimated based on everyday intuition like constant acceleration.What about Newton's law of gravity? It gives the force between two massive objects. What's its potential energy function? Calculus has the answer; without it, you aren't going to be able to compute anything so basic as the escape velocity of Earth.And forget about electromagnetism. Even if you ignore Maxwell's equations, just doing simple problems with closed circuits and all the formulas fed to you leads immediately to second-order differential equations.Sure, you can take a survey course that gives you some idea what the concepts of physics are without getting into the math. You'll end up memorizing a lot of formulas with no apparent origin and never gain insight into their meaning.
Calculus Question; Focal Length f,p,q?
1 pt) If is the focal length of a convex lens and an object is placed at a distance from the lens, then its image will be at a distance from the lens, where f, p, and q are related by the lens equation (1/f)=(1/p)+(1/q) Suppose that f=8 . What is the rate of change of p with respect to q when q=1 ? (Make sure you have the correct sign for the rate.)
An amateur bowler calculated his bowling average for the season. if the date are normally distributed, about h?
Assuming that the games are normally distributed, 68% of the games are within 1 SD of the mean (34% games are 1 SD below the mean and 34% games are 1 SD above the mean). Therefore, (0.68)(50) = 34 games are within 1 SD of the mean. I hope this helps!
Calculus application question?
to find the average, take the initial velocity add the instantaneous velocity at certain time then divide by two. To get the velocity at certain time, you differentiate the position equation. Also the initial velocity is 0 v(t) = -10(t) then plug in the certain times to get the velocity at each time. v(1) = -10(1) = -10 m/s so the average velocity (0 + -10)/2 = -5 m/s avg velocity v(3) = -10(3) = -30 m/s avg v = (0 +-30)/2 = -15 m/s or you can integrate from initial to certain time then divide by how many seconds difference so integral of ∫v(t) = -5t^2 [∫v(1) - ∫v(0)]/t = [(-5(1)^2) - (-5(0)^2)]/1= -5m/s [∫v(3) - ∫v(0)]/3 = {(-5(3)^2) - (-5(0)^2)]/3 = -15m/s hope it helps
What are the applications of multivariable calculus in computers?
What are you interested in, I guess? There are lots and lots and lots of applications of multivariate calculus in computer science. One of the more obvious applications is in computer graphics, where just about every problem is at least two-dimensional (since the computer screen is two-dimensional). Take, for example, the problem of scaling an image to make it larger or smaller. This is a resampling problem, and in general it requires a two-dimensional convolution, which means computing a whole bunch of two-dimensional integrals. (In practice, approximations are used.) Another example is optimisation, which is a common task in numeric applications (e.g. physics and engineering simulations). The Gauss-Newton algorithm (see link), for example, can be used to fit curves to data in an optimal way. The algorithm requires computing the Jacobian matrix of the problem, which means computing all partial derivatives of the function that you're optimising.
How is 'Calculus Made Easy' by Thompson/Gardner for learning Calculus?
I have used that book, when i was a 13 year old teen. In those days, learning new things from a standard indian mathematics textbook was one of the toughest things of world. I wanted to learn calculus, out of curiosity, to see, what new powers does the subject give me. The book started with a memorable quote,“what one fool can do , another too can” and the author had wittingly dubbed all mortals as fools.The book helped me understand basic calculus right from scratch, it began with an algebraic approach to calculus, but did outline the geometrical significance of the topic. It is perhaps the best book, if you are a beginner or an amateur enthusiast. It is a bit lengthy book, and you won’t find it anywhere near to the standard textbooks. The author has written down the matter, that it might very well qualify as a novel of mathematics. It lucidly brings up the intuition behind calculus and makes the seemingly horrifyingly tedious topic a piece of cake.Reading that book will cost you time, do not spend much time with it, just get the feel of subject and then proceed to the mainstream books for a nice “regular” practise. However if time is not an issue to you, then pick that book..if possible get a hard copy of it, and solve along as the author narrates you the saga of beautiful field of mathematics !
How well does an understanding of calculus translate to becoming a mathematician?
Very poorly.To be sure, there are no mathematicians who do not understand calculus (although there are a few ultrafinitists who reject the whole idea and do solely discrete mathematics), but there are also no illiterate mathematicians—calculus might be a prerequisite, but that doesn't mean that much.It is entirely possible to go through the whole calculus curriculum, have stellar grades, have an excellent intuitive understanding of the material, and have zero idea how to write a mathematical proof. And that is key—there is plenty of math that uses no calculus (none of the work I have done so far has used it), but there is no mathematics without the idea of proof.Most calculus students do not become mathematicians. I won't comment on whether they could become mathematicians (I’m inclined to say ‘yes’, given time and desire), but clearly becoming a mathematician is a much more involved process than just getting a grip on calculus.
Does being bad in calculus and trigonometry imply that I'll never be a great competitive coder?
Thanks for A2AAlthough I am too a amateur programmer, but as far as I have programmed or talked with other professional counterparts yet, I concluded that no hardcore mathematical knowledge is required during programming. But only the basics and the way of thinking is required. I will give you a personal advice that you should practice the programming algorithms more and more. It will surely outshine your expertise(pun included) in calculus and trigonometry.