Do i have to take advanced functions before calculus and vectors?
It's not like i have no clue of what advanced functions is. I took it last month and dropped it right on the trig unit. As i was finding it really hard due to me not having the knowledge of trig of the grade 11 course. Can one really be successful in calculus in vectors and vectors without having the recommended advanced functions class. I have taken grade 11 physics so i do know what vectors and such are and how to apply it to my mathematical work . Will i be able to succeed-roughly get a 75-85 in the class if i come to class everyday and ask questions a lot. And study a lot at home>? I've never taken this class yet.
Calculus III help, vector functions?
Suppose that a particle's position is described by r(t) = sin(t)i +4cos(t)j Give an equation (in the form of a formula involving x and y set equal to 0 ) whose whose solutions consist of the path of the particle.
What are vector-valued functions?
Vectors, as opposed to scalars, are physical quantities that include both magnitude and direction.Speed, for example, is a scalar. It is measured in distance/time (in the U.S., usually miles / hour). Nobody gets a speeding ticket that contains a speed and a direction.Velocity, however, is a vector. A correct velocity contains a magnitude and direction. Vector considerations can be very technical, but some examples are rather simple.Both velocity and acceleration are vectors. If a problem states that a ball is launched upward with an initial velocity of 10 meters per second, it is giving you the magnitude and direction. Acceleration due to gravity in earth is 9.8 m/s^2 at the earth’s surface and always pulls toward the earth. But you must be careful here.Note here that acceleration OPPOSES the initial velocity in this case. When you launch a ball upward, the acceleration due to gravity goes against that initial velocity.What is the velocity? If you say it’s 10 m/s, then acceleration is -9.8 m/s^2. If you say that acceleration due to gravity is 9.8 m/s^2, then the initial velocity is -10 m/s. How your conventions here are defined is up to you, but the two quantities are of opposite sign.Another example to paint a picture would be, “two cars collide. Car 1 was travelling 10 meters / second while car 2 was travelling 15 m/s. Describe the situation.”You can’t. How did they collide? Head on? Did car 2 rear-end car 1? Did they hit at right angles? Here, you would need their speeds and their directions, hence, their velocities, to accurately describe what happened.
What are some good calculus of vector-valued functions books (I don't want links)?
I always like to start with Dover books because they are easy to get and not too expensive so I would first recommend Vector Calculus by Peter Baxandall and Hans Liebeck.This book ranges from very elementary information for an undergrad taking calc 3 to a good resource for a graduate student needing review.If you want a good introductory book that is more of a standard textbook with nice graphics then I would check outMultivariable Calculus by Ron Larson and Bruce Edwards.
Calculus 3 Vector-Valued Function Question?
s(t) = ∫(x = 0 to t) ||r'(x)|| dx ......= ∫(x = 0 to t) ||<4 cos x, -4 sin x, 3>|| dx ......= ∫(x = 0 to t) 5 dx ......= 5t. Since s = 5t, we have t = s/5. So, parameterizing C in terms of s yields r(s) = <4 sin(s/5), 4 cos(s/5), 3s/5>. I hope this helps!
What is vector calculus?
I’m going to guess a simple answer is wanted (rather than some of the more “complicated” answers already given):Calculus is usually referred to ‘single variable calculus’ which is essentially calculus on a line (1 dimensional). Typical setting is you want to understand/approximate some function as its input variable changes a little. For example, one can look at how an object moves on a line under some force.Vector calculus upgrades (single variable) calculus to 3 dimensions. This is very natural for applications because the world we know it (with our eyes and hands) is 3 dimensional. In this vector calculus framework, we can look at how an object moves in 3 dimensional space (left/right, up/down, forwards/backwards) under some force acting possibly on all 3 dimensions. This framework allows one to look at rotations (of objects - so useful in computer graphics and physics say) which does not really have a counterpart in one dimensions.Vector calculus courses, like its single variable courses, studies relationships and results when one works in 3 dimensional space. The classic “fundamental theorem of calculus” for single variable can be upgraded to vector calculus.
Derivative vector function help calculus?
r = ta X (b+tc) = t( a X b ) + t²( a X c ) dwrt “t” : r' = ( a X b ) + 2t( a X c ) a X b = ( 1, 4, 2 ) X ( −1, 5, −2 ) = ( −18, 0, 9 ) a X c = ( 1, 4, 2 ) X ( 3, 1, 5 ) = ( 18, 1, −11 ) ∴ r' = ( −18, 0, 9 ) + 2t( 18, 1, −11 ) = ( −18+36t, 2t, 9−22t )
What are calculus and vector calculus?
Calculus is a branch of mathematics which deals with the change. Change means like instantaneous rate of change and all that. Limits and continuity forms the backbone of Calculus. Integration and differentiation are essentially derived from derived from these two.On the other hand vector calculus is an advanced form of Calculus. It is basically part of multivariable Calculus. You can say that in single variable calculus you take function of one variable which means you have liit x goes to two like that. In multivariable calculus you have both X and Y goes to some number i.e limit (x,y) goes to (1,2) like that. In vector calculus you have vector fields to deal with. Vector fields are nothing fancy. For example you know Earth is gravitational field and you also know about vectors that they represent magnitude and the direction. Soniye the earth Eros will be more longer than for from the Earth I mean in the space because gravitational field is more near the Earth then in the space. Hence this forms a vector field. Where you can plot all the arrows take x axis y axis plot all the arrows and their length and all that. Vector calculus deals with the vector function which I have just described now. You integrate vector function differentiate vector function just like you do for the normal functions. Other topics include divergence theorem, Stokes theorem, Green's theorem ,line integration, surface integration, and all that.To learn both calculus as well as vector calculus I recommend the following video lecturesThe Calculus Lifesaver
Is grade 12 Vectors and Calculus harder or Advanced functions?
Hi im trying to get into university of Toronto for Kinesiology. And i require Biology and either Vectors or Advanced Functions. I am currently in grade 11 and has only taken grade 11 mixed functions math. I have no room in my years to take grade 11 university math to prepare me . Which math course is more easier for myself not being that good at math (70%) Vectors or Advanced functions?(UNIVERSITY)
Where can I exercise calculus of functions with vectors and matrices in machine learning?
Question is not really clear but still see if the 2 links help. Page on ImmMatrix Manual: Matrix Calculus