coursera calculus 1

any complex function, A is any element of Banach algebra B, in fact a^2 is obviously definable, generally, when f is a complex coefficient polynomial, according to B is a linear space on C and the multiplication defined on it, f (a) Definition is also clear, so when F is more complex, we also want to define an F (a).To give a simple example, for an arbitrary A to be B, we use a power series to define the e^a=∑a^n/n!, and to discuss whether the definition is meaningful only needs to discuss whet

length of the cell, the better the approximate degree; the better the approximation, the less it is. Therefore, in order to get the exact value of the area, we only need to subdivide the interval infinitely, so that the length between each cell tends to zero. If you remember, the length of each cell tends to be 0 of the price. Thereby (1) Three, the speed of linear movement of the distance To set an object as a straight line motion, the known velocit

What are machine learning?The definitions of machine learning is offered. Arthur Samuel described it as: "The field of study that gives computers the ability to learn without being explicitly prog Rammed. " This was an older, informal definition.Tom Mitchell provides a more modern definition: 'a computer program was said to learn from experience E with R Espect to some class of tasks T and performance measure P, if it performance at tasks in T, as measured By P, improves with experience E."Examp

interval.2. Function transformationHorizontal and Vertical transformations:Take y=ƒ (x) as an example:y=ƒ (x) +c, the function moves up the C distance;y=ƒ (x) –C, the function moves downward by a C distance;Y=ƒ (x+c), the function moves to the left of the C distance;Y=ƒ (x–c), the function moves the C distance to the right.Stretching, shrinking, and reflection transformations:Take y=ƒ (x) as an example:y=cƒ (x), the function stretches the C-fold in the vertical direction;y= (

x in T1 is replaced with T2.Example: (λx.x) y→y(λx.x (λx.x)) (u r) →u R (λx.x)"Because the abstract body:x (λx.x) on the left, only the first X is free. 】The term is called redex("reducible expression"), and the above rule overrides a redex, called Beta-reduction.Third, the Lambda-calculus evaluation strategy:1.full Beta-reduction:any Redex is reduced at any time.2.normal Order strategy: The leftmost and m

continuous. If the $x _0\not\in\bbq$, then to $\forall\ \ve>0$, to meet the $1/n\geq \ve$ of the $N $ only a limited number, while in $ ([x_0],[x_0]+1) $ can form into $M/n$\ ($M \in\bbz,\ 1/ N\geq \ve$) has only a finite number of rational numbers. Take $\delta>0$, so that the $U (X_0,\delta) $ does not contain these rational numbers, then $$\bex x\in U (X_0,\d

Week 1 Practice quizhelp Center Warning:the hard deadline has passed. You can attempt it, but and you won't be. You are are welcome to try it as a learning exercise. In accordance with the Coursera Honor Code, I certify this answers here are I own work. Question 1 Consider the instantiation of the vector space model where documents and queries are represented as

NTU-Coursera ml: HomeWork 1 Q15-20Question15 The training data format is as follows: The input has four dimensions, and the output is {-1, + 1 }. There are a total of 400 data records. The question requires that the weight vector element be initialized to 0, and then "Naive Cycle" is used to traverse the training s

(Paddle2_pos,1,'Blue',' White') #determine whether paddle and ball collide ifBall_pos[0] Pad_width:ifBALL_POS[1] >= paddle1_pos[0][1] andBALL_POS[1] ]: Spawn_ball (right)Else: Score2+ = 1ifBall_pos[0] >= Width-pad_width-Ball_radius:ifBALL_POS[1] >= paddle2_pos[0][

(stop_num)#define event handlers for buttons; "Start", "Stop", "Reset"defStart_handler (): Timer.start ()defStop_handler (): Timer.stop ()defReset_handler (): Timer.stop ()GlobalTGlobalt_str Reset_score ()#Define event handler for timer with 0.1 sec intervaldefTimer_handler ():GlobalTGlobalT_str T= t + 1T_str=format (t)defTimer_score_handler (): Update_score ()#Define Draw HandlerdefDraw_handler (Canvas): Canvas.draw_text (t_str, Position,36," White") Canvas.draw_text (SCORE_STR, [160, 20], 16,

]; - } - System.out.println (arrays.tostring (aux)); the intL = 0; - intR =N; - for(intk = 0; k){ - if(l >= N) Break;//The array of auxiliary elements is exhausted, and the right side of the array does not need to be shifted. + Else if(R>=2*n) array[k]=aux[l++];//all elements of the right element of array are placed in the appropriate position, then simply move the elements of the auxiliary array to the right of the array - Els

Original title:Given Arrays a[] and b[], each containing n distinct 2D points in the plane, design a subquadratic algorithm to count The number of points that is contained both in array a[] and array b[].The goal of the topic is to calculate the number of duplicate point, very simple, the code is as follows1 ImportJava.awt.Point;2 Importjava.util.Arrays;3 ImportJava.util.HashSet;4 ImportJava.util.Set;5 6 ImportEdu.princeton.cs.algs4.StdRandom;7 8 Public classplanepoints {9 PrivatesetNewHash