calculus for idiots

Calculus learning turning? It's a strange story. In fact, Calculus, like a car, turns slowly. In November 11, 1675, German mathematician Leibniz wrote the points and differential symbols in his notebook: Attention and D. This was the beginning of calculus. He insisted that differential dx is an infinitely small number (infinitesimal), So he developed paradoxing p

Rudin's This "functional analysis" is really not very good to read, in general, because the books in the details of the place is indeed too much, not very good grasp. I look at this book with the purpose of learning operator algebra, so I don't want to fall into the function space, especially the Fourier transformation problem associated with it, soAfter studying the relevant knowledge about the topological and space, the local convex space and the completeness, I studied the last three chapters

3-idiotsTime limit:10000/5000 MS (java/others) Memory limit:32768/32768 K (java/others)Total submission (s): 3560 Accepted Submission (s): 1241Problem Description King OMeGa catched Three men who had been streaking in the street. Looking as idiots though, the three men insisted that it is a kind of performance art, and begged the king to free them. Out of hatred to the real idiots, the king wanted to check

The mean value theorem for definite integrals:The definition of the integral itself is simple, but in the teaching process people often remember only its calculation method, in the introduction of the concept of integral, often it is tightly tied to the calculation method, in fact, in the simple definition of integrals, the basic theorem of calculus tells us the calculation method of integral.Basic theorem of calculus:Can see, it is based on such a ba

Original article link "If people don't believe in the simplicity of mathematics, they just don't realize the complexity of life ." -- Johnvon norann Dec mainly discusses extra points in discrete situations, which are used in the computer field. We know that it is impossible to use a computer to process geometric images completely smooth (the computer is a discretization world consisting of 0 and 1 ), the concept of Dec also provides us with a better tool to portray discrete ry. For example,

1. Differential Application 1.1 Differential 1.1.1 monotonicity, extremum and asymptote of unary functionThe derivative gives the direction of the function, which is very useful for the graphical properties of our analytic functions, and here we use the knowledge of calculus to understand the nature of the function. The effect of the first derivative on the function is the most direct one, where first-order derivative is seen. For the constant functio

Long) (T1[i].real () +0.5); theLc=Len; - }Wuyi intMain () { the intT; -scanf"%d",T); Wu while(t--){ -scanf"%d",n); About for(intI=1; i"%d",a[i]); $mxnum=0; - for(intI=1; iStd::max (Mxnum,a[i]); - for(intI=1; i; - intLC; AMul (a,mxnum+1, b,mxnum+1, C,LC); + for(intI=1; i2]--; the for(intI=1; i2; i++) c[i]/=2; -sum[0]=0; $ for(intI=1; i2; i++) thesum[i]=sum[i-1]+C[i]; theStd::sort (A +1, A +1+n); thell ans=0; the for

)Const{ returnComplex (r-a.r,i-A.I); } Complexoperator*(ConstComplex a)Const{ returnComplex (r*a.r-i*a.i,r*a.i+i*A.R); }};voidChange (complex x[],intLen) { inti,j,k; for(i=1, j=len/2; i1;++i) { if(ij) Swap (X[i],x[j]); K=len/2; while(j>=k) {j-=k;k>>=1;} if(jK; }}voidFFT (complex x[],intLenintOn ) {Change (X,len); for(intI=2; i1) {Complex wn (cos (-on*2*pi/i), sin (-on*2*pi/i)); for(intj=0; ji) {Complex W (1,0); for(intk=j;k2;++k) {Complex U=X[k]; Complex T= w*x[k+i/2]; X[K]=u+

Discussion-how to promote LINUX in China? How can we make it available to almost computer idiots? -- Linux general technology-Linux technology and application information. For details, refer to the following section. Discussion-how to promote LINUX in China? How can we make it available to almost computer idiots? The biggest problem with LINUX is ease of use. If a person with a low computer level can use

Machine. Why is this definition? Because they follow the Java Virtual Machine specification, is Dalvik VM a Java Virtual Machine? It is estimated that only the author of the book you read thinks so" Later, the debate began on the proposition that "is Dalvik a Java Virtual Machine. It reminds me of the white horse and non-Horse Theory. "Seeking horses and black horses can both be done. Seeking white horses and black horses cannot be done ". However, some of his statements are worthy of recogniti

{ returnComplex (r*t.r-i*t.i,r*t.i+i*T.R); }}x1[500100];voidFFT (Complex y[],intNintrev) { for(intI=1, j,k,t;i){ for(j=0,k=n>>1, t=i;k;k>>=1, t>>=1) j=j1|t1; if(ij) Swap (Y[i],y[j]); } for(ints=2, ds=1; s1) {Complex WN=complex (cos (rev*2*pi/s), sin (rev*2*PI/S)), W=complex (1,0), t; for(intk=0; kWN) { for(inti=k;is) {T=w*y[i+DS]; Y[i+ds]=y[i]-T; Y[i]=y[i]+T; } } } if(rev==-1) for(intI=0; iN;}Long LongTemp,ans;intMain () {inti,j,k,t,n,m; while(SCANF (

); - for(intI=0; i) AAns[i]=a[i].real () +0.5; + } the intMain () - { $ inttest; thescanf"%d",test); the while(test) the { thetest--; -scanf"%d",n); inL=0; theMemset (A,0,sizeof(a)); thememset (b,0,sizeof(b)); About for(i=1; i) the { thescanf"%d",v); thec[i]=v; + intQ=a[v].real () +1; - a[v].real (q); the b[v].real (q);BayiL=Max (l,v); the } thelen=1; - while(len2) len*=2; - Conv (A,b,len); the for(i=1; i) theans[c[i]+c[i]]--; the for(i=0; i)

Description King OMeGa catched Three men who had been to the street. Looking as idiots though, the three men insisted that it is a kind of art, and performance the king to free begged. Out of hatred to the "real idiots", the king wanted to check if they were lying. The three men were sent to the king's forest, and each of them is asked to pick a branch one after another. If the three branches they bring ba

Document directory 2.1 variables and functions 2.2 functions and Calculus 2.3 limit and Calculus 3.1 micro-Learning 3.2 points 5.1 law of opposites 5.2 examples of corresponding points Now we have started a round of postgraduate mathematics review, using the sixth edition of Tongji higher mathematics. For postgraduate entrance exams, it is a good teaching material, and all the knowledge points a

It seems to us that calculus is called "decentralization" in secondary school, but in the Russian context it is necessary, not "decentralized", to teach calculus at the secondary level. This is why. Let's get things straight, and we can't just talk. According to the research of the School of Mathematics Science of Beijing Normal University, the course of "algebra and Mathematical Analysis preliminary" in 10

In 1960 Abraham Robinson (1918-1974) solved the three hundred year old problem of giving a rigorous development of the calculus based on infinitesimals. Robinson's achievement was oneThe major mathematical advances of the twentieth century. This is an exposition of Robinson's Infinitesimal calculus at the advanced undergraduate level. It is entirely self-contained but is Keyed to the 2000 digital edition of

Relational calculus: based on predicate calculus in mathematical logicDifferent classification by predicate variable1. Tuple Relationship calculus:Primitive objects with tuple variables as predicate argumentsTuple Relationship Calculus Language alpha2. Domain Relational calculus:Base object with domain variable as predicate argumentDomain Relational

In our country, calculus textbooks often say the basic theorem of calculus is "Newton-" Leibniz formula, and the spirit of the theorem is avoided. In essence, the core idea of this important theorem is that the numerical calculation of definite integral can be replaced by the technique of "symbolic integration", which saves a lot of numerical cost. The first part of the theorem proves the existence of the o

When it comes to calculus, everyone is unfamiliar, and people who go to college are basically the ones who have been on it, and countless people are hanging on that tall tree every semester ... Liberal arts students in the "University of Mathematics" in the look of its face, engineering students in the "higher mathematics" and it met, and science students in the "mathematical analysis" see its true colors. But to tell the truth, compared with other ab

Recently more idle, intend to tidy up the previous study on the language of the program knowledge. The main content is to design the program language while writing the interpreter to implement it. This knowledge is essentially derived from programming Languages and Lambda calculi and essentials of programming Languages these two books. I remember the high School Olympiad training when the teacher said: "To solve problems must grasp the definition." "As with programming and reconciliation questi