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Combined display of all available logs of Applied Science. You can narrow down the view by selecting a log type, the username (case-sensitive), or the affected page (also case-sensitive).

• 15:53, 26 July 2022 0kelvin talk contribs uploaded File:Longdivision example pt.png
• 12:47, 26 July 2022 0kelvin talk contribs created page Propriedades dos logaritmos (Created page with "Definimos <math class="big">b^n = a</math> como um número <math>b</math> elevado a <math>n</math> que é igual a <math>a</math>. Com zero elevado a zero indefinido. O logaritmo é definido como <math class="big">\log_{b}a = n</math>. Isto é, um número <math>a</math>, na base <math>b</math>, tal que <math class="big">b^n = a</math>. Com a exponenciação queremos encontrar o resultado das multiplicações. Com o logaritmo queremos encontrar o número de multiplicaçõ...")
• 19:03, 25 July 2022 0kelvin talk contribs created page Completamento de quadrados e a fórmula de Bháskara (Created page with "O completamento dos quadrados é melhor entendido com uma interpretação geométrica. Primeiro me permita mostrar a figura: <div style="text-align:center;"> 200px </div> A associação gráfica é bem clara. O que não fica tão óbvio muitas vezes é o fato de que <math>(a + b)^2</math> pode ser visto de maneira literal. Todo o quadrado tem lados cujo comprimento é a soma de dois lados menores<math>a</math> e <math>b</math>. A ideia do...")
• 18:30, 25 July 2022 0kelvin talk contribs created page Propriedades das potências (Created page with "Numa aula de métodos numéricos um professor me disse que a adição é uma função. Se você prestar atenção, uma potência é uma função. Estamos juntando um número, um outro número e produzindo um terceiro a partir dos anteriores. A adição faz o mesmo. Traçar o gráfico de <math class="big">a^x</math> ajuda a ver as potências como funções. * <math class="big">a^m \cdot a^n = a^{m \ + \ n}</math>. Por quê não <math class="big">a^{m \cdot n}</math>? Pr...")
• 19:27, 23 July 2022 0kelvin talk contribs created page Propriedades do valor absoluto (Created page with "Todos aprendemos na escola que um número só pode ser positivo ou negativo, com os positivos não precisando de um sinal de mais porque é um padrão adotado no mundo. Sempre assumimos que um número sem o sinal é positivo. Agora os livros e os professores que eu tive na escola sempre diziam que o módulo ''"apaga"'' o sinal. Eu sempre achei esta operação sem sentido porque se um número não tem sinal, então ele não é nem positivo e nem negativo? O que ele é?...")
• 19:16, 23 July 2022 0kelvin talk contribs created page Resolvendo equações (Created page with "Qual o significado de resolver uma equação? Qual o significado de achar as raízes de uma equação? Numa interpretação geométrica, se temos dois quadrados iguais um ao outro e um deles tem uma variável controlando o seu lado ou área, resolver a equação significa encontrar o valor da variável que faz ambos os quadrados terem a mesma área ou lado. Se a equação representa uma função, pode ser o caso de achar uma distância mínima, energia máxima ou um inst...")
• 17:48, 23 July 2022 0kelvin talk contribs created page Propriedades das raízes (Created page with "A associação entre raiz quadrada e quadrados é natural. A raiz cúbica é associada com cubos e não há maiores complicações até aí. Com dimensões maiores perdemos a visualização geométrica e temos que nos contentar com a álgebra. <div style="text-align:center;"> 500px </div> A relação entre <math>a^2</math> e <math>\sqrt{a}</math> é a mesma que entre a exponencial e o logaritmo, um é o inverso do outro. Toda que temos um n...")
• 17:48, 23 July 2022 0kelvin talk contribs created page File:Root square2 pt.png
• 17:48, 23 July 2022 0kelvin talk contribs uploaded File:Root square2 pt.png
• 17:47, 23 July 2022 0kelvin talk contribs deleted page File:Root square pt.png (Deleted old revision 20220724004719!Root_square_pt.png)
• 17:47, 23 July 2022 0kelvin talk contribs uploaded a new version of File:Root square pt.png
• 17:43, 23 July 2022 0kelvin talk contribs created page File:Root square pt.png
• 17:43, 23 July 2022 0kelvin talk contribs uploaded File:Root square pt.png
• 15:50, 22 July 2022 0kelvin talk contribs created page Erros cometidos com álgebra (Created page with "Muitos dos erros cometidos em Cálculo se originam em erros de álgebra. Quase todos os livros de cálculo tem no começo uma parte dedicada às propriedades dos números reais. Não é preciso fazer todas as demonstrações. Mas é importante lê-las pelo menos uma vez porque muitos dos erros cometidos em operações com funções frequentemente se originam em erros com operações com os números reais. Há um problema, que eu não sei a causa, nas escolas que é dar...")
• 15:09, 22 July 2022 0kelvin talk contribs created page Erros cometidos em demonstrações (Created page with "Eu tive uma professora de álgebra linear que repetia diversas vezes '''"Se você escrever 0 = 0 na prova eu vou te dar um zero!"'''. Uma das operações mais comuns é multiplicar ambos os lados da equação por um número. Porém este número não pode ser o zero porque senão estaremos assumindo que 0 = 0. <math>a^x = a^y \iff x = y</math>. Suponhamos que escrevemos <math>a^x - a^y = a^y - a^y \iff x - y = y - y</math>. Portanto, <math>x - y = 0 \iff x = y</math>. H...")
• 11:42, 22 July 2022 0kelvin talk contribs created page Algebra-pt (Created page with "* '''Demonstrações''' <div style="width:100%; float:left; padding-bottom:1.5em;"> <div style="width: 50%; float:right;"> </div> <div style="width: 50%; float:lef;"> * Erros cometidos em demonstrações </div> </div> * '''Algebra e propriedades''' <div style="width:100%; float:left; padding-bottom:1.5em;"> <div style="width: 50%; float:right;"> * Propriedades das raízes * Propriedades do valor absoluto * Completamento de quadrados e a fórmula de Bháska...")
• 20:21, 29 May 2022 0kelvin talk contribs created page Principal (Created page with "Eu não tenho um diploma.")
• 13:31, 22 May 2022 0kelvin talk contribs created page File:Max min theorem2.png
• 13:31, 22 May 2022 0kelvin talk contribs uploaded File:Max min theorem2.png
• 11:22, 22 May 2022 0kelvin talk contribs created page File:Max min theorem.png
• 11:22, 22 May 2022 0kelvin talk contribs uploaded File:Max min theorem.png
• 20:25, 21 May 2022 0kelvin talk contribs created page Finding critical points of a multivariable function (Created page with "In the same way we have to rely on derivatives to find critical points of a single variable functions, we have to rely on partial derivatives to find critical points of a multivariable function. The idea of looking for points were we have horizontal tangent lines or zeroes of a function remains the same for multivariable functions. <div style="text-align:center; background-color: #f8f9fa; padding:1em;"> Let <math>f</math> be a function with a domain <math>D</math>. <mat...")
• 18:37, 18 May 2022 0kelvin talk contribs created page Finding extreme values of a multivariable function (Created page with "The general idea is analogous to single variable functions. Whether we are discussing the function's domain or a subdomain of it, we have to use derivatives to analyse how the function behaves to know whether a point is a maximum or a minimum. For two variables the idea is the same as for one variable, in a certain interval the function ca be constant, crescent or decrescent. For three and more variables we lose the function's graph, but the algebra is the same.")
• 18:50, 8 May 2022 0kelvin talk contribs created page Chain rule for multivariable functions (Created page with "With a single variable function the chain rule tells us that <math>[f(g(x))]' = g'(x)f'(g(x))</math>. For multivariable functions the idea is the same, it's still a product of derivatives. Both functions have to be differentiable for the chain rule to work.")
• 10:40, 8 May 2022 0kelvin talk contribs created page File:Normal line.png
• 10:40, 8 May 2022 0kelvin talk contribs uploaded File:Normal line.png
• 18:14, 6 May 2022 0kelvin talk contribs created page Linear approximation for two variables (Created page with "To approximate a function of two variables with a tangent plane is the natural extension of approximating a function of one variable with a tangent line. In the same way that zooming in a function of one variable makes it render closer to a straight line, with a tangent plane we see that the level curves become closer to straight parallel lines if we zoom in enough. <div style="text-align:center;"> 600px ''(not to scale)'' </...")
• 14:24, 6 May 2022 0kelvin talk contribs created page File:Linear approximation example2.png
• 14:24, 6 May 2022 0kelvin talk contribs uploaded File:Linear approximation example2.png
• 13:25, 1 May 2022 0kelvin talk contribs created page File:Differentiability condition.png
• 13:25, 1 May 2022 0kelvin talk contribs uploaded File:Differentiability condition.png
• 15:39, 28 April 2022 0kelvin talk contribs created page A sufficient condition for differentiability for many variables (Created page with "From a graphical perspective, when the derivative of a single variable function is continuous at a point, we can safely assume that the function is differentiable there. This is a mathematical way of defining the "smoothness" of a function. The same concept can be extended to multivariable functions. If the partial derivatives are continuous, the function is differentiable. This theory is a shortcut, a tool, to be used when we want to find whether a function is different...")
• 17:31, 22 April 2022 0kelvin talk contribs created page Conditions for differentiability for many variables (Created page with "For single variable functions we learn that being differentiable implies in being continuous. We also learn that being continuous doesn't imply in being differentiable because there are some exceptions to the rule. For multivariable functions differentiability also requires continuity, but we also have specific cases where we can calculate partial derivatives while the function is also discontinuous at a point. <math>f(x) = |x|</math>. This single variable example shows...")
• 12:17, 22 April 2022 0kelvin talk contribs created page Commented exercises (Created page with "* '''The two algorithms below attempt to calculate xn. However, both are wrong, explain the error in each one:''' <div style="margin-left:1.5em;"> {| class="wikitable" |<div class="code">for (i = 1; i <= n; i++) x = x * i;</div> || It's successively multiplying by an increasing counter. For x = 4, we have 4 * 1 * 2 * ... * n |- |<div class="code">for (i = 0; i < n; i++) x = x * x;</div> || It's squaring the number over and over n times. For x = 4, we have 42, then 162, t...")
• 11:14, 22 April 2022 0kelvin talk contribs created page Programming practices (Created page with "Some recommendations and small programming techniques are employed in the introduction. They are small details that do not determine whether you pass or fail, but are useful for learning purposes anyway. <div style="text-align:center;"> '''Comments''' </div> * All teachers recommend that you comment your programs, both because that counts for grading of the programming exercises, as well as because that makes your code more accessible for other people, or even yoursel...")
• 09:39, 22 April 2022 0kelvin talk contribs created page Characters and strings (Created page with "It's a common practice to teach how to use characters only after teaching how to operate with numbers and variables. This is done because characters are represented by numeric codes. There is one fundamental concept about how computers work. Deep down the computer works by doing elementary logic operations. That's very hard or very easy to grasp depending on the person. It's unnatural to think on words with logical operations. The algorithms that deal with characters ar...")
• 08:14, 22 April 2022 0kelvin talk contribs created page Random numbers (Created page with "For this introductory level, random numbers are not studied. They show up when we need to test programs with random inputs. To study algorithms that generate random numbers or the mathematical theory behind them is not a subject to be discussed at this stage. Random numbers do not obey to any law or formula, therefore they are impossible to be generated by any computer running some algorithm. The numbers that we see are pseudo-random, numbers that have a law of formatio...")
• 08:01, 22 April 2022 0kelvin talk contribs created page Dynamic memory allocation (Created page with "When variables and functions are created they go in the computer's memory. At this introductory level we ignore how memory is managed. We are assuming that it is correctly allocated and deallocated by the operational system. There is a whole class of algorithms that deal with memory management that we won't go in detail at this time. '''There are many natural questions that arise when we think about how the operational system handles memory:''' ''"Where in the memory a...")
• 17:19, 21 April 2022 0kelvin talk contribs created page Search and sort (Created page with "In this introduction we study the most elementary algorithms for searching and sorting. They are less efficient, but are easier to understand. The faster ones rely on more advanced knowledge that is beyond the objectives of this course. There are some probability theories behind such problems but we skip those for now. The usual way to tech these algorithms is by showing a sequence of values and performing a search or sort operation by hand. After that we attempt to tra...")
• 07:25, 21 April 2022 0kelvin talk contribs created page Struct data ype (Created page with "There are many situations in which many variables are related to each other, with the values stored in each variable are pieces of information belonging to one object or entity. It would be desirable to have a way to store that information in a cohesive way, without having to resort to using many unique variables with their relationship achieved through some programmer's defined naming convention. Fortunately, we have '''structs''' to allow us to link different data type...")
• 19:31, 19 April 2022 0kelvin talk contribs created page Introduction to recursive functions (Created page with "In the introduction to functions' chapter we learned that, in computing, the definition of a function borrows the mathematical definition. We also learned that, much like in mathematics, a function can call another function. If you have wondered if a function can call itself, you were right and that's called recursion. The question about recursive algorithm's performance vs non recursive algorithms is not studied in this course, that is left for later disciplines. For no...")
• 17:57, 19 April 2022 0kelvin talk contribs created page Functions, structs and pointers (Created page with "Pointers to struct provide a convenient way to access struct's members. The concept of pointers to struct is the same as pointer to any other variable: we first have to declare the variable and the pointer to it, then make the pointer point to that variable's memory address. The advantage of using pointers to structures is that in case we have a function that does something which requires data from a struct we don't have to pass all the struct's values to the function, j...")
• 13:23, 19 April 2022 0kelvin talk contribs created page Introduction to pointers (Created page with "In the simplest exercises and examples, about conditional structures, loops, arrays and matrices and functions, a pointer was not required to solve the problem. In some occasions the pointer showed up, like in the case of scanf() function, but the details about how it works were omitted to simplify and maker it easier to understand. Can a function calculate two values and return both? Calculate two different values yes, but return both no. That's when we need pointers....")
• 11:26, 19 April 2022 0kelvin talk contribs created page Functions that return a struct (Created page with "* '''Function that returns both roots of a second degree polynomial equation:''' <div class="code"> <span class="codecomment">Struct to store two values: </span><br /> struct roots { float x1, x2; }; <span class="codecomment">Function that receives the coefficients a, b and c and returns the roots of the second degree polynomial (it doesn't cover the case of a negative delta): </span><br /> Quadratic (int a, int b, int c) {<div style="margin-left:1.5em;"> struct...")
• 10:56, 19 April 2022 0kelvin talk contribs created page Functions, arrays and matrices (Created page with "After learning how to use functions, arrays and matrices, it's time to learn how to use arrays and matrices as function's parameters. A matrix with 10 columns and 10 rows can store up to 100 values, but a function doesn't make 100 calls when we use that matrix in that function. We can have a function with 100 parameters, but if they are all part of a matrix it's much simpler to just use the matrix and then reference to it by a single name. To explain why matrices and ar...")
• 18:26, 18 April 2022 0kelvin talk contribs created page Introduction to functions (Created page with "It's not really avoidable, functions in a program are analogous to functions in mathematics. During high (secondary) school we learn that <math>f(x) = x^2</math> is a function. Each <math>x</math> is associated with <math>x^2</math>. You should be familiar that a function can only be a function if, for each <math>x</math>, there is only one corresponding <math>y</math>. From the mathematical definition: a function can have different parameters and return the same result...")
• 07:52, 18 April 2022 0kelvin talk contribs created page Arrays and matrices (Created page with "''For some reason, in portuguese, the word "vetor" (vector in english) means both vector, the mathematical object, and array, the computing object. In C a matrix is a matrix for the user and the programmer who is not dealing with pointer arithmetic, but when pointer arithmetic is exposed, a matrix turns out be an "array of array".'' In the beginning of the introduction to computing discipline we learn what's the use of arrays and how to use one. The mathematical side of...")
• 06:52, 18 April 2022 0kelvin talk contribs moved page Repetition structures to Loops and repetition without leaving a redirect
• 06:43, 18 April 2022 0kelvin talk contribs moved page Iteration structures to Repetition structures without leaving a redirect
• 19:03, 17 April 2022 0kelvin talk contribs created page Iteration structures (Created page with "''"Computers never get tired and never complain"'' - Cute joke that my teacher used to make during the classes Initially, when we learn how to use loops, we don't worry about the performance of the algorithms. To study the performance of algorithms is left to later, more advanced, disciplines, where search or sorting algorithms are studied. However, we can already think about performance like this: one extra iteration and our algorithm is slower than another algorithm t...")