LarCalc9_ch04_sec1
... many solutions (each differing from the others by a constant). This means that the graphs of any two antiderivatives of f are vertical translations of each other. ...
... many solutions (each differing from the others by a constant). This means that the graphs of any two antiderivatives of f are vertical translations of each other. ...
CUSTOMER_CODE SMUDE DIVISION_CODE SMUDE
... We need numerical integration techniques in the following situations: 1. Functions do not possess closed form solutions. 2. Closed form solutions exist but these solutions are complex and difficult to use for calculations. 3. Data for variables are available in the form of a table, but no mathematic ...
... We need numerical integration techniques in the following situations: 1. Functions do not possess closed form solutions. 2. Closed form solutions exist but these solutions are complex and difficult to use for calculations. 3. Data for variables are available in the form of a table, but no mathematic ...
Note-Taking Guides
... Now it's your turn to identify linear equations from looking at the equations. Determine if each is a linear equation. If one is not a linear equation, explain why. 1) x + y = 6 2) xy = 10 3) x2 + y2 = 1 ...
... Now it's your turn to identify linear equations from looking at the equations. Determine if each is a linear equation. If one is not a linear equation, explain why. 1) x + y = 6 2) xy = 10 3) x2 + y2 = 1 ...
PowerPoint slides
... Consider the boy’s reasoning when he says: “There’s two pears and a lemon and there’s two pears and an orange – that means a lemon is seven greater than an orange.” Work through the problem on the following slide and consider the strategies you would use to solve the problem. ...
... Consider the boy’s reasoning when he says: “There’s two pears and a lemon and there’s two pears and an orange – that means a lemon is seven greater than an orange.” Work through the problem on the following slide and consider the strategies you would use to solve the problem. ...
4.NF.4 Task 5 - 3-5 Formative Instructional and Assessment Tasks
... addition equation that totals 10/3 (2/3 + 2/3+2/3+2/3+2/3).They show the sum on a number line as five ‘jumps’ of 2/3 or as an area model, and clearly explain how the model matches their addition equation. Part 2: Student writes a correct multiplication equation 2/3 x 5 = 10/3). They show the total 1 ...
... addition equation that totals 10/3 (2/3 + 2/3+2/3+2/3+2/3).They show the sum on a number line as five ‘jumps’ of 2/3 or as an area model, and clearly explain how the model matches their addition equation. Part 2: Student writes a correct multiplication equation 2/3 x 5 = 10/3). They show the total 1 ...
Lecture notes for Section 2.1
... When we want to visually summarize all the possible answers to an equation, we graph the equation. The easiest way to do this is to calculate a few points by hand, and then plot those points on a graph. Usually, it is easy enough to “connect the dots” to fill in the rest of the graph. One thing to r ...
... When we want to visually summarize all the possible answers to an equation, we graph the equation. The easiest way to do this is to calculate a few points by hand, and then plot those points on a graph. Usually, it is easy enough to “connect the dots” to fill in the rest of the graph. One thing to r ...
Equation
In mathematics, an equation is an equality containing one or more variables. Solving the equation consists of determining which values of the variables make the equality true. In this situation, variables are also known as unknowns and the values which satisfy the equality are known as solutions. An equation differs from an identity in that an equation is not necessarily true for all possible values of the variable.There are many types of equations, and they are found in all areas of mathematics; the techniques used to examine them differ according to their type.Algebra studies two main families of equations: polynomial equations and, among them, linear equations. Polynomial equations have the form P(X) = 0, where P is a polynomial. Linear equations have the form a(x) + b = 0, where a is a linear function and b is a vector. To solve them, one uses algorithmic or geometric techniques, coming from linear algebra or mathematical analysis. Changing the domain of a function can change the problem considerably. Algebra also studies Diophantine equations where the coefficients and solutions are integers. The techniques used are different and come from number theory. These equations are difficult in general; one often searches just to find the existence or absence of a solution, and, if they exist, to count the number of solutions.Geometry uses equations to describe geometric figures. The objective is now different, as equations are used to describe geometric properties. In this context, there are two large families of equations, Cartesian equations and parametric equations.Differential equations are equations involving one or more functions and their derivatives. They are solved by finding an expression for the function that does not involve derivatives. Differential equations are used to model real-life processes in areas such as physics, chemistry, biology, and economics.The ""="" symbol was invented by Robert Recorde (1510–1558), who considered that nothing could be more equal than parallel straight lines with the same length.