Section 1-4 -- Trapezoid Rule
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The document discusses using the trapezoidal rule to evaluate definite integrals by approximating the area under a curve between bounds with trapezoids. It explains that the trapezoidal rule is a more exact method than counting squares. To use the rule, the integral bounds are divided into trapezoids, the function is evaluated at the endpoints, and the areas are calculated by multiplying the average base by the height and summing the results, with endpoints weighted by one half.
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Data analysis,Grouped-Ungrouped data,Mean,Median,Mode,Percentile,Standard Deviation,Variance,Frequency Distribution Graphs,Corelation
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Integration
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Es272 ch6
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Numerical integration
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This document provides an introduction to and overview of engineering mathematics for the GATE exam. It aims to give GATE aspirants basic knowledge of topics like linear algebra, calculus, differential equations, and probability and statistics. The author advises students to review the syllabus and previous questions for their specific paper to understand what depth of topics is required. The book contains solved problems from past papers of popular branches but is still a work in progress. Readers are asked to provide feedback to the author.
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Numerical integration
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Matlab lecture 7 – regula falsi or false position method@taj
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This lecture is from my class lectures in IIT-JU.
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The document discusses several numerical methods for finding the roots or zeros of equations:
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Lecture 17 M4.pdf
1) Several methods are described for calculating the area of land from surveying data, including graphical, instrumental, and computational methods using field notes.
2) Computational methods include dividing the land into geometric shapes and calculating the area of each shape. Common shapes are triangles, squares, rectangles, and trapezoids.
3) Areas can be calculated from plotted plans using methods like dividing the land into triangles and calculating each triangle's area, or dividing the land into squares of equal size and counting the number of squares.
AOT3 Multivariable Optimization Algorithms.pdf
This document provides an overview of multi-variable optimization algorithms. It discusses two broad categories of multi-variable optimization methods: direct search methods and gradient-based methods. For gradient-based methods, it describes Cauchy's steepest descent method, in which the search direction at each iteration is the negative of the gradient to find the direction of maximum descent. It also introduces the simplex search method as a direct search method that manipulates a set of points to iteratively create better solutions without using gradients.
April 8, 2015
This document provides information about graphing parabolas from quadratic functions, including key points such as:
- The x-intercepts, axis of symmetry, and vertex of a parabola.
- How to find the axis of symmetry using the formula x = -b/2a and the vertex by substituting the x-coordinate back into the original equation.
- Whether the parabola opens up or down depends on if the leading coefficient a is positive or negative.
- Examples of finding the axis of symmetry and vertex for various quadratic functions are provided.
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Variance and standard deviation are measures of spread used to describe the shape of distributions associated with the mean. While two distributions may have the same mean, their variance and standard deviation can show that they have very different shapes. To calculate variance and standard deviation, you first find the deviation of each value from the mean, square the deviations, and sum them. You then divide the sum by n-1 to get the variance, and take the square root of the variance to find the standard deviation.
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Section 1-4 -- Trapezoid Rule
- 1. The Trapezoidal Rule Evaluating definite integrals by counting squares can be a rather tedious and inexact process. There is a more exact way to estimate the value, using the area of trapezoids. We will use the trapezoidal rule to evaluate the definite integral of with respect to x , from x = 0 to x = 6
- 2. x y 0 1 2 3 4 5 6 To find the area of the trapezoids, we need to find the lengths of their bases. We can make a chart: Trapezoid 1: Trapezoid 2: Trapezoid 3: Trapezoid 4: Trapezoid 5: Trapezoid 6: