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Bearing Capacity of a Shallow Foundation Using ABAQUS

Engineering Dynasty

Engineering Dynasty

Bearing Capacity of a Shallow Foundation Using ABAQUS

Static Analysis of a Truss Using Abaqus

waves in horizontal layered half-space

Basic equations of elastic elastodynamic

Let X0=1, X2=4, X3=9, find the interpolation polynomial p(x) for the function y= √x in [1,9]

For the following data, find the least square approximation y=a+bx | Interpolation and Approximation

f(-2)=-5 f(-1)=-2 f(0)=3 f(1)=10 f(2)=19 f(3)=30. Find the interpolation polynomial p(x) for f(x)

Compute the integral by the trapezoidal rule and the Simpson's rule

Find the quadratic Lagrange interpolating polynomial p(x) an approximate f(1.5) using p(x)

Compute the integral by the trapezoidal rule and the Simpson's rule respectively.

Find root of x=e^(-x) near x=0.5 Such that the absolute error is less than | Simple Iterative Scheme

Can the Jacobi or the G-S method converge?

Use Newton's method & Modified Newton's mtd, Find the numerical approximation to the double root √2

Example on Iterative techniques for solving linear systems

How is the error of the solution x for Ax=b affected by A and b? | Norms of Vectors and Matrices

Let A=(1 0 0, 0 2 4, 0 -2 4), determine ||A||1, ||A||∞, ||A||2, p(A). Norms of Vectors and Matrices

Example 2 on Norms of Vectors and Matrices

Example on Norms of Vectors and Matrices

Find L1, L2, L0, norms of the vector x=(-1, 2, 4)^T | Norms and Vectors

Example on LU factorization with Partial Pivoting

Use Gaussian elimination to solve Ax=b | Gaussian elimination and matrix LU factorization

Which matrix has an LU factorization? and unique? Gaussian elimination and matrix LU factorization

Example. Round off error stability. Compute the integrals, 0 to 1 of x^/(x+5)dx, n=0,1,2,...,7.

Sparse matrix A, write its compression representation Triple & Orthogonal list

Compute the integrals, 0 to 1 of x^/(x+5)dx, n=0,1,2,...,7. Round off error stability

Example 8: error analysis for function value. Use five-digit arithmetic to compute x=63015 +...

Draw the Huffman Tree & design huffman codes for each character & calculate its WPL

Roots of x^2 - 16x + 1 = 0 are x1 = 8 + √ 63, x2 = 8 - √ 63. Use three-digit arithmetic, √ 63 ≈ 7.94

Transform the following forest to a binary tree

The digits of a1 a2 a3 are significant digits. Find the bound of the relative error of a1 + a2.a3.

Draw the binary tree and write its post order & level order traversal sequences

Norms of Vectors and Matrices

The bound of the absolute error for the numbers is 0.005, find the significant digits of each number

A weighted undirected graph, using Prim & Kruskal algorithm to construct its MST

Adjacency list representation for an undirected graph, perform DFS & BFS algorithm, spanning tree

Straight insertion sort, bubble sort, simple selection sort, heap sort, 2 way merge sort, radix, qui

Draw a Hash Table with linear probing, quadratic probing and separate probing

Perform a binary search, Draw the decisions tree, Calculate ASL with equal searching probability

Example 6: Find the significant digits of each number. Error analysis

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Example 5: Suppose that a is an approximation to x. Find its significant digits. Error analysis

Example 4: Find relative error and absolute error - Error analysis

Example 3: Find the bounds for the absolute and relative errors

Example 2: What is an efficient algorithm? Error analysis and round-off error stability

Example 1: Find the path of each snail | Error analysis and round off error stability

4.4 Applications of Interpolation | Interpolation and Approximation

4.3 Discrete Least Squares Approximation | Interpolation and Approximation

4.4 Applications of Interpolation - part 2 | Interpolation and Approximation

4.4 Applications of Interpolation - part 3 | Interpolation and Approximation

4.2.2 Newton Interpolation Formula - part 1 - Lagrange Interpolation

4.2.3 Remainder term of interpolation - Lagrange Interpolation

4.2.2 Newton Interpolation Formula - part 2 - Lagrange Interpolation

4.2.5 Piecewise interpolation by low degree polynomials - Lagrange Interpolation

4.2.1 Lagrange Interpolating Polynomials - Lagrange Interpolation

4.2.4 Hermite Interpolation - Lagrange Interpolation

4.1 Interpolation problem - Interpolation and Approximation

3.1.2 Convergence of iterative schemes - Iterative techniques for solving linear systems

3.2.1 Iterative techniques for solving nonlinear equations - Simple iterative schemes - part 2

3.2.2 Newton’s method ant its deformations - Iterative techniques for solving nonlinear equations

2.5 Norms of Vectors and Matrices - part 5

2.5 Norms of Vectors and Matrices - part 3

2.5 Norms of Vectors and Matrices

3.2.1 Iterative techniques for solving nonlinear equations - Simple iterative schemes

3.1.2 Convergence of iterative schemes - part 2 - Iterative techniques for solving linear systems

2.5 Norms of Vectors and Matrices - part 4

3.1.1 Simple iterative schemes - Iterative techniques for solving linear systems

2 5 Norms of Vectors and Matrices part 2

2 5 Norms of Vectors and Matrices - part 6

2.4 The triangular factorization of the tridiagonal matrices

2.3 Cholesky factorization for the symmetric and positive definite matrix

2.4 The triangular factorization of the tridiagonal matrices - part 2

2.3 Cholesky factorization for the symmetric and positive definite matrix part 2

2.2 Gaussian Elimination and LU factorization with Partial Pivoting

2.2 Gaussian Elimination and LU factorization with Partial Pivoting - part 2

2.2 Gaussian Elimination and LU factorization with Partial Pivoting - part 3

2.1 Gaussian elimination and matrix LU factorization - part 5 | Matrix factorization

2.1 Gaussian elimination and matrix LU factorization - part 4 | Matrix factorization