#3 Matlab scientific coding for engineers, students&science

Learn to initialize MATLAB matrices with zeros and ones, specifying size for efficiency. Use diag to build diagonal matrices and extract their main diagonal.

Construct a block diagonal matrix by placing matrices A, B, and C on the main diagonal using blkdiag, allowing zero elements elsewhere and differing block sizes.

Reshape a vector into a matrix with a chosen row–column layout using matlab's reshape function. Matlab fills columns first, so ensure the total elements remain the same, checked with size.

Explore Matlab functions flip left or right, flip up or down, and rotate 90 degrees to rearrange matrix columns and rows automatically.

Learn to build a 3x3 matrix in MATLAB by reshaping a vector, then extract the lower triangular part with tril and the upper with triu around the main diagonal.

Replicate a matrix in Matlab by tiling a pattern using repmat, stacking patterns vertically or horizontally, and understand how a single dimension can define both axes.

Explore matrix concatenation in Matlab by vertically or horizontally stacking matrices with cat, vertcat, horzcat, or square brackets, ensuring matching rows for horizontal and matching columns for vertical combinations.

Explore how to identify non-zero elements in matrices with MATLAB's any, all, and find functions. Learn to generate logical arrays, apply dimension-aware checks, and extract row and column indices.

Use MATLAB to build a magic matrix and apply logical indexing to find elements that exceed four, then compute their mean with mean(A(A>4)).

Learn how to sort vectors and matrices in MATLAB using sort to arrange elements in ascending or descending order, with duplicates preserved and sortrows to reorder rows.

Use MATLAB ismember to test if elements of one matrix appear in another, producing a logical array; then use find to locate the indices of common elements, including row-wise checks.

Learn how MATLAB's intersect finds common elements and their indices between two matrices, shows results and optional stable ordering to preserve original matrix order.

Discover how MATLAB setdiff compares arrays to show elements in one array not in another, with row options, sorting behavior, non-repeating results, and mention of intersect and ismember.

Explore Matlab cell arrays that store numbers, strings, and text using curly brackets. Visualize contents with cell plot and learn to access, modify, and delete cells, rows, or columns.

Demonstrate MATLAB cell arrays by contrasting parentheses and curly brackets for data type versus content, and convert the second column to numeric with cell2mat to compute the mean age.

Explore how to filter a company list by department using MATLAB string comparison and find, yielding a logical array to extract names and departments.

Explore how MATLAB structures organize data with labeled fields, create multi-field entries, and access information using dot notation and indexing, illustrated by a student records example.

Import grades from an Excel file, convert them into a structure, and compute the average grade for the course communication using find and strcmp in Matlab.

Learn to calculate limits in Matlab with symbolic expressions, defining x and the point of interest, using sin(x)/x as x approaches 0 and exploring infinity and left/right limits.

Explore Taylor and Maclaurin series as derivative-based infinite sums and build Taylor polynomials in Matlab with symbolic x, choosing center points and polynomial order.

Use Matlab's symbolic toolbox to define variables and compute sums and products. Evaluate finite and infinite sums and products with examples like 1 to 100, 1/k^2, and pi^2/6.

Compute cumulative sums from a vector x and extend to matrices by dimension, using MATLAB's cumsum to obtain running totals along rows or columns, including whole-vector sums.

Learn how to use Matlab loops, including for and while constructs, with loop variables and iterations, and apply them to tasks like displaying even numbers, while avoiding infinite loops.

Explore Matlab loops with for and while exercises that handle alternating signs and exponents, and build a function with two outputs: number of terms and the resulting sum until 10000.

Explore Matlab coding with loops: implement for and while loops to compute sums of odd numbers, powers, and alternating sign sequences, rename variables, and compare results with built-in functions.

Present the MATLAB solution to exercise 2 loops: a while loop sums alternating signed even terms until the sum reaches 10000, returning the number of terms and the resulting sum.

Learn Matlab coding for Fibonacci numbers, starting with 0 and 1, using a for loop to sum the two preceding values and display the sequence.

Compare using a for loop versus a while loop to calculate Fibonacci numbers in a Matlab script, emphasizing initialization, index handling, and increment rules.

Create a MATLAB Fibonacci function with a function header, input and output arguments, and a file name that matches the function name; unlike scripts, functions do not share base workspace.

Practice Matlab coding to compute the variance of a sequence for n from 2 to its length, using the mean and variance formula, and output these variances for data x.

Compute the variance as a function of n for a vector in MATLAB by iterating over n, updating the mean of the first n values, and using preallocation for efficiency.

Demonstrates calculating and drawing the Lorenz curve from a sorted income vector in MATLAB, using absolute, cumulative, and relative frequencies to visualize income distribution and inequality.

Plot the Lorenz curve for an equal distribution in MATLAB, ensuring the data runs from 0 to 100 and labeling axes as accumulated frequency and income percent.

Introduce Fourier transformation and show how signals become sums of sine and cosine in the frequency domain, with Matlab, then return via the inverse transform.

Explore building a Matlab function that generates a Fourier sound sample by summing sine components with amplitudes, using sampling rate and a limit-based stop, then plot.

Define a signal as the sum of two sine waves, sample it, and compute its Fourier transform with Matlab to reveal the half-spectrum and Nyquist-limited peaks.

Apply Newton's method to locate real roots of a function from an initial guess, iterating x_new = x_old - f(x)/f'(x), and implement with MATLAB function handles and symbolic differentiation.

Modify a MATLAB Newton's method to use a user-defined tolerance with a while loop, running until the absolute error falls below the tolerance, and compare iterations.

Apply Newton's algorithm to compute square roots with iterative updates x_{k+1} = 1/2(x_k + a/x_k). Implement tolerance-based stopping criteria, first |x^2 − a| ≤ epsilon, then |x_{k+1} − x_k| ≤ epsilon, for accuracy.