#2 Matlab intermediate for engineers, students & scientists

Learn to solve linear systems in MATLAB by forming the matrix A and the column vector b. Compute x using A \ b or inv(A)*b, and verify with A*x.

Use linsolve to solve a linear system by specifying A and B, then obtain the solution. Use the backslash operator (mldivide), which yields a similar result and benefits sparse matrices.

This lecture shows a non-unique solution with two equations and three unknowns, forming A and b, and demonstrates Matlab's solve yielding one solution while inverse fails for non-square matrices.

Explore the difference between scripts and functions in MATLAB, including m-files, input and output handling, and the function syntax with name and file rules.

Learn to define symbolic variables in MATLAB using syms or sym, enabling symbolic differentiation and integration of expressions like x^2+5x without assigning numeric values.

Define symbolic variables in Matlab, build expressions, and compute derivatives and indefinite integrals. Specify the differentiation or integration variable when multiple variables exist to avoid wrong results.

Explore how Matlab handles symbolic polynomial expressions and polynomial vectors, converting between forms, pretty-printing, factoring, and expanding to reveal roots.

Explore how Matlab's simplify and collect functions reduce a complex expression to a neat polynomial by gathering like terms for a clearer overview.

Learn to substitute values into symbolic variables in matlab using subs, by defining x and y and f = x + y, and specifying which variable gets value in order.

Plot symbolic expressions or symbolic functions with ezplot, avoiding double conversion. Set the x-range manually, such as -2 pi to 2 pi or -25 to 20, to reveal the function.

Learn to solve symbolic equations and systems with MATLAB's solve function, handling exponentials, nonlinear systems, and symbolic to numeric conversions.

Learn to collect user input in MATLAB using input, assign it to age, and display results with fprintf, using %d for integers and %.2f for floats, including newlines.

Create a MATLAB function that computes an aquarium's volume from user-entered height, width, and length in centimeters, converts to liters, and prints the result with guidance.

Master function handles and anonymous functions in MATLAB, creating handles and applying element-wise operations on vectors. Use the integral function to compute results from a function handle or anonymous function.

Learn to solve differential equations straightforwardly in Matlab using dsolve, write equations with D, set initial values like y(1)=1, and plot symbolic solutions with x as the independent variable.

Solve a two-equation first-order differential system in Matlab using dsolve, with dx1/dt = 4 x1 + 7 x2 and dx2/dt = 2 x1 - 5 x2, and specify independent variable.

This lecture shows how to use Matlab symbolic to find the particle's position p(t) from p'(t)=t^2+t with p(1)=1, and obtain acceleration a(t)=2t+1 by differentiating the velocity.

Learn to solve ordinary differential equations numerically in MATLAB using ode45 as the first choice; set up the equation, integration range, and initial value with function handles and graphical output.

Convert a second-order differential equation to a system of first-order equations and solve it in matlab using ode45 with initial conditions y(0)=0 and y'(0)=1, highlighting vectorized y and function handles.

Solve a first-order differential equation in Matlab by defining the equation in a function and using a function handle with a solver, 0 to 10, initial condition 1, and plot.

Solve the Lorentz equations in MATLAB using ode45 to illustrate the butterfly effect, defining a butterfly function with x, y, z and parameters sigma, rho, beta, and plotting 3-D trajectories.

Learn to solve non linear equations in matlab using the roots function on descending-coefficient vectors, illustrated by x^2+5x+6=0 yielding -3 and -2, and handling higher-order polynomials with complex roots.

Find roots of non-linear equations in Matlab with fzero by locating sign changes, starting from an initial guess, and using function handles or anonymous functions.

Explore how to choose and customize MATLAB plots for 2-D and 3-D functions, including contour, image, color bar, and symbolic plots, with practical tips for scaling and orientation.