Learn more about fzero. Movies and animation. MATLAB Commands – 11 M-Files eval Interpret strings containing Matlab expressions. Define a MATLAB function that takes a one parameter argument, in this case the steam-function at the body, and returns the velocity magnitude at the trailing edge. Each m-file contains exactly one MATLAB function. 0 (R14), you can use the 'MultiSelect' parameter with UIGETFILE to allow the selection of multiple files. Fzero solution, vector solution,plot. Ray-tracing is also used in computer graphics for generating photorealistic 3D images. fzero defines a zero as a point where the function crosses the x-axis. Expert Answer. FZero NaN help!. A continuación, fzero reduce iterativamente el intervalo donde fun cambia el signo para llegar a una solución. Another possible solution for your problem is to immediately return a number different from 0 (e. Berbeda dengan tutorial sebelumnya mengenai menyelesaikan persamaan matematika di MATLAB yang menggunakan symbolic math, syntax fzero merupakan syntax independent yang hanya dapat menghitung persamaan matematika dengan satu variabel. 我也很好奇 就试了一下 fzero(@(x)x^2-1,0. MATLAB knows the number , which is called pi. Using fzero to solve equations. The Far-Reaching Impact of MATLAB and Simulink Explore the wide range of product capabilities, and find the solution that is right for your application or industry. This means that fzero(f(x)) is acceptable, but fzero(f(x,y)) is not. Esta función de MATLAB. MATLAB Answers. What is a concept of zero crossing in image processing. Work with your files from anywhere, share with others. For example, fzero(@tan,1) returns 1. Una versión de Algol 60, con algunas mejoras, se da en. Learn more about fzero. Java Project Tutorial - Make Login and Register Form Step by Step Using NetBeans And MySQL Database - Duration: 3:43:32. Surveys Use fzero function in Matlab. arglist is a comma-separated list of input arguments. Simple unconstrained optimization problem. ) Check function or try again with a different starting value. The calling syntax is ynew = interp1(x, y, xnew, method). Then fzero iteratively shrinks the interval where fun changes sign to reach a solution. MATLAB - Concatenating Matrices - You can concatenate two matrices to create a larger matrix. Parameters func callable. But my question is how do I find x given y and z using "fzero" function on MATLAB?. and you are trying to determine the value of \(x\) for which \(f(x)=0\). how to use fzero?. Built-in Command fzero The Matlab command ' fzero ' is powerful. As an example, assume you want MATLAB to numerically find the minimum of the function \(y=3x^2+11x-2\) using the built-in min command. which has three arguments for arrayfun: the function handle, X, and al. ContentsSeeking a sign change. Inf) to "fzero" if "fzero" wants to evaluate your function with an infeasible value for c0. But for solving basic algebraic equations, both MATL. What Is the Function of the Linspace in MATLAB? The "linspace" function in MATLAB creates a vector of values that are linearly spaced between two endpoints. This example shows several different methods to calculate the roots of a polynomial. Instead the fminbnd and potentially also fminsearch MATLAB functions are appropriate here, and works in the same way as fzero. Polynomial roots. We use this form because fzero solves for roots of the input function. By the way: Before applying "fzero" to your function, I'd plot it to see whether its shape is reasonable. Return the roots of the (non-linear) equations defined by func(x) = 0 given a starting estimate. fminsearch can often handle discontinuity, particularly if it does not occur near the solution. 005x4 –cos(x) and determine approximate location of roots • Use MATLAB fzero to find roots in [-2 8] –Copy commands and results to Word file • Use Excel Goal Seek to all. Answer to 1. Eventually, I would prefer to have a slightly coarser granularity of the packages. The dark blue asterisk is what fzero found? Looks pretty close to zero to me, but you could zoom the y-axis so that we could see better. If A is a matrix, Scilab sum(A) gives the sum of all elements of A but Matlab returns the sum of each column. MATLAB - Concatenating Matrices - You can concatenate two matrices to create a larger matrix. Recall that fzero() is a function function, and that it that it expects that the function argument which you pass it will only accept one argument. I want to solve a problem in which I am given a function (seen below) where W is 4. In the portion of the isotherm where , the isotherm fails to describe real materials, which phase separate into a liquid and gas in this region. y = linspace(a,b,n) generates a row vector y of n points linearly spaced between and. xzero = fzero(’sinm’,2) which gives the solution to the equation sinx = 2x-2. If you have any feedback please feel free to reach me at @the_ozzinator, or osvaldo. The sample program below illustrates how Newton's Method is used to find the root of an equation. Let's consider the following examples. MatLab is a high performance numeric computing environment, which includes numerical analysis, matrix computation, signal processing, and graphics to provide answers to the most troubling of mathematical problems. [Source: MATLAB User's Guide, version 3. r = roots(c) Description. The following MATLAB code plots polynomials of third, fourth, and fth degree approximating data given by the vectors x and y:. Hello, I'm trying to know all the roots of my function in a specific range, I know that "roots" function will work for my polynomial but I'm trying to do it with "fzero" also because I want to build an algorithm that will work for any function that the user will enter. Calculate polynomial roots numerically, graphically, or symbolically. Movies and animation. Read more [2019] SOLIDWORKS File Types: Everything You Need to Know. fzero コマンドは関数ファイルです。T. MATLAB Central. Solving an implicit function, fsolve vs. real and complex. Use the “disp” function. Points where the function touches, but does not cross, the x-axis are not valid zeros. Typically, you use an output function to generate graphical output, record the history of the data the algorithm generates, or halt the algorithm based on the data at the current iteration. As long as the coefficients of the polynomial are real, the roots will be real or occur in complex conjugate pairs. help in fzero function. out=n) or just. Eventually, I would prefer to have a slightly coarser granularity of the packages. Learn more about fzero, equation, vector. dll' submission on the MATLAB Central File Exchange to do this on a Windows platform. Note that in Matlab, A can contain complex values (in these cases, only real part of A is taken in account), what Scilab function do not tolerate. y = linspace(a,b,n) generates a row vector y of n points linearly spaced between and. MATLAB Cheat Sheet Basic Commands % Indicates rest of line is commented out. All methods converge to an answer of approximately f = 0. The initial and nal. Symmetry helps. Roots of Polynomials. x = fzero(fun,x0) tries to find a zero of fun near x0, if x0 is a scalar. Avijith Chandramouli. The pair of square brackets '[]' is the concatenation operator. I am solving in using fzero. This tutorial uses the fzero function in MATLAB to find the root of an equation. Just for reference, Matlab classifies fzero as. A complete list of the elementary functions can be obtained by entering "help elfun": help elfun. fzero tries to find a zero of f near x, if x is a scalar. MatLab is a high performance numeric computing environment, which includes numerical analysis, matrix computation, signal processing, and graphics to provide answers to the most troubling of mathematical problems. Exiting fzero: aborting search for an interval containing a sign change because NaN or Inf function value encountered during search. r = roots(c) returns a column vector whose elements are the roots of the polynomial c. real and complex. Note that in Matlab, A can contain complex values (in these cases, only real part of A is taken in account), what Scilab function do not tolerate. Using MATLAB solvers and optimizers to make design decisions 12. which has three arguments for arrayfun: the function handle, X, and al. 1 Running interactively If you want to run something while you are logged in, type matlab at the command prompt. More complicated functions. quiz questions from semester. 0, you can use the `uigetfiles. This MATLAB function returns the scalar 0. Learn more about fzero. The meaning of those intersections is that the given lines or curves have the same coordinate values at some points. The command can only find one root at a time, and can only find roots in one variable at a time. fsolve¶ scipy. 005x4 –cos(x) and determine approximate location of roots • Use MATLAB fzero to find roots in [-2 8] –Copy commands and results to Word file • Use Excel Goal Seek to all. MatLab is a high performance numeric computing environment, which includes numerical analysis, matrix computation, signal processing, and graphics to provide answers to the most troubling of mathematical problems. ContentsSeeking a sign change. X = fzero(FUN,X0) tries to find a zero of the function FUN near X0, if X0 is a scalar. fun is a function handle, inline function, or string containing the name of the function to evaluate. When working with differential equations, MATLAB provides two different approaches: numerical and symbolic. I'm basically suppose to develop a function in Matlab that finds the zeros of a cubic polynomial. As such, it can easily be accessed programmatically. Example Illustrating the Use of MATLAB's fzero Routine MATLAB has a built-in routine called fzero that approximates roots of functions. Finally, if A is a multidimensional array, Matlab works on the first non-singleton dimension of A what Scilab does not. This should give me a matrix of the 25 H values. General Purpose Commands. nargin Number of function input arguments. If the function is to be used in several different problems or the function requires more than one MATLAB command, then you need to create a function m-file. Calculus with MATLAB. So you could also enter the vector a as. MATLAB Cheat Sheet Basic Commands % Indicates rest of line is commented out. fzero tries to find a zero of f near x, if x is a scalar. Berbeda dengan tutorial sebelumnya mengenai menyelesaikan persamaan matematika di MATLAB yang menggunakan symbolic math, syntax fzero merupakan syntax independent yang hanya dapat menghitung persamaan matematika dengan satu variabel. MATLAB fzero function I just copied some matlab code, then edited with my equation. Expert Answer. Using fzero to solve equations. The Far-Reaching Impact of MATLAB and Simulink Explore the wide range of product capabilities, and find the solution that is right for your application or industry. FUN is a function handle. The dark blue asterisk is what fzero found? Looks pretty close to zero to me, but you could zoom the y-axis so that we could see better. Points where the function touches, but does not cross, the x -axis are not valid zeros. That code might look like:. FUN is a function handle. The fminbnd command can find a single independent value that will minimize a one-dimensional function over a specific domain. Note If you have purchased the Optimization Toolbox, you can also use optimset to create an expanded options structure containing additional options specifically designed for the functions provided in that toolbox. 05)时，ans=1,。fzero是一个数值搜索过程，依赖于函数特性，值的指定，以及matlab所能识别的最小步长。. For example, the equation P(x) = x4 + 7x3 - 5x + 9 could be r. MATLAB File Search. (b) Write a Matlab program that evaluates the second derivative of the function (using a centered difference approximation O(h2)) on the interval [-4 , 4] with a step sizes of h = 0. A Roots package seems quite reasonable. No, there is no way to force fzero to go to the next positive root. Functions handles are data types in Matlab. creating for loop in fzero. 1BestCsharp blog 6,527,372 views. when i graph it i can see these values but fzero wont give me the correct answeres. To set options for Optimization Toolbox™ or Global Optimization Toolbox solvers, the recommended function is optimoptions. If the function is not continuous, fzero may return values that are discontinuous points instead of zeros. In the fzero function, according to the help, it is possible to specify a TolX parameter (higher TolX value means less function calls, which in my situation will greatly reduce computation time). 6 Charles J. input your answer to 4 decimal places. I started off by using the bisection method and it's not working for a basic polynomial i know the roots to. The effort you put into asking a question is often matched by the quality of our answers. Furthermore, fzero freaks out when it runs into an interval with an asymptote (Inf) or non a number (NaN). Applications of MATLAB: Ordinary Diﬁerential Equations (ODE) David Houcque Robert R. This chapter lists MATLAB commands by functional. 3545 As noted by @rayryeng, fzero also accepts a function handle to define its input function. Numeric formats affect only how numbers appear in Command Window output, not how MATLAB ® computes or saves them. The function requires two inputs for the endpoints of the output vector, and it also accepts a third, optional input to specify the number of points to include between the endpoints. The process is then repeated for the new interval [1. Let us try fzero instead, which solves equations numerically, using something akin to Newton's method, starting at a given initial value of the variable. Polynomial roots. Using the built-in Matlab function "fzero, estimate the average of the root(s) of 10 sin(x)exp(-x) within 0 x 10. MATLAB fzero function I just copied some matlab code, then edited with my equation. Introduction. If you give fzero a starting point x0, fzero first searches for an. Complex numbers in MATLAB are doubles with a real part and an imaginary part. Yes, it is true that careful use of arrayfun would succeed here, there is no need to use a complicated function syntax when a trivial loop would suffice. X = fzero(FUN,X0) tries to find a zero of the function FUN near X0, if X0 is a scalar. Useful MATLAB functions: fzero There are no primers or exercises for this module. Read more [2019] SOLIDWORKS File Types: Everything You Need to Know. Learn more about fzero. As long as the coefficients of the polynomial are real, the roots will be real or occur in complex conjugate pairs. 5708, a discontinuous point in tan. : [x, fval, info, output] = fzero (…) Find a zero of a univariate function. If you use the command fzero(@f, [x1, x2]) MATLAB will look for a root in the interval [x1, x2]. y = linspace(a,b,n) generates a row vector y of n points linearly spaced between and. Yes, it is true that careful use of arrayfun would succeed here, there is no need to use a complicated function syntax when a trivial loop would suffice. One could imagine: [1] V/V0 = f(x) where V is the volume, and V0 is the initial. Solving and Optimizing in Matlab 1 SOLVING AND OPTIMIZING IN MATLAB Note that you can copy code from the pdf and paste into a Matlab editor window to try out the code, or look for the code in Matlab/SuppExamples. So, if A is a vector, then Scilab and Matlab work in the same way. The ‘fzero’ function in MATLAB is a function that finds the roots of a non-linear equation of a single variable unlike ‘fsolve’ which solves two or more than two variables. The table shows the entire iteration procedure of bisection method and its MATLAB program: Thus, the root of x 2 -3 = 0 is 1. >> fzero('x+sin(x)+exp(x)', -1) ans = -0. fzero defines a zero as a point where the function crosses the x-axis. In the fzero function, according to the help, it is possible to specify a TolX parameter (higher TolX value means less function calls, which in my situation will greatly reduce computation time). I am solving in using fzero. I was thinking about the function fzero. Outline Overview Optimization Toolbox. I need to find out for each combination of (P,Q) i. Roots of Polynomials. The fzero command defines a zero as a point where the function crosses the x-axis. Other MATLAB differential equation solvers 14. - Andras Deak Aug 16 '15 at 14:27. A polynomial of order p has p + 1 coefficients, this is, a quadratic has three coefficients and a polynomial of degree p will have p roots. MATLAB FOR MATH 303 Abstract. MATLAB stands for MATrix LABoratory. To find the derivatives of f, g and h in Matlab using the syms function, here is how the code will look like. Tools such as MATLAB create new. when i graph it i can see these values but fzero wont give me the correct answeres. One of the methods fzero uses is the Secant Method, described in. Built-in Command fzero The Matlab command ' fzero ' is powerful. fzero コマンドは関数ファイルです。T. Then fzero iteratively shrinks the interval where fun changes sign to reach a solution. MATLAB - Concatenating Matrices - You can concatenate two matrices to create a larger matrix. For example, y = x. By the way: Before applying "fzero" to your function, I'd plot it to see whether its shape is reasonable. Open Mobile Search. This is my equation, i want to ge. Typically, you use an output function to generate graphical output, record the history of the data the algorithm generates, or halt the algorithm based on the data at the current iteration. Math 111: MATLAB Assignment 2: Newton's Method. Matrices in MATLAB 9. How to use fsolve or fzero to find the equilibrium points of an ode nonlinear system - fsolve stopped because the last step was ineffective. 1 Governing. If the function is continuous, this is also a point where the function has a value near zero. An inline function is. fzero | fzero | fzero matlab | fzero64 | fzero function | fzero in matlab | fzero command matlab | fzero command | fzero gdq | fzero news | fzero bessel | fzero. r = roots(c) Description. Polynomial roots. For my initial guess, I used 0. If A is a matrix, Scilab sum(A) gives the sum of all elements of A but Matlab returns the sum of each column. solve trigonometric equation with plot ,fzero. Matlab the basics functions vectors plotting fzero roots Theory Bisection from ECOR 2606 at Carleton University. MATLAB news, code tips and tricks, questions, and discussion! We are here to help, but won't do your homework or help you pirate software. A Roots package seems quite reasonable. Find Intersections - an engineering approach. Polynomial roots. GNU Octave/Matlab Primer Sachin Shanbhag∗ August 27, 2007 1 Introduction The objective of this tutorial is to get you up and running with MATLAB or GNU Octave. The function handle is a standard MATLAB data type. Here there are two solutions and Matlab returns a vector sol with two components: sol(1) is 0 and sol(2) is -1/(t^2/2 + C3) with an arbitrary constant C3. fminsearch may only give local solutions. The fzero command finds a point where the function changes sign. Dot notation for operations on vectors 7. I'm basically suppose to develop a function in Matlab that finds the zeros of a cubic polynomial. fzero MATLAB builtin command for nding a root of a continuous, scalar-valued, univariate function [x,fval,exitflag,output] = fzero(fun,x0,options) Inputs fun- function handle containing scalar-valued function x0- initial guess for root options- structure containing options Outputs x- root found fval- value of funat x exitflag- convergence ag. ^2 is a parabola that touches the x-axis at 0. r = roots(c) returns a column vector whose elements are the roots of the polynomial c. Learn more about fzero. 2-element vector — fzero checks that fun(x0(1)) and fun(x0(2)) have opposite signs, and errors if they do not. Have fun playing SNES games online using our flash emulator. Learn more about solve equation, solve, von karman, fzero, vector, equation, input, logarithmic equations, squaresqqsas. Functions handles are data types in Matlab. This example shows how to solve an equation repeatedly as a parameter changes by starting subsequent solutions from the previous initial point. Using fzero to solve equations. This is a short notes on Matlab for Math 303. If the function only requires one line of code to write, you can put the anonymous function that does the calculation directly in the fzero command. Description Take an example of a non-linear equation having only one variable. how can I show all zeros in a figure window I want to see all zeros with *(star) not only one and I want to present them with legend ?. The fzero function attempts to find a root of one equation with one variable. Long story short: if there's a way to get all zeros using matlab, I'm not aware of it. Finding Zeros of cubic without using fzero or roots in Matlab [closed] Ask Question Matlab Coding finding zeros without using fzero or roots function. So, to have a good chance to find a solution to your equations system, you must ship, a good starting point to fsolve. Fzero is a Matlab command that find the roots of nonlinear equations. creating for loop in fzero. If c has n+1 components, the polynomial it represents is. brent, a MATLAB library which contains algorithms for finding zeros or minima of a scalar function of a scalar variable, by Richard Brent. ^2 is a parabola that touches the x-axis at 0. 5708, a discontinuous point in tan. In fact, as observed by @horchler, using a string is currently undocumented, and it's slower. The fzero command finds a point where the function changes sign. However, your function does not have any true zero-crossings in the sense that fzero can locate them. For example, y = x. function Creates a user-defined function M-file. If you have a function that has multiple roots within an interval of your choice, is there a way to show all the roots as an array, instead of only one root closest to the guess?. 我也很好奇 就试了一下 fzero(@(x)x^2-1,0. 5 ; end x=fzero (@fun, 0. Nonlinear system solver. 5708, a discontinuous point in tan. For my assignment I'm asked to solve the colebrook equation using various root finding numerical methods. ) Check function or try again with a different starting value. Just for reference, Matlab classifies fzero as. X = fzero(FUN,X0) tries to find a zero of the function FUN near X0, if X0 is a scalar. MATLAB FOR MATH 303 Abstract. Solving an implicit function, fsolve vs. As long as the coefficients of the polynomial are real, the roots will be real or occur in complex conjugate pairs. I am solving in using fzero. and you are trying to determine the value of \(x\) for which \(f(x)=0\). Plotting and graphics in MATLAB 10. A complete list of the elementary functions can be obtained by entering "help elfun": help elfun. -Use MATLAB fzero (copy command window to Word document) -Use goal seek method of Excel -Write MATLAB and VBA code 27 Exercise for Tonight • Sketch f(x) = 0. MATLAB integrates computation, visualization, and programming in an easy-to-use en- vironment, and allows easy matrix manipulation, plotting of functions and data, implementation of algorithms, creation of user interfaces, and interfacing with programs in other languages. I have a function called 'concrete' which contains a variable 'L' (for length). If the function only requires one line of code to write, you can put the anonymous function that does the calculation directly in the fzero command. It is slightly different from the one obtained using MATLAB program. fzero(' fun ',x) where x is a scalar value, uses x as a starting point. Esta función de MATLAB. Also use the function M-file and the fminbnd command to find (and display) the point (xmin,ymin) on the curve that is closest to the origin and display the minimum distance (i. (a) Write a MATLAB program and function M-file to plot d(x) for −100 ≤ x ≤ 100. MATLAB Answers. You can only exclude the area you already searched from the area fzero is to search next. Here there are two solutions and Matlab returns a vector sol with two components: sol(1) is 0 and sol(2) is -1/(t^2/2 + C3) with an arbitrary constant C3. We use this form because fzero solves for roots of the input function. fzero does not solve multiple problems at once. Documentation; MathWorks. Search All Support Resources. –Use MATLAB fzero (copy command window to Word document) –Use goal seek method of Excel –Write MATLAB and VBA code 27 Exercise for Tonight • Sketch f(x) = 0. brent, a MATLAB library which contains algorithms for finding zeros or minima of a scalar function of a scalar variable, by Richard Brent. Specifically fzero finds one zero since it uses a kind of intersection method. Learn more about fzero. 5 ; end x=fzero (@fun, 0. This is my equation, i want to ge. Find more Mathematics widgets in Wolfram|Alpha. Determinant of a matrix is calculated using the det function of MATLAB. The drag coefficient (c) is the root in this example. The interp1 command is a MATLAB M-file. Enjoy the videos and music you love, upload original content, and share it all with friends, family, and the world on YouTube. Documentation; MathWorks. Please refer to a Numerical Methods textbook for further details and examples. Be Sure To Use The Exact F(P) = 0 From The Last Page. Use Matlab “ fzero” function to find the zeros of the following functions in the given domain Compute the followings: Show transcribed image text. Description Take an example of a non-linear equation having only one variable. Read more [2019] SOLIDWORKS File Types: Everything You Need to Know. feval Function evaluation. To get the most precise answer possible, you will want to give MATLAB a very large number of points - say, 1 million. If the function is continuous, this is also a point where the function has a value near zero. A continuación, fzero reduce iterativamente el intervalo donde fun cambia el signo para llegar a una solución. McCormick School of Engineering and Applied Science - Northwestern University 2145 Sheridan Road Evanston, IL 60208-3102 Abstract Textbooks on diﬁerential equations often give the impression that most diﬁerential. Learn more about solve equation, solve, von karman, fzero, vector, equation, input, logarithmic equations, squaresqqsas. for P from 1 to 5 and Q from 1 to 5 the value of H for which A=0. Scilab help >> Matlab to Scilab Conversion Tips > Matlab-Scilab equivalents > Variables > pi (Matlab variable) pi (Matlab variable) Ratio of a circle's circumference to its diameter. The fminbnd command can find a single independent value that will minimize a one-dimensional function over a specific domain. MATLAB FOR MATH 303 Abstract. I am solving in using fzero. The fzero function attempts to find a root of one equation with one variable. Open Mobile Search. In this problem we consider the function f 0 10 R defined by f x x 2 1 a Verify from MATH 252-1 at New York University. Each m-file contains exactly one MATLAB function. MATLAB Functions 12. If the function is continuous, this is also a point where the function has a value near zero. Learn MATLAB's language fundamentals including syntax, operators, and data types. 1 Using FZERO for a function defined by inline command The following command solves the equation y = f(x) = x3 - 5x2-x +2 ;, starting from an. So, if A is a vector, then Scilab and Matlab work in the same way. MATLAB integrates computation, visualization, and programming in an easy-to-use en- vironment, and allows easy matrix manipulation, plotting of functions and data, implementation of algorithms, creation of user interfaces, and interfacing with programs in other languages. To find the derivatives of f, g and h in Matlab using the syms function, here is how the code will look like. Theline warning o MATLAB:fzero:UndeterminedSyntax simplyturns o anerrormessageMATLABissued every time it called fzero(). Free 2-Day Shipping w/ Amazon Prime. Use uppercase AND and OR to search for combinations of terms Options: # context lines: Full words Search Areas: Examples Labs Projects. Can pass functions to other functions (feval, eval, fzero, ezplot). By the way: Before applying "fzero" to your function, I'd plot it to see whether its shape is reasonable. A function accepts one or more MATLAB variables as inputs, operates on them in some way, and then. Points where the function touches, but does not cross, the x -axis are not valid zeros. The Far-Reaching Impact of MATLAB and Simulink Explore the wide range of product capabilities, and find the solution that is right for your application or industry. $\begingroup$ I have not touched Matlab for a long time, but something looks weird in your code: you are assigning a scalar to "eq", then you pass it to "fzero" as if it was a function. The fzero command defines a zero as a point where the function crosses the x-axis. ) Check function or try again with a different starting value. Finding Zeros of cubic without using fzero or roots in Matlab [closed] Ask Question Matlab Coding finding zeros without using fzero or roots function. fminsearch can often handle discontinuity, particularly if it does not occur near the solution. Simple unconstrained optimization problem. The Matlab package provides both command-line and programming language interfaces, allowing the user to test simple state-. For example, fzero(@tan,1) returns 1. Fzero is a Matlab command that find the roots of nonlinear equations. The original source for the exposition and examples is the old notes by Prof. Using fzero to solve equations.