# Tutorial: Systems of Nonlinear Equation ## Problem 1 Solve for **x, y** from $$ 𝑓\_1 (𝑥,𝑦)=𝑦−1/2 (𝑒^{(𝑥/2)}+𝑒^{(−𝑥/2)} )=0 \\ 𝑓\_2 (𝑥,𝑦)=9𝑥^2+25𝑦^2−225=0 $$

### Tutorial: MATLAB #### Create MATLAB program for solving a system of non-linear equations Download the tutorial source file and fill in the blanks. * MATLAB tutorial source file : [TU\_SystemNonlinear.zip](https://github.com/ykkimhgu/NumericalProg-student/blob/main/tutorial/TU_Nonlinear/TU_nonlinear_student.mlx) *** #### 1) Define functions that returns vector F(x) and matrix J(x). `Matrix myFuncEx1(Matrix X); // X: vector in. Returns Vector F (nx1)` `Matrix myJacobEx1(Matrix X); // X: vector in. Returns Matrix J (nxn)` #### 2) Define a system non-linear solver `Matrix nonlinearSys(Matrix Func(Matrix _Z), Matrix Jacob(Matrix _Z), Matrix _Z0, double tol);` returns solution vector XN (nx1) #### 3) Then, solve the example problem ### Tutorial: C-Programming 1. Create a new project “ **TU\_SystemNonlinear**” with Visual Studio, under the directory `\NP\tutorial\` 2. Download the tutorial source file from * C-program tutorial source file : [TU\_SystemNonlinear\_student.cpp](https://github.com/ykkimhgu/NumericalProg-student/blob/main/tutorial/TU_Nonlinear/TU_nonlinear_student.cpp) 3. Add the downloaded source file under the project folder. 4. Fill-in the blanks ## Problem 2 Solve for the 3-DOF transformation, angle (θ) and translation T=\[Δx, Δy], to move the vehicle to the new pose? > Solution= \[θ=30 deg , Δx =100 , Δy= 100 ]