In this class, you will be learning how to use Visual Basic for Applications (VBA) to program and solve engineering problems. The type of class can be adapted to your needs, from a beginner (VBA basics) to an experienced user (advanced numerical methods). Complete Program: Programming -Introduction to Visual Basic for Applications (VBA) -Subroutines basics: variables and syntax -Indexed variables and input data -Communication Excel/VBA: read and write to/from the worksheet -Loops and conditional statements -External Functions Numerical Methods -Introduction to numerical methods: linear, non-linear equations and convergence criteria -Errors and approximations -Solving non-linear equations – Bracketing methods: Bisection and False Position -Solving non-linear equations – Iterative methods: Newton, Secant and Fixed Point -Solving systems of linear equations – Direct methods (n < 1000): Gauss Elimination and LU Decomposition -Solving systems of linear equations – Direct methods (n < 3): Substitution method and Crame Rule -Solving systems of linear equations – Direct methods (Tridiagonal matrices): Thomas algorithm -Solving systems of linear equations – Iterative methods (large matrices): Jacobi, Gauss-Seidel -Solving systems of linear equations – Gauss-Seidel convergence and relaxations -Solving systems of non-linear equations – Newton and Fixed-point -Differentiation: Taylor series and approximations -Differentiation: first and second order differences: centred, forward and backward -Integration: Lagrange interpolating polynomials -Integration: Trapezoidal, Simpson’s 1/3, Simpson’s 3/8 Rules -Integration: Composite rules Advanced Numerical Methods -Introduction to ODE’s and PDE’s -Solving ODE’s – Initial Value Problems: Euler and Runge-Kutta -Solving ODE’s – Boundary Value Problems: Shooting Method, Finite Differences -Solving ODE’s – Finite Differences for linear BVP: Gauss and Thomas -Solving ODE’s – Finite Differences for non-linear BVP: Newton-Raphson, Gauss-Seidel -Solving PDE’s – Discretization and transformation into SODE -Solving PDE’s – Application to Elliptic and Navier-Stokes -Solving PDE’s – SEDO’s Stiff problems: Runge-Kutta and Predictor/Corrector methods.