CVEN Exam 1 Review

Matlab Basic commands and syntax Basic commands and syntax Creation of functions and programs Creation of functions and programs Using functions at command prompt Using functions at command prompt IF, FOR, and WHILE structures IF, FOR, and WHILE structures Arrays, matrices Arrays, matrices Element-by-element operations Element-by-element operations Logical operators and order of operation Logical operators and order of operation

Matlab, continued Built-in functions: Built-in functions: –roots, fzero, feval, and help elfun Passing functions to functions Passing functions to functions

Taylor Series Taylor series expansion Taylor series expansion What is a base point? What is a base point? Order of the expansion Order of the expansion Error term Error term

Finite Difference Approximate derivatives numerically Approximate derivatives numerically Forward, Backward and Central difference Forward, Backward and Central difference Order of the method Order of the method Behavior of error compared to the step size Behavior of error compared to the step size

Roots of Equations Bracketing methods: bisection and false position Bracketing methods: bisection and false position Open methods: Newton-Raphson and secant Open methods: Newton-Raphson and secant Initial guesses and update equations Initial guesses and update equations Calculating relative error Calculating relative error Using fzero or roots Using fzero or roots

Matrices Matrix operations: addition, subtraction, multiplication, transpose Matrix operations: addition, subtraction, multiplication, transpose Entering matrices in Matlab Entering matrices in Matlab Matrix indexing: A mn Matrix indexing: A mn What is the matrix inverse? What is the matrix inverse? Identity matrix Identity matrix

Linear Algebra Write system of equations in matrix form Write system of equations in matrix form Convert to row-echelon form using Gauss elimination (naïve and regular) Convert to row-echelon form using Gauss elimination (naïve and regular) LU decomposition LU decomposition Solution: x = A -1 b Solution: x = A -1 b

Ground rules One sheet of notes, double sided One sheet of notes, double sided Hand-held calculator Hand-held calculator Show all your work on work-out problems Show all your work on work-out problems 7:30-9:00 – location TBA 7:30-9:00 – location TBA