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NUMERICAL METHODS AND ANALYSIS, TWO CATEGORIES IN FINDING THE ROOTS, TWO…
NUMERICAL METHODS AND ANALYSIS
SOURCES OF ERRORS
DISCRETISATION
ABSOLUTE ERRORS
DATA UNCERTAINTY
RELATIVE ERRORS
MODELLING / FORMULATION
ROUNDOFF ERRORS
2 MAJOR FORMS OF ERRORS
BLUNDERS / GROSS/ HUMAN ERRORS
TRUNCATION / CHOPPING ERRORS
ROOT FINDING
OPEN METHOD
SIMPLE FIXED POINT
NEWTON-RAPHSON METHOD
SECANT METHOD
employ a data to predict the root
BRACKETING METHOD
BISECTION METHOD
FALSE POSITION METHOD
two initial guesses for the root are required
FUNDAMENTAL THEOREMS OF
ARITHMETIC
ax^2 + bx + C = 0
PRIME FACTORIZATION
UNIQUE FACTORIZATION
CALCULUS
DIFFERENTIAL
INTEGRAL
ALGEBRA
LINEAR ALGEBRA
b = Ax , Ax = b
COMPLEX NUMBERS
ax^n + bx^n-1 + ...C
n roots
SYSTEMS OF LINEAR EQUATIONS
NUMERICAL SOLUTION OF LINEAR SYSTEMS Ax = b
DIRECT METHODS
GAUSS ELIMINATION
GAUSS-JORDAN ELIMINATION
INDIRECT OR INTERACTIVE METHODS
JACOBI ITERATION
GAUSS-SEIDEL METHOD
USED CRAMER'S RULE
FUNCTION APPROXIMATION AND INTERPOLATION
FOURIER SERIES
FOURIER TRANSFORM
DOMAIN TRANSFORM
LAPLACE TRANSFORM
POWER SERIES
TAYLOR SERIES
MACLAURIN SERIES
LEAST-SQUARE APPROXIMATION
FITTING A STRAIGHT LINE
FITTING TO A LINEAR COMBINATION OF FUNCTIONS
INTERPOLATION
POLYNOMIAL INTERPOLATION
NEWTON'S DIVIDED-DIFFERENCE INTERPOLATING POLYNOMIALS
LINEAR INTERPOLATION
QUADRATIC INTERPOLATION
LAGRANGE INTERPOLATION POLYNOMIALS
INVERESE INTERPOLATION
VANDERMONDE MATRIX
NUMERICAL INTEGRATION
NEWTON-COTES INTEGRATION FORMULAS
TRAPEZOIDAL RULE
SIMPSON’S RULE
MIDPOINT RULE
TWO CATEGORIES IN FINDING THE ROOTS
TWO TYPES