Topic |
Text Section |
Approx. Date of Completion |
---|---|---|
Preliminaries |
||
review of essential calculus, Taylor's Theorem | 1.2 | |
floating-point arithmetic, round-off error | 1.3 | |
sources of errors in scientific computation | 1.4 | |
software for scientific computation | 1.5 | Sept. 12 |
Solving Nonlinear Algebraic Equations |
||
the bisection method | 2.2 | |
the secant method, regula falsi | 2.3 | |
Newton's method | 2.4 | |
complex-valued functions and Newton's method | none | |
Muller's method, roots of polynomials | 2.6 | |
Brent's algorithm and other methods | 2.7 | |
Newton's method for systems of non-linear equations | 10.2 | Sept. 26 |
Interpolation using Polynomials |
||
approximating functions using polynomials | 3.1 | |
Lagrange polynomials, Neville’s method | 3.2 | |
Newton’s divided difference formula | 3.3 | |
Hermite interpolation, piecewise Hermite polynomials | 3.4 | |
interpolation using cubic splines | 3.5 | Oct. 10 |
Numerical Integration and Differentiation |
||
basic and composite quadrature rules | 4.2, 4.3 | |
Romberg integration | 4.4 | |
Gaussian quadrature | 4.5 | |
adaptive quadrature | 4.6 | |
numerical differentiation | 4.9 | Oct. 31 |
Initial Value Problems for Ordinary Differential Equations |
||
review of first-order ordinary differential equations | 5.1 | |
Euler’s method, Taylor methods | 5.2 | |
Runge-Kutta methods | 5.3 | |
adaptive techniques | 5.6 | |
methods for systems of equations | 5.7 | |
stiff differential equations and numerical stability | 5.8 | Nov. 14 |
Solving Systems of Linear Algebraic Equations |
||
Gaussian elimination with partial pivoting | 6.2, 6.3 | |
matrix factorization and its use in solving systems | 6.5 | |
factorization techniques for special matrices | 6.6 | |
vector and matrix norms | 7.2 | |
error bounds and iterative improvement | 7.6 | Nov. 28 |
Presentations of Student Projects |
Dec. 5 |