Course Outline

Topic Text
Approx. Date
of Completion

      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