Textbook: Atkinson and Han: Elementary Numerical Analysis, 3nd edition.
Sample codes: http://www.wiley.com/college/atkinson 
Errors and Other course materials:
            http://www.math.uiowa.edu/ftp/atkinson/ENA_Materials
              (see also page viii of the textbook) 
Course contents:
Chap 1: Taylor Polynomials.
1.1: The Taylor Polynomial
1.2: The Error in Taylor's Polynomial
1.3: Polynomial Evaluation

Chap 2: Error and Computer Arithmetic.
2.1: Floating Point Numbers
2.2: Errors: Definition, Source and Examples.
2.3: Propagation of Error
2.4: Summation

Chap 3: Root Finding.
3.1: The Bisection Method
3.2: Newton's Method
3.3: Secant Method
3.4: Fixed Point Iteration
3.5: Ill-Behaving Root-finding Problems

Chap 4: Interpolation and Approximation. 
4.1: Polynomial Interpolation
4.2: Error in Polynomial Interpolation
4.3: Interpolation Using Spline Functions
4.4: The Best Approximation Problem
4.5: Chebyshev Polynomials
4.6: A Near-Minimax Approximation method
4.7: Least Square Approximations

Chap 5: Numerical Integration and Differentiation.
5.1: The Trapezoidal Rule and Simpson Rules
5.2: Error Formulas
5.3: Gaussian Numerical Integration
5.4: Numerical Differentiation

Chap 6: Solution of Systems of Linear Equations.
6.1: Systems of Linear Equations
6.3: Gaussian Elimination
6.4: The LU Factorization
6.5: Error in Solving Linear Systems
6.6: Iterative Methods