Midterm 1 ================================================================

1       Scientific Computing
1.2        Approximations in Scientific Computation
1.2.2         Absolute vs Relative errors
(1.2.4)       Truncation Error vs Rounding Error (identify concept only)
1.2.5         Forward vs Backward errors
1.2.6         Sensitivity and Conditioning
              (general concept: examples will be taken from polynomial roots)
1.3        Computer Arithmetic - Floating Point
1.3.1         Floating Point Numbers
1.3.2         Normalization
1.3.3         Properties of Floating Point Numbers
1.3.4         Rounding
1.3.5         Machine Precision
1.3.6         Subnormals and Gradual Underflow
1.3.9         Cancellation (recognize concept only)

2       Systems of Linear Equations
2.1        Ax=b
2.2        Existence & Uniqueness of Solutions
2.4        LU Factorization via Gaussian Elimination
(2.4.1)       Problem Transformation (general idea)
2.4.2         Triangular Linear Systems
2.4.3         Elementary Elimination Matrices
2.4.4         Gaussian Elimination and LU Factorization
2.4.5         Pivoting (only up to and including example 2.15)


5       Nonlinear Equations
5.1        Nonlinear equations
(5.2)      Existence and Uniqueness (just the examples)
5.3        Sensitivity and Conditioning (just the examples)
5.4        Convergence Rates and Stopping Criteria
5.5        Nonlinear Equations in One dimension
5.5.1         Interval Bisection
5.5.2         Fixed Point Iteration
5.5.3         Newton's Method
5.5.4         Secant Method