AMSC/CMSC 460 Study Outline for the final
The following outline consists of topics that may appear on the final exam. (Note
the absence of barycentric interpolation, Gaussian quadrature, and ordinary differential
equations.) Although any topics covered in the course may appear on the final, the
emphasis will be on topics covered after the midterm. In the accompanying references,
V refers to Van Loan’s Introduction to Scientific Computing, S refers to Stewart’s Af-
ternotes on Numerical Analysis and C refers to material treated in class. If an item
contains references to both books you should study both.
1. Error
1. Measurement error (C)
2. Truncation error (V1.4.2, S24)
3. Rounding error (V1.4.3, S6.11–6.22)
4. Absolute and relative error (V1.4.1, S1.10–1.14)
2. Floating-point arithmetic (V1.4.4, S6)
1. base, fraction (significand), exponent, normalization
2. IEEE floating point
3. Overflow and underflow
4. Rounding unit
5. Error in floating-point arithmetic
3. Rounding error analysis (S7-8)
1. Backward error analysis
2. Perturbation analysis
3. Cancellation
4. Polynomial interpolation
1. Natural form (V2.1, S18.1-18.10)
2. Lagrange form (S18.11–18.14)
3. Newton form (V2.2–2.3, S19.5–19.12)
4. Evaluation (V2.1.4, V2.2.3, S19.2–19.4, S19.7–19.8)
5. Error (V2.3.2, S20.1–20.5)
5. Piecewise polynomial interpolation
1. Piecewise linear interpolation (V3.1)
2. Table lookup (V3.1.2)
3. Spline interpolation (V3.3)
6. Numerical integration
1. Change of interval (S21.4–21.7)
2. Newton-Cotes formulas (V4.1)
3. Construction by undetermined coefficients (S21.19–21.20)
4. Simple and composite trapezoidal rule (S21.8–21.15)
5. Simple and composite Simpson’s rule (S21.19–22.8)
6. Singularities (S22.9–22.13)
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