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Quiz 1 (Unit I) Study Guide

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MATLAB®

  • Data types (in particular, logical and floating point (double)).
  • Basic operations on scalars: assignment, arithmetic, relational and logical, flow control (if, for, while).
  • Single-index arrays: assignment, indexing, indirect indexing (in which the index is itself a single-index array of integers), concatenation, the colon; dotted arithmetic operators; relational and logical operators.
  • Key MATLAB built-in functions: basic mathematical functions such as the trigonometric and exponential functions; "data" creation and manipulation functions such as "length", "find", "sum", "max", "min", "ones", "zeros".
  • Text pages to review: pages 49–77 (minus Section 4.6).
  • Also review MATLAB Exercises Recitation 1 and Recitation 2.

Numerics

  • Interpolation
    • Piecewise-constant, left; piecewise-constant, right; piecewise-linear.
    • Understand the "piecewise" part in which you find the segment in which the point of interest $x$ resides; understand the "constant left, constant right, and linear" part which determines the functional form of the interpolant within the segment, and the interpolation points at which the interpolant and the function (to be interpolated) must agree.
    • Basic concepts and attributes: accuracy, convergence, convergence rate and order, smoothness, resolution, computational cost, memory.
    • Text pages to review: pages 15–26 (minus the advanced material/proofs and also minus Example 2.1.3 and Example 2.1.5).
  • Integration
    • Rectangle rule, left; rectangle rule, right; trapezoidal.
    • Understand the decomposition over segments and understand the "rule" within each segment (and the geometric/area picture corresponding to this rule).
    • Also understand the integration formulas in terms of a sum of [quadrature weights times function values at quadrature points].
    • Basic concepts and attributes: accuracy, convergence, convergence rate and order, smoothness, resolution, computational cost, memory.
    • Text pages to review: pp. 101–10 (minus the advanced material/proofs and also minus Example 7.1.3).