Numerical Analysis: Methods and Error Analysis
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Questions and Answers

What does the dependent variable indicate in a mathematical model?

  • External influences acting upon the system
  • Time and space dimensions
  • The behavior or state of the system (correct)
  • The system's properties or composition
  • In significant figures, which of the following is always considered significant?

  • Limited number of digits
  • Estimated digits
  • Non-zero digits (correct)
  • Zeros contained between two non-zero numbers
  • What do parameters reflect in a mathematical system?

  • External influences acting upon the system
  • The system's properties or composition (correct)
  • The significant digits of a number
  • The reliability of a numerical value
  • Which type of solution satisfies the original differential equation?

    <p>Analytical solution</p> Signup and view all the answers

    What is the concept of significant figures used for in numerical methods?

    <p>To designate the reliability of a numerical value</p> Signup and view all the answers

    Which of the following quantities cannot be expressed exactly by a limited number of digits?

    <p>$ ext{π}$</p> Signup and view all the answers

    What are some of the issues involved in using numerical methods?

    <p>Speed of convergence and approximation</p> Signup and view all the answers

    In what instances are numerical methods often used?

    <p>When only approximate solutions are feasible</p> Signup and view all the answers

    What characteristic do numerical methods share in terms of arithmetic computations?

    <p>They involve large numbers of tedious arithmetic computations</p> Signup and view all the answers

    What was a common approach engineers used before the computer era for problem-solving?

    <p>A combination of analytical and graphical methods</p> Signup and view all the answers

    What does mathematical modeling entail in engineering?

    <p>Expressing physical systems or processes in mathematical terms</p> Signup and view all the answers

    How do numerical methods help in problem-solving?

    <p>By offering approximations when exact solutions are impractical</p> Signup and view all the answers

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