MTH 2232 units200 LevelSecond Semester

Introduction to Numerical Analysis

B.Sc. Data Science, University of Uyo

How to compute answers to mathematical problems that have no closed-form solution, and how to know when the computed answer is wrong. Error, convergence and stability — the reason floating-point arithmetic sometimes betrays you.

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Course outline

  1. 01Sources of error: round-off, truncation, and floating-point representation
  2. 02Absolute, relative and percentage error; error propagation and conditioning
  3. 03Solution of nonlinear equations: bisection, false position, Newton–Raphson, secant method
  4. 04Convergence criteria and rates of convergence
  5. 05Solution of linear systems: Gaussian elimination, LU decomposition, pivoting
  6. 06Iterative methods: Jacobi and Gauss–Seidel
  7. 07Interpolation: Lagrange and Newton divided-difference polynomials; spline interpolation
  8. 08Numerical differentiation and integration: trapezoidal rule, Simpson's rules
  9. 09Numerical solution of ordinary differential equations: Euler and Runge–Kutta methods

Recommended textbooks

  • Numerical Analysis — Richard L. Burden & J. Douglas Faires

    10th ed. — the standard text, with algorithms in pseudocode

  • Numerical Methods in Engineering with Python 3 — Jaan Kiusalaas

    Implements each method in Python — ideal for this programme

How to pass MTH 223

  • Implement every method in Python as you learn it — a method you have coded is a method you understand
  • Newton–Raphson is the same algorithm family as gradient descent; recognising that makes UUY-DTS 313 far less mysterious
  • Learn WHY floating-point comparison with == is unsafe; this single fact prevents a whole class of real bugs in data pipelines
  • Exam questions usually ask for two or three iterations by hand — practise tabulating iterations neatly and carrying enough decimal places

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