MTH 2112 units200 LevelFirst Semester

Mathematical Methods I

B.Sc. Data Science, University of Uyo

The analytical toolkit for scientific computing: sequences and series, partial differentiation, vector calculus and an introduction to differential equations. These are the methods that underpin optimisation, gradient-based learning and statistical modelling.

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Course outline

  1. 01Sequences and infinite series; tests of convergence
  2. 02Power series, Taylor and Maclaurin expansions
  3. 03Functions of several variables; limits and continuity in several variables
  4. 04Partial derivatives; the chain rule for multivariable functions
  5. 05Total differential, gradient, directional derivative, divergence and curl
  6. 06Maxima and minima of functions of several variables; Lagrange multipliers
  7. 07Multiple integrals: double and triple integrals and their applications
  8. 08First-order ordinary differential equations: separable, homogeneous, exact and linear
  9. 09Second-order linear differential equations with constant coefficients

Recommended textbooks

  • Advanced Engineering Mathematics — Erwin Kreyszig

    10th ed. — the comprehensive reference for these methods

  • Engineering Mathematics — K.A. Stroud

    8th ed. — gentler, with fully worked programmes

How to pass MTH 211

  • The gradient is THE central object of machine learning — every training algorithm you meet in UUY-DTS 313 is gradient descent on a loss surface. Learn it here properly and that course becomes much easier
  • Lagrange multipliers are constrained optimisation, which is exactly what a support vector machine solves — the connection is not decorative
  • Taylor series is how numerical methods approximate everything; MTH 223 next semester assumes you have it cold
  • Practise partial differentiation until you stop confusing it with total differentiation — that specific mistake costs marks every year

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