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MTH 322 Mathematical Methods III

HND1 levelSciences22 topics

MTH 322 covers 22 topics. StudyPath paces them into daily study sessions that finish before your exam date, with practice questions and worked answers for each one.

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Course outline

The topics this course covers, in teaching order.

  1. Vector spaces and subspaces
  2. Basis and dimension
  3. Linear dependence and independence
  4. Row space and dimension of a matrix
  5. Basis construction for finite-dimensional spaces
  6. Inner product
  7. Euclidean vector spaces
  8. Orthogonal basis and Gram-Schmidt process
  9. Systems of simultaneous linear equations
  10. Consistency and existence of solutions of AX = B
  11. Homogeneous and non-homogeneous linear systems
  12. Row and column operations
  13. Determinants and Cramer's rule
  14. Iterative methods for linear systems
  15. Symmetric matrices and quadratic forms
  16. Reduction of quadratic forms to canonical form
  17. Positive definite and semi-definite forms
  18. Eigenvalues, eigenvectors and diagonalization
  19. Cayley-Hamilton theorem
  20. Introduction to partial differential equations
  21. Solutions of first-order first-degree PDEs
  22. Separation of variables and change of variables

A sample from this course

One topic, as StudyPath teaches it.

Vector spaces and subspaces

Vector spaces and subspaces are the foundation of linear algebra, defining the algebraic structure where vectors can be added and scaled. Mastering the axioms, examples such as ℝⁿ, function spaces, and polynomial spaces, and recognising subspace criteria (non‑empty, closed under addition and scalar multiplication) is essential for solving linear systems, proving linear dependence, and analysing linear…

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