Mat2705 Lecture Notes (by bob jantzen)

These hand written lecture notes have been scanned using the mobile phone app Adobe Scan. The textbook is Edwards, Penney, Calvis DEs and LinAlg (4th edition) and its section numbers name the lecture files. Supplementary details from PDF notes and Maple worksheets are found at the homework log page.

These notes were written of Zoom delivered classes during the pandemic and only should be taken as a guide to the key ideas of each section which should not subsitute for reading the textbook. Current classes will have some overlap with similar examples but more interactivity in the classroom.

  1. 1-1a-odecheck.pdf   DEs: Differential Equations: how to state them and "check" a solution
  2. 1-1b-DEs-Inits.pdf   DEs: Differential Equations: initial conditions
  3. 1-2-intDE.pdf           First order DEs independent of the unknown: Integration = solving DE
  4. 1-3-dirfields.pdf       Direction fields for first order DEs and complications
  5. 1-4a-sepDEs.pdf      Separable first order DEs
  6. 1-4b-exps.pdf          Exponential behavior
  7. 1-5a-linear1DEs.pdf Linear 1st order DEs
  8. 1-5b-linear1DEs-complications.pdf Linear 1st order DEs: complications
  9. 1-5c-linear1DEs-mixing.pdf mixing tank problems
  10. 2-1a-logistic.pdf        Logistic Equation
  11. 2-1b-popmodels.pdf      Population models
  12. 2-3-accmodels.pdf      acceleration models
  13. 2-4-euler.pdf  Euler's method for numerical approximation of solutions
  14. 3-1-linsyseliminationDEs.pdf linear system elimination, high school style, linear IVPs produce linear systems to solve
  15. 3-2-matrixrowreduction.pdf matrix row reduction to solve linear systems by elimination
  16. 3-3-rowreductionsoln.pdf Row reduction solution of linear systems
  17. 3-3b-chemlinalg.pdf balancing chemical reactions
  18. 3-4-matrices.pdf matrix operations
  19. 3-5-matrixinverse.pdf matrix inverses
  20. 3-6-determinants.pdf matrix determinants
  21. 4-1-linind.pdf the vector spaces R^n and linear independence
  22. 4-2-vectorspaces.pdf vector spaces and subspaces
  23. 4-3-span.pdf span etc
  24. 4-7-bases.pdf functions as "vectors"
  25. 4-7-functionvectors.pdf functions as "vectors"
  26. 5-1a-2ndorderlinear-intro.pdf 2nd order linear DEs: an intro
  27. 5-1b-2ndorderCCLHDEs.pdf 2nd order CCLH DEs
  28. 5-2-wronskians.pdf Wronskians and linear DEs
  29. 5-3-0-complexstuff.pdf complex arithmetic and complex exponentials
  30. 5-3a-higherorderDEs.pdf higher order linear DEs and complex exponentials
  31. 5-3b-higherorderDEs-multiplicity.pdf higher order linear DEs and multiplicity
  32. 5-3c-sinusoidals.pdf sinusoidal and decaying sinusoidal functions
  33. 5-4-dampedharmonicoscillators.pdf damped harmonic oscillators
  34. 5-5-undeterminedcoeffs.pdf
  35. 5-6-ddho.pdf driven damped harmonic oscillators
  36. 5-6b-ddho-specialcases.pdf driven damped harmonic oscillators: special cases
  37. 6-0-eigen2x2.pdf eigenvectors and eigenvalues for 2x2 matrices
  38. 6-1a-eigenvectors.pdf eigenvectors and eigenvalues
  39. 6-1b-eigenvectors-more.pdf eigenvectors and eigenvalues: more (linear independence, complex eigenvectors)
  40. 6-2-diagonalization.pdf diagonalization
  41. 6-2b-diaggeometry.pdf diagonalization geometry in the plane
  42. 7-3a-1storderDE-realeigen.pdf 1st order linear homogeneous DEs: real eigenvalues
  43. 7-3b-1storderDE-complexeigen.pdf 1st order linear homogeneous DEs: complex eigenvalues
  44. 7-3c-nonhom1storderDE.pdf nonhomogeneous 1st order linear homogeneous DEs, and extending eigevalue decoupling
  45. 7-3d-mixingtanks.pdf mixing tank problems
  46. 7-5a-massspringsystems.pdf mass spring systems
  47. 7-5c-2axels.pdf mass spring systems
  48. 7-5c.pdf damped coupled harmonic oscillator systems
  49. 7-5c-2axels.pdf mass spring systems
  50. 7-5d-damping.pdf mass spring systems
  51. 7-5e-resonance.pdf resonance