﻿ MAT2705 Jantzen Lecture Notes (Zoom delivery)

# 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. They are intended to be explained in the classroom setting, and without bob's verbal explanation, should be taken as a guide to the key ideas of each section which should not subsitute for reading the textbook.

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 coplex 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. 5-4-dampedharmonicoscillators.pdf damped harmonic oscillators
33. 5-5-undeterminedcoeffs.pdf
34. 5-6-ddho.pdf driven damped harmonic oscillators
35. 5-6b-ddho-specialcases.pdf driven damped harmonic oscillators: special cases
36. 6-1a-eigenvectors.pdf eigenvectors and eigenvalues
37. 6-1b-eigenvectors-more.pdf eigenvectors and eigenvalues: more (linear independence, complex eigenvectors)
38. 6-2-diagonalization.pdf diagonalization
39. 6-2b-diaggeometry.pdf diagonalization geometry in the plane
40. 7-3a-1storderDE-realeigen.pdf 1st order linear homogeneous DEs: real eigenvalues
41. 7-3b-1storderDE-complexeigen.pdf 1st order linear homogeneous DEs: complex eigenvalues
42. 7-3c-nonhom1storderDE.pdf nonhomogeneous 1st order linear homogeneous DEs, and extending eigevalue decoupling
43. 7-3d-mixingtanks.pdf mixing tank problems
44. 7-5a-massspringsystems.pdf mass spring systems
45. 7-5c-2axels.pdf mass spring systems
46. 7-5c-2axels.pdf mass spring systems
47. 7-5d-damping.pdf mass spring systems
48. 7-5e-resonance.pdf resonance