- Syllabus.
- Textbook: See the course Canvas page.

Email: nagata(at)math(dot)ubc(dot)ca

Office: Mathematics building, room 112

Office hours: M W F 1:00-1:50 pm, or appointment by email

Telephone: 604-822-2573 (no voice mail)

- Bring UBCcard (or other official photo I.D., if UBCcard is unavailable), it must be checked during the exam.
- Laplace transform table PROVIDED, trig identities (if required) provided.
- No books, notes, etc. allowed.
- No calculators, cell phones, etc. allowed. Numerical answers may be given as "calculator ready".
- Topics: all

- write clear explanations of solutions to mathematical problems, showing logical steps and arguments
- draw or interpret a
*slope field*for any first order ODE, draw approximate*solution curves*consistent with a slope field - determine if a first order ODE is
*separable*or*linear*or*exact*and if so, solve the ODE - determine if a first order ODE is
*autonomous*and if so, find all*critical points*(*equilibrium solutions*), draw the*phase portrait*, determine the*stability*of all critical points - determine if there exists an
*integrating factor*that makes a first order ODE into an exact equation and if so, find the integrating factor and solve the ODE - solve an initial value problem (IVP) for a first order ODE
- set up, solve and analyze a mathematical model that involves a first order ODE
- use MATLAB to plot graphs of functions, or find roots of functions
- use MATLAB to plot slope fields or solution curves for a first order ODE
- use
*Euler's method*to construct, by hand or with MATLAB, an approximation of the solution to an IVP for a first order ODE - determine if a second order ODE is
*linear*and if so, if it is*homogeneous*or*nonhomogeneous* - determine if solutions of a homogeneous linear second order ODE are
*linearly independent*or*linearly dependent* - find the
*general solution*of a homogeneous linear second order ODE, or solve an IVP for such an equation - set up, solve and analyze a mathematical model that involves a constant coefficient homogeneous linear second order ODE (e.g. mass-spring system with or without damping, with zero external forcing)
- =====================
- find the general solution of a nonhomogeneous linear second order ODE (undetermined coefficients, variation of parameters), or solve an IVP for such an equation
- set up, solve and analyze a mathematical model that involves a constant coefficient nonhomogeneous linear second order ODE (e.g. mass-spring system with or without damping, with constant or sinusoidal external forcing)
- write a higher order ODE as an equivalent system of first order ODEs
- determine if a system of first order ODEs is
*linear*and if so, if it is*homogeneous*or*nonhomogeneous* - determine if solutions of a homogeneous linear system of first order ODEs are
*linearly independent*or*linearly dependent*; form a*fundamental matrix*from linearly independent solutions; express the general solution of a homogeneous linear system in terms of a fundamental matrix - find the
*general solution*of a homogeneous linear system of first order ODEs, or solve an IVP for such a system - for a 2-dimensional autonomous (constant coefficient) linear system of 1st order ODEs, classify the behaviour near the
*critical point*(*equilibrium solution*) at the origin, draw the*phase portrait* - find the general solution of a nonhomogeneous linear system of first order ODEs (variation of parameters), or solve an IVP for such a system
- determine if a 2-dimensional system of first order ODEs is
*autonomous*and if so, find all*critical points*(*equilibrium solutions*), use*linearization*to classify (if possible) the local behaviour and find the*stability*(if possible) at each critical point; draw the*global*phase portrait (incorporating*local*phase portraits, near each critical point) - =====================
- determine if a second order ODE is
*conservative*and if so use this fact to draw the phase portrait for the associated system of first order ODEs - use the definition to find the
*Laplace transform*of a function f(t) - find the
*inverse Laplace transform*of a function F(s) - use Laplace transforms to solve an IVP for a nonhomogeneous linear second order ODE, with a piecewise continuous and/or impulsive (delta function) nonhomogeneous (forcing) term
- to be continued (updated approximately weekly)

See the course Canvas page.

- 1. Mon Jan 6: 0.2, 0.3, 1.1, 1.2, 1.3... [ Introduction, Slope fields, Separable equations ]
- 2. Wed Jan 8: ...
- 3. Fri Jan 10: ..., 1.4... [ Linear equations and the integrating factor ]
- Webwork Assignment W1 opens on Canvas, due Jan 17

- 4. Mon Jan 13: ..., 1.6 [ Autonomous equations ]
- 0. Wed Jan 15: (UBC classes cancelled)
- 5. Fri Jan 17: 1.8... [ Exact equations ]
- Homework Assignment HW1 opens on Canvas, due Jan 24

- 6. Mon Jan 20: ..., 1.7... [ Euler's method ], MATLAB orientation [ Where to find the MATLAB source codes for HW and how to use them etc. ]
- 7. Wed Jan 22: ..., 2.1... [ Linear 2nd order ODEs ]
- 8. Fri Jan 24: ..., 2.2... [ Constant coefficient homogeneous linear 2nd order ODEs ]
- Webwork Assignment W2 opens on Canvas, due Jan 31

- 9. Mon Jan 27: ...
- 10. Wed Jan 29: 2.4... [ Mechanical vibrations ]
- 11. Fri Jan 31: ...
- Homework Assignment HW2 opens on Canvas, due Feb 14
- Information on Midterm Test 1 available on Canvas

- 12. Mon Feb 3: ..., 2.5... [ Nonhomogeneous equations ]
- 13. Wed Feb 5: ...
- 14. Fri Feb 7: Midterm Test 1
- 15. Mon Feb 10: ..., 2.6... [ Forced oscillations and resonance ]
- 16. Wed Feb 12: ...
- 17. Fri Feb 14: ..., 3.1, 3.3... [ Introduction to systems of ODEs, Linear systems of ODEs ]
- Homework Assignment HW3 opens on Canvas, due Feb 28

- ----------------------------
- 18. Mon Feb 24: ..., 3.4... [ Eigenvalue method ]
- 19. Wed Feb 26: ..., 3.5... [ Two dimensional systems and their vector fields ]
- 20. Fri Feb 28: ...
- Webwork Assignment W3 opens on Canvas, due Mar 6

- 21. Mon Mar 2: ..., 3.7... [ Multiple eigenvalues ]
- 22. Wed Mar 4: ..., 3.9... [ Nonhomogeneous systems ]
- 23. Fri Mar 6: ..., 8.1... [ Linearization, critical points and equilibria ]
- HW4 Homework Assignment opens on Canvas, due Mar 13

- 24. Mon Mar 9: ..., 8.2... [ Stability and classification of isolated critical points ]
- 25. Wed Mar 11: ...
- 26. Fri Mar 13: ...
- Information on MT2 Midterm Test 2 (now cancelled) available on Canvas

- ---------------------------- UBC classes move online ----------------------------
- 27. Mon Mar 16
- 27-1: example of a conservative equation notes pdf 5 pages (colour p.3 pdf 4MB, colour p.4 pdf 5MB), audio (mp3, 18MB), link to video 1, link to video 2
- 27-2: part 1/2 pendulum notes pdf 3 pages, audio mp3 12MB

- 28. Wed Mar 18
- W4 Webwork Assignment opens on Canvas, due Mar 25
- 28-1: part 2/2 pendulum notes pdf 3 pages (colour p.2 pdf), audio mp3
- 28-2: part 1/2 competing species notes pdf 3 pages, link to video

- 29. Fri Mar 20
- 29-1: part 2/2 competing species notes pdf 5 pages (colour p.3 pdf, colour p.4 pdf), link to video
- 29-2: 6.1.1 Lapace transform definition notes pdf 1 page, audio mp3

- 30. Mon Mar 23
- 30-1: 6.1.1 unit step (Heaviside) function, 6.1.2, 6.1.3 the inverse tranform notes pdf 3 pages , audio(a) mp3, audio(b) mp3 (typo in Ex.6.1.C corrected 03-23 09:36 PDT)
- 30-2: 6.1.3 first shifting property notes pdf 2 pages, audio mp3

- 31. Wed Mar 25
- HW5 Homework Assignment opens on Canvas, due Apr 1
- 31-1: 6.2.1 transforms of derivatives, 6.2.2 solving ODEs notes pdf 4 pages, link to video
- 31-2: part 1/4 6.2.3 using the Heaviside function notes pdf 2 pages, link to video

- 32. Fri Mar 27
- 32-1: part 2/4 6.2.3 using the Heaviside function notes pdf 4 pages (typo on p.2 corrected, page of details added 04-01 14:46 PDT), link to video
- 32-2: part 3/4 6.2.3 using the Heaviside function notes pdf 2 pages, audio mp3

- 33. Mon Mar 30
- 33-1: part 4/4 6.2.3 using the Heaviside function notes pdf 4 pages, audio mp3
- 33-2: 6.4.1 rectangular pulse notes pdf 2 pages, audio mp3

- 34. Wed Apr 1
- W5 Webwork Assignment opens on Canvas, due Apr 8
- 34-1: 6.4.1 the delta function, 6.4.3 impulse response notes pdf 3 pages, audio mp3
- 33-2: 6.4.3 impulse response notes pdf 2 pages (typo on p.5 corrected 03-31 21:25 PDT), audio mp3