This page contains the notes from each class and any additional material useful for your study and exam preparation. The numbers are the textbook sections to read for each week.
Week 13:
Monday: Lecture 33: LT of the unit step function and its application S6.2.3
Wednesday: Lecture 34: LT of Dirac delta function
Friday: Lecture 35: Final Review , Solution (to some of the practice problems)
Week 12: Laplace Transform: S6.1-6.2
Monday: Lecture 30: Pendulum motion (cont’d)
Wednesday: Lecture 31: Laplace Transform
Friday: Lecture 32: Inverse of Laplace transform
Week 11:
Monday: Remembrance day
Wednesday: Midterm Review
Friday: Midterm 2 in class
Week 10: Nonlinear systems: S 8.1-8.3
Monday: Lecture 26: Damped forced vibrations
Wednesday: Lecture 27: Nonlinear systems and their linearization
Friday: Lecture 28: Competing species and damped pendulum
Week 9: Chapter 2 except 2.3
Monday: Lecture 23: Forced (non-homogeneous) 2nd order ode
Wednesday: Lecture 24: More about undetermined coefficients
Friday: Lecture 25: Undamped forced vibrations (beats and resonance)
Week 8:
Monday: Lecture 20: Non-homogenous systems (Method of undetermined coefficients)
Wednesday: Lecture 21: Second-order ODE and physical applications Chapter 2
Friday: Lecture 22: Undamped and damped vibrations Chapter 2
Week 7: (3.8, 3.9)
Monday: Lecture 17: Fundamental Matrix and Wronskian
Wednesday: Lecture 18: Matrix Exponential
Friday: Lecture 19: Non-homogenous systems (Method of variation of parameters)
Week 6: Midterm1
Monday: Turkey Day! 🙂
Wednesday: Midterm Review
Friday: Midterm 1 in class
Week 5: (3.4, 3.5, 3.7)
Monday: Lecture 12: ODE system with complex eigenvalues
Wednesday: Lecture 13: systems with complex eigval cont’d and their vector fields (Midterm up to the end of this lecture)
Friday: Lecture 14: systems with a repeated eigenvalue (also special case when one eigenvalue is 0).
Week 4: (1.7, 3.1, 3.4)
Monday: Lecture 9: Euler and Improved Euler Method
Wednesday: Lecture 10: ODE systems (two distinct real eigenvalues)
Friday: Lecture 11: Stability and vector fields in ODE systems (2*2 case: two real eigenvalues) This lecture is edited and re-uploaded with some changes, check if you have the correct version.
Week 3: (1.2, 1.8, 1.7)
Monday: Lecture 6: Stability (cont’d), Picard’s Thm (existence and uniqueness)
Wednesday: Lecture 7: Exact equations
Friday: Lecture 8: Integrating factor for non-exact equations
Week 2: (1.4, 1.2, 1.6)
Monday: Lecture 3: Integrating factor (cont’d)
Wednesday: Lecture 4: Slope/direction field (Falling object model)
Friday: Lecture 5: Stability of steady states
Week 1: (0.2, 1.1, 1.3, 1.4)
Monday: Labour day
Wednesday: Lecture 1: Intro to ODE
Friday: Lecture 2: Separable eqt, integrating factor
Integral Cheat Sheet