# MATH 215

Syllabus: pdf

Outline:

• Jan 6: (textbook 0.2, 0.3, 1.2, 1.3) First order ODE: Definitions, slope field, separable equation (notes). Matlab code to display slope field (link to Canvas).
• Jan 8: (textbook 1.3, 1.4)  Separable equation, linear equation & integrating factor method (notes)
• Jan 10: (textbook 1.2, exercices) Picard theorem, examples and applications (notes)
• Jan 13: (textbook 1.6) Autonomous equations (notes)
• Jan 17: (textbook 1.8) Autonomous equations, exact equations (notes)
• Jan 20: (textbook 1.8) Introduction to Matlab, exact equations (notes)
• Jan 22: (textbook 1.7 & 2.2) Euler method, 2nd order linear ODE with constant coefficients (notes)
• Jan 24 (textbook 2.4) Physical applications (notes)
• Jan 27 (textbook 2.1) Theory of second order linear ODEs (notes)
• Jan 29 (textbook 2.1) Theory of second order linear ODEs, Euler’s formula (notes)
• Jan 31: We covered midterm sample exam (from Canvas)
• Feb 3 (textbook 2.5.2): Nonhomogeneous 2nd order linear ODEs, undetermined coefficients (notes)
• Feb 5 (textbook 2.5.2, 2.5.3): undetermined coefficients, variation of parameters (notes)
• Feb 10 (textbook 2.5.3): variation of parameters (notes)
• Feb 12 (textbook 2.6): variation of parameters, forced oscillations (notes)
• Feb 14 (textbook 2.6): forced oscillations (notes)
• Feb 24 (textbook 3.1, 3.3): System of ODE’s (notes)
• Feb 26 (textbook 3.4): Eigenvalue method (notes)
• Feb 28 (textbook 3.4, 3.5): Phase portrait for 2D linear systems (notes)
• Mar 2 (textbook 3.5, 3.7): Phase portrait for 2D linear systems, nullclines, multiple eigenvalues (notes)
• Mar 4 (textbook 3.7): multiple eigenvalues (notes)
• Mar 6 (textbook 3.9): non-homogeneous systems, variation of parameters (notes)
• Mar 9 (textbook 8.1,2): non-linear systems, critical points and linearization (notes)
• Mar 11 (textbook 8.2): Stability, phase portrait (notes)
• Mar 13 (textbook 8.3, 8.4): Center, conservative equations (notes)
• Mar 16/18/20: From now on we move to online course (see Canvas where videos will be posted -> see pages section)
– Conservative equations (notes: see Wayne Nagata’s Mon 16 notes here),
– Applications of non linear systems: competing species (notes)
– pendulum ( link to 201 section content)
– Intro to Laplace Transform (link to 201 section content)
• Mar 23/25/27
-Unit step function, inverse transforms (link to 202 section content)
-first shifting property (link to 202 section content)
– Laplace transform of derivatives and ODE’s (notes and video on Canvas)
– Use of Heaviside function (notes 1 notes 2 and video on Canvas)
• Mar 30: Use of Heaviside function/ rectangular section (link to 202 section content)
• April 1: Delta function/ Impulseresponse link to 202
• April 3: Special lecture on modeling of COVID-19: deterministic modeling / stochastic modeling (~27.MB, to watch video at the end, open with acrobat reader)