WClasses

AMATH 451 - Introduction to Dynamical Systems

A unified view of linear and nonlinear systems of ordinary differential equations in Rn. Flow operators and their classification: contractions, expansions, hyperbolic flows. Stable and unstable manifolds. Phase-space analysis. Nonlinear systems, stability of equilibria, and Lyapunov functions. The special case of flows in the plane, Poincare-Bendixson theorem, and limit cycles. Applications to physical problems will be a motivating influence.

Prerequisites

AMATH250 or AMATH251

Corequisites

None

Antirequisites

None

Offerings

Winter 2026 [1261]

Section	Class	Enrolled	Time	Days	Location	Instructor
LEC 001	5763	13 / 40	10:00 - 11:20	M,W
TUT 101	8570	13 / 40	14:30 - 15:20	M

Winter 2025 [1251]

Section	Class	Enrolled	Time	Days	Location	Instructor
LEC 001	5844	29 / 40	10:30 - 11:20	M,W,F
TUT 101	6463	29 / 40	13:30 - 14:20	M

Winter 2024 [1241]

Section	Class	Enrolled	Time	Days	Location	Instructor
LEC 001	5865	27 / 40	11:30 - 12:20	M,W,F
TUT 101	6538	27 / 40	14:30 - 15:20	M

Winter 2023 [1231]

Section	Class	Enrolled	Time	Days	Location	Instructor
LEC 001	5992	21 / 40	13:30 - 14:20	M,W,F	E2 1732	Xinzhi Liu
TUT 101	6789	21 / 40	14:30 - 15:20	M	E2 1732

Winter 2022 [1221]

Section	Class	Enrolled	Time	Days	Location	Instructor
LEC 001	5856	36 / 40				Xinzhi Liu
TUT 101	8777	36 / 40	10:30 - 11:20	W	MC 2038	Xinzhi Liu

Winter 2021 [1211]

Section	Class	Enrolled	Time	Days	Location	Instructor
LEC 041	5907	33 / 80				Xinzhi Liu

Winter 2020 [1201]

Section	Class	Enrolled	Time	Days	Location	Instructor
LEC 001	5752	25 / 40	10:30 - 11:20	M,W,F	MC 2017	Sue Ann Campbell

Winter 2019 [1191]

Section	Class	Enrolled	Time	Days	Location	Instructor
LEC 001	5627	39 / 40	13:00 - 14:20	M,W	QNC 2501	Sue Ann Campbell

Winter 2018 [1181]

Section	Class	Enrolled	Time	Days	Location	Instructor
LEC 001	5683	20 / 40	10:30 - 11:20	M,W,F	DWE 1502	Sue Ann Campbell

Winter 2017 [1171]

Section	Class	Enrolled	Time	Days	Location	Instructor
LEC 001	5414	34 / 45	09:30 - 10:20	M,W,F	DWE 3522A	Jun Liu

Winter 2016 [1161]

Section	Class	Enrolled	Time	Days	Location	Instructor
LEC 001	5953	20 / 45	10:30 - 11:20	M,T,Th	DWE 3522A	Jun Liu

Winter 2015 [1151]

Section	Class	Enrolled	Time	Days	Location	Instructor
LEC 001	5741	28 / 45	09:30 - 10:20	M,W,F	RCH 309	David Siegel

Winter 2014 [1141]

Section	Class	Enrolled	Time	Days	Location	Instructor
LEC 001	5552	25 / 45	11:30 - 12:20	M,W,F	MC 4045	Xinzhi Liu

Winter 2013 [1131]

Section	Class	Enrolled	Time	Days	Location	Instructor
LEC 001	5308	33 / 45	11:30 - 12:20	M,W,F	DWE 1515	David Siegel

Winter 2012 [1121]

Section	Class	Enrolled	Time	Days	Location	Instructor
LEC 001	5086	29 / 45	11:30 - 12:20	M,W,F	MC 4064	Sue Ann Campbell

Winter 2011 [1111]

Section	Class	Enrolled	Time	Days	Location	Instructor
LEC 001	5040	15 / 45	11:30 - 12:20	M,W,F	MC 4064	Sue Ann Campbell

Winter 2010 [1101]

Section	Class	Enrolled	Time	Days	Location	Instructor
LEC 001	4991	23 / 45	11:30 - 12:20	M,W,F	MC 4064	Sue Ann Campbell

Winter 2009 [1091]

Section	Class	Enrolled	Time	Days	Location	Instructor
LEC 001	4200	16 / 45	11:30 - 12:20	M,W,F	MC 4041	Xinzhi Liu

Winter 2008 [1081]

Section	Class	Enrolled	Time	Days	Location	Instructor
LEC 001	3363	15 / 45	11:30 - 12:20	M,W,F	MC 4041	Xinzhi Liu

Winter 2007 [1071]

Section	Class	Enrolled	Time	Days	Location	Instructor
LEC 001	3297	15 / 45	11:30 - 12:20	M,W,F	MC 4040	Sue Ann Campbell

Winter 2006 [1061]

Section	Class	Enrolled	Time	Days	Location	Instructor
LEC 001	3171	16 / 45	11:30 - 12:20	M,W,F,D,W,E		Xinzhi Liu

Winter 2005 [1051]

Section	Class	Enrolled	Time	Days	Location	Instructor
LEC 001	3115	19 / 45	11:30 - 12:20	M,W,F,M,C		Sue Ann Campbell

Winter 2004 [1041]

Section	Class	Enrolled	Time	Days	Location	Instructor
LEC 001	2964	13 / 45	08:30 - 09:20	M,W,F,M,C		David Siegel

Winter 2003 [1031]

Section	Class	Enrolled	Time	Days	Location	Instructor
LEC 001	3557	16 / 45	11:30 - 12:20	M,W,F,M,C		David Siegel

Winter 2002 [1021]

Section	Class	Enrolled	Time	Days	Location	Instructor
LEC 001	1131	10 / 45	11:30 - 12:20	M,W,F,M,C		Xinzhi Liu