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56:49 The natural log II 5.2, Math 221 Winter 2021 The natural log II 5.2, Math 221 Winter 2021	The natural log II 5.2, Math 221 Winter 2021 11995 log power function rule times properties derivative thing temperature question alright property graph coffee x. things minus chain 3x degrees relation definition q. p. From Rakesh Rakesh 0 likes 3 plays 0
36:02 Discussion HW 3.6, 4.1, Math 221 Winter 2021 Discussion HW 3.6, 4.1, Math 221 Winter 2021	Discussion HW 3.6, 4.1, Math 221 Winter 2021 11995 question slope max prime function point relation alright thing points min things peaks calculus helicopter graph derivative distance law role variables variable man picture t. x. sense times side respect equals dt problem height From Rakesh Rakesh 0 likes 1 plays 0
10:18 Relative max/min I - 4.2, Math 221 Winter 2021 Relative max/min I - 4.2, Math 221 Winter 2021	Relative max/min I - 4.2, Math 221 Winter 2021 11995 question slope max prime function point relation alright thing points min things peaks calculus helicopter graph derivative distance law role hollows definition peak x. numbers maximum men places relative word From Rakesh Rakesh 0 likes 7 plays 0
52:39 Competing species III (phase portrait) Competing species III (phase portrait)	Competing species III (phase portrait) We combine the information obtained in parts I and II to draw the phase portrait. 11995 region point arrows axis alright picture nullclines curve thing trajectory orbits field vector direction component times side things step points From Rakesh Rakesh 0 likes 14 plays 0 Department Name Mathematical Sciences Date Established December 05, 2020
35:27 Competing species II (Nullclines) Competing species II (Nullclines)	Competing species II (Nullclines) Nullclines and direction field chart for a competing species problem. 11995 arrows component nullclines points side minus point axis region times nullcline lines thing quadrant picture arrow things boundary alright direction From Rakesh Rakesh 0 likes 23 plays 0 Department Name Mathematical Sciences Date Established December 02, 2020
50:52 Competing species I Competing species I	Competing species I Drawing the global phase portrait for a system of ODEs modeling two species competing for the same source of food in an ecosystem. 11995 point side points region vector minus component idea field theorem curve orbit alright trajectory things species dot arrow 3d thing From Rakesh Rakesh 0 likes 16 plays 0 Department Name Mathematical Sciences Date Established December 02, 2020
49:16 Closed orbits II and the Poincare-Bendixson… Closed orbits II and the Poincare-Bendixson theorem	Closed orbits II and the Poincare-Bendixson theorem Duluc's criterion for the non-existence of closed orbits and the statement of the Poincare-Bendixson theorem followed by remarks. 11995 region point orbit trajectory delta divergence theorem times vector regions dimensions dot field 3d d. orbits solution points boundary alright From Rakesh Rakesh 0 likes 33 plays 0 Department Name Mathematical Sciences Date Established November 23, 2020
40:30 Linearization near a fixed point II Linearization near a fixed point II	Linearization near a fixed point II 11995 point dot linear things x1 linearization origin thing x2 picture matrix times minus alright behavior saddle spiral vector eigenvalue eigenvalues From Rakesh Rakesh 0 likes 20 plays 0 Department Name Mathematical Sciences Date Established November 20, 2020
32:24 Closed orbits I Closed orbits I	Closed orbits I Also includes Duluc's criterion for ruling out closed orbits. 11995 orbit seconds vector solution point gamma velocity dot equation path side hand thing field divergence theorem curve argument things direction From Rakesh Rakesh 0 likes 21 plays 0 Department Name Mathematical Sciences Date Established November 20, 2020
13:56 Linearization near a fixed point I Linearization near a fixed point I	Linearization near a fixed point I 11995 solution point pendulum velocity x1 x2 square dot tools factor equation points alright thing minus question beginning linear position sense From Rakesh Rakesh 0 likes 15 plays 0 Department Name Mathematical Sciences Date Established November 18, 2020
01:00:47 Elementary properties of non-linear systems Elementary properties of non-linear systems	Elementary properties of non-linear systems 11995 vector point dot trajectory solution pendulum position field velocity seconds trajectories thing theta forces x2 alright ode behavior arrows problem From Rakesh Rakesh 0 likes 11 plays 0 Department Name Mathematical Sciences Date Established November 18, 2020
01:15:35 First order linear systems of ODEs - II First order linear systems of ODEs - II	First order linear systems of ODEs - II 11995 lambda solution solutions infinity power linear eigenvalues times eigenvector star point systems eigenvectors matrix vector dot things eigen cosine exponentials From Rakesh Rakesh 0 likes 15 plays 0 Department Name Mathematical Sciences Date Established November 13, 2020
01:01:24 Introduction and the damped driven pendulum Introduction and the damped driven pendulum	Introduction and the damped driven pendulum An introduction to Nonlinear Dynamics. A model for the damped driven pendulum and the qualitative questions of interest for its motion. 11995 theta dot pendulum motion equation ode questions alpha things resistance force torque position od question equilibrium thing air velocity direction From Rakesh Rakesh 0 likes 85 plays 0 Department Name Mathematical Sciences Date Established November 11, 2020
08:00 First order linear system of ODEs - I First order linear system of ODEs - I	First order linear system of ODEs - I What is a linear system of ODEs? 11995 linear systems matrix dot alright behavior eigenvectors eigenvalues side hand form x2 minus x1 equations vector function solutions approximation equation From Rakesh Rakesh 0 likes 9 plays 0 Department Name Mathematical Sciences Date Established November 11, 2020
01:14:03 Derivation of Euler-Lagrange equation : Integral… Derivation of Euler-Lagrange equation : Integral constraints	Derivation of Euler-Lagrange equation : Integral constraints 11995 function problem problems minimizer things eta functions thing constraint point endpoints points times prime variables condition parts integration calculus lagrange From Rakesh Rakesh 0 likes 67 plays 0 Department Name Mathematical Sciences Date Established November 06, 2020
21:43 Variable end points - general theory Variable end points - general theory	Variable end points - general theory 11995 point curve problem endpoint end thing curves parabola hand points things endpoints od shape phi notes problems times left function From Rakesh Rakesh 0 likes 6 plays 0