**TEXT: **
James R. Brannan and William E. Boyce,
**Differential Equations**
(an introduction to modern methods & applications),
**3rd edition**, John Wiley & Sons, 2015.
[Publisher's website for the text]

**SYLLABUS: ** Click here

05/16 (Mon) Course description. What do we need for Math2552? What do we learn in Math2552? 1.1 Diff Eqs, Math Models 1.3 Classification of Differential Equations (orders, single eqs vs systems, linear vs nonlinear) Exercises: 1.3 (1-6,13,16,21,23,32) (Some Solutions) 05/18 (Wed) 2.1 Separable equations: dy/dx=f(x)g(y) 2.2 Linear Equations: Method of Integrating Factor Homogeneous linear equations: dy/dt+a(t)y=0 Nonhomogeneous linear equations: dy/dt+a(t)y=b(t) 1.2 Direction Fields. Exercises: 2.1 (29,35, and click here), 2.2 (click here), 1.2 (14,19,25,26,28) 05/20 (Fri) 2.3 Modeling with 1st order eqs 2.4 Differences between homog linear, nonhomog linear, & nonlinear eqs Exercises: 2.3 (1,3,5,25), 1.1 (4,12,14), 2.4 (2,3,11,12,13,14) Some Fun: If you are a sports maniac, try 2.3 (32,33).

05/23 (Mon) 2.4 continued! 2.5 Autonomous eqs and population dynamics. See p.458 for the formal definitions of "stable", "unstable" and "asymptotically stable". This Scholarpedia article may be helpful too. Exercises: 1.2 (1,9), 2.4 (click here), 2.5 (1,2, and click here) 05/25 (Wed) 2.6 Exact Equations and Integrating Factors Exercises: 2.6 (3,5,16,21,27,28) 05/27 (Fri) 3.2 Linear 2-D systems 3.3 Homog 2-D linear systems with const coefficients (distinct real & nonzero eigenvalues) Exercises: 3.2 (1-8), 3.3 (6,10,11,15,16,17,19,23) and review Linear Algebra: (Section 3.1 can be of some help) how to solve linear systems Ax=b, determinants, eigenvalues, eigenvectors

05/30 (Monday) Official School Holiday 05/31 (Tuesday) ---------2:00pm-2:25pm, Quiz 1--------- Place: Your recitation room Coverage: Lectures & Recitations of 05/16-05/26 Policy: No calculator. Closed book. Only one sheet of handwritten note (front & back, letter size) is allowed. 06/01 (Wed) 3.3 continued! A Catalogue of Phase Portraits of Homog 2-D Linear Systems Exercises: 3.2 (1-8), 3.3 (6,10,11,15,16,17,19,23) 06/03 (Fri) 3.4 Homog 2-D linear systems with const coefficients (complex eigenvalues). Exercises: 3.4 (2,4,5,6,7) 3.3 Homog 2-D linear systems with const coefficients (zero eigenvalue). Exercises: 3.3 (5,12 and click here)

06/06 (Mon) 3.5 Homog 2-D linear systems with const coefficients (repeated real eigenvalues). Exercises: 3.5 (2,3,10) Shifted systems of the form:x'=A(x-a) andx'=Ax+b. Exercises: click here 06/08 (Wednesday) ---------Midterm 1, Normal Class Time--------- Place: College of Computing 17 (not your recitation room) Coverage: Lectures & Recitations of 05/16-06/03 Policy: No calculator. Closed book. Only one sheet of handwritten note (front & back, letter size) is allowed. 06/10 (Fri) 3.6 & 7.2 Nonlinear 2-D systems (local phase portraits near critical points). Linearization: Neutral eigenvalues. Non-neutral eigenvalues. Exercises: 3.6 (15,16) and some more here

06/13 (Mon) Some applications: salt in tanks 7.3 Competing species. Slides: click here Exercises: p.144 (31), 7.3 (1,2) 06/15 (Wed) 4.1 Second order linear eqs: definitions and examples 4.2 Second order linear homogeneous eqs: y''+p(t)y'+q(t)y=0 Exercises: 4.1 (1-9,16), and click here 4.3 Second order linear homogeneous eqs with const coefficients: ay''+by'+cy=0 Exercises: 4.3 (2,6,7,11,13,19,21,23,25,29,30,36,39,43) 06/16 (Thursday) ---------2:00pm-2:25pm, Quiz 2--------- Place: Your recitation room Coverage: Lectures & Recitations of 06/06-06/14 Policy: No calculator. Closed book. Only one sheet of handwritten note (front & back, letter size) is allowed. 06/17 (Fri) 4.3 (continued)

06/20 (Mon) 4.5 Nonhomogeneous linear eqs (method of undetermined coefficients). Supplementary material: Higher order linear eqs with constant coefficients Exercises: 4.5 (1-5,18,21,26,27,37) 06/22 (Wed) 4.7 Nonhomogeneous linear eqs (variation of parameters). Exercises: 4.7 (3,7,11,19) 06/23 (Thursday) ---------2:00pm-2:25pm, Quiz 3--------- Place: Your recitation room Coverage: Lectures & Recitations of 06/15-06/21 Policy: No calculator. Closed book. Only one sheet of handwritten note (front & back, letter size) is allowed. 06/24 (Fri) 4.4 Free vibrations. Spring-mass systems. Series RLC circuits. Exercises: 4.4 (3,5,6,11,17. 8,12,18)

06/27 (Mon) 4.6 Forced vibrations. Resonance. Exercises: 4.6 (9,12,15,16,17) 06/29 (Wed) 5.1 Definition of the Laplace transform 5.2 Properties of the Laplace transform Exercises: 5.1 (13,15,16,22), 5.2 (5,7,9,11a,18,19,20,24) * Review partial fractions. * Transform the initial value problem, y'(t)-4y(t)=2-5t, y(0)=7, into an algebraic equation for Y(s)=ℒ{y(t)}. Then find Y(s). 07/01 (Fri) 5.3 The inverse Laplace transform Exercises: 5.3 (9,10,11,18,19,21,23) 5.4 Solve diff eqs with Laplace transforms Exercises: 5.4 (1,2,5,10,12,18)

07/04 (Monday) Official School Holiday 07/05 (Tuesday) School Break 07/06 (Wednesday) ---------Midterm 2, Normal Class Time--------- Place: Coll of Computing 17 (not your recitation room) Coverage: Lectures & Recitations of 06/06-06/30 Policy: No calculator. Closed book. Only one sheet of handwritten note (front & back, letter size) is allowed. 07/08 (Fri) 5.4 Solve diff eqs with Laplace transforms (continued) 5.5 Discontinuous functions and periodic functions Exercises: 5.5 (2,8,11,14,15,22)

07/11 (Mon) 5.6 Diff eqs with discontinuous forcing functions Exercises: 5.6 (2,4,6,12) 07/13 (Wed) 5.7 Impulse function. Delta function. Exercises: 5.7 (1,2,3,9,10,17,18) 5.8 Convolution Exercises: 5.8 (2,4,6,8,9,12,16,20) 07/15 (Fri) 6.1 Linear systems (n diff eqs): definition and examples 6.2 Linear systems (n diff eqs): basic theory Exercises: 6.1 (2,4,5,10,12), 6.2 (8,9,12,16) 6.3 Homogeneous linear systems with const coefficients (distinct eigenvalues) Exercises: 6.3 (4,10,16,21)

07/18 (Mon) 6.4 Homogeneous linear systems with const coefficients (complex eigenvalues) Exercises: 6.4 (4,6,13) 6.5 Fundamental matrices and matrix exponential Additional Notes Exercises: 6.5 (2,8,14,16,17) 07/19 (Tuesday) ---------2:00pm-2:25pm, Quiz 4--------- Place: Your recitation room Coverage: Lectures & Recitations of 07/01-07/14 Policy: No calculator. Closed book. Only one sheet of handwritten note (front & back, letter size) is allowed. 07/20 (Wed) 6.7 Homogeneous linear systems with const coefficients (repeated eigenvalues) Exercises: 6.7 (1,3,5,8) 6.6 Nonhomogeneous linear systems (variation of parameters) Exercises: 6.6 (6,8,12,13), and Exercise [3] in this file. 07/22 (Fri) 7.1 Autonomous systems. Stability. Exercises: Consider 6.3 (1,2,3,4), 6.4 (2,4,6,13), 6.7 (1,3,5,8). Is the equilibrium (critical point)x=0asymptotically stable, stable, or unstable? Ans: 6.3 (AS, US, US, S but not AS), 6.4 (US, AS, S but not AS, S but not AS), 6.7 (US,US,US,AS) 7.2 Almost linear systems in N-dimensions Exercises: click here

07/25 (Mon) Last Class 7.6 Chaos in the Lorenz attractor. "Chaos Theory" on Wikipedia 07/26 (Tue) Last Recitation July 29 (Friday) ---------Final Exam (see syllabus for times)--------- Place: Coll of Computing 17 (not your recitation room) Coverage: the whole semester Policy: No calculator. Closed book. Only one sheet of handwritten note (front & back, letter size) is allowed.