L1 – Monday, August 26 – 1.1 Some Basic Mathematical Models; Direction Fields; handout and solutions; and calculus review problems and solutions; do Webassign 1
L2 – Wednes, August 28 – 1.2 Solutions of Some Differential Equations (and chemical mixing application); handout and solutions; do Webassign 2
L3 – Friday, August 30 – 1.3 Classification of Differential Equations, and 2.1 Linear Equations, Method of Integrating Factors; handout and solutions; do Webassign 3
Monday, September 2 – Labor Day (no class)
L4 – Wednes, September 4 – 2.1 Integrating Factors cont., and 2.3 Example 3 (more chemical mixing); handout and solutions; do Webassign 4
L5 – Friday, September 6 – 2.2 Separable Equations; handout and solutions; do Webassign 5
L6 – Monday, September 9 – Application to sling, and finite-time blow-up, 2.4 Existence and Uniqueness for Linear Equations; handout and solutions; do Webassign 6
L7 – Wednes, September 11 – 2.4 cont. Existence and Uniqueness for Nonlinear Equations; and the Bernoulli DE; handout and solutions; do Webassign 7
L8 – Friday, September 13 – 2.5 Autonomous Equations and Population Dynamics; handout and solutions; do Webassign 8
L9 – Monday, September 16 – 2.5 cont., and second order reduction methods from problems at end of Chapter 2; handout and solutions; do Webassign 9
L10 – Wednes, September 18 – 2.7 Euler’s method; handout and solutions; direction field 1 and direction field 2; do Webassign 10
L11 – Friday, September 20 – 3.1 Homogeneous Equations with Constant Coefficients; handout and solutions; do Webassign 11
L12 – Monday, September 23 – 3.2 Solutions of Linear Homogeneous Equations; handout and solutions [substitute instructor – Prof. Leisman]; do Webassign 12
L13 – Wednes, September 25 – 3.3 Complex Roots of the Characteristic Equations; handout and solutions [substitute instructor – Prof. Leisman]; do Webassign 13
Friday, September 27 – no class, to compensate for evening midterm
L14 – Monday, September 30 – 3.4 Repeated Roots; Reduction of Order; handout and solutions; do Webassign 14
Wednes, October 2 – in-class review, and evening Midterm 1
L15 – Friday, October 4 – 3.5 Nonhomogeneous Equations; Method of Undetermined Coefficients; handout and solutions; and (optional handout) why the Undetermined Coefficient method works; do Webassign 15
L16 – Monday, October 7 – 3.6 Variation of Parameters; handout and solutions; do Webassign 16
L17 – Wednes, October 9 – 3.7 Mechanical and Electrical Vibrations; handout and solutions; do Webassign 17
L18 – Friday, October 11 – 3.7 cont.; handout and solutions; do Webassign 18; video showing damped oscillators (note the video only shows release from rest, in which case the critically damped and overdamped oscillators never reach zero displacement; but if one gave the oscillator a sufficiently large initial velocity, it could pass through the zero point before relaxing back toward it)
L19 – Monday, October 14 – 3.8 Forced Vibrations; handout and solutions; forced response graph (showing that the amplitude blows up as the forcing frequency w approaches the natural frequency 2), a forced undamped oscillator example (which shows some typical general solutions); also a beating graph, and a 2 minute demo from MIT on resonance and beating (using tuning forks, which vibrate similar to a mass-spring system); do Webassign 19
L20 – Wednes, October 16 – 3.8 cont.; handout and solutions; forced damped response graph; here are some resonance applications (videos of Millennium Bridge swaying, Bay of Fundy tides, glass shattering; and an explanation of radio tuning); do Webassign 20
L21 – Friday October 18 – 5.2 Series Solutions; handout and solutions; do Webassign 21
From this point onward the lectures will be based on Chapters 8, 9 and 10 of the book Differential Equations by Polking, Boggess and Arnold (2006). The following section numbers refer to that book.
L22 – Monday, October 21 – 8.1 and 8.2 Systems of DEs; handout and solutions; do Webassign 22
L23 – Wednes, October 23 – 8.3 and 8.4 Equilibrium Points, and Existence and Uniqueness; handout and solutions; do Webassign 23
L24 – Friday, October 25 – 8.5 Linear Independence and General Solutions; handout and solutions; no Webassign on today’s class
L25 – Monday, October 28 – 9.1 Homogeneous Linear Systems with Constant Coefficients; Distinct Real Eigenvalues; handout and solutions; do Webassign 25
Wednes, October 30 – in-class review, and evening Midterm 2
L26 – Friday, November 1 – 9.2 Complex Eigenvalues, Repeated Real Eigenvalues; handout and solutions; do Webassign 26
L27 – Monday, November 4 – 9.3 Phase Plane (saddles and nodes); handout and solutions; do Webassign 27
L28 – Wednes, November 6 – 9.3 Phase Plane (spirals), 9.4 Trace-determinant plane; handout and solutions; do Webassign 28
L29 – Friday, November 8 – 9.6 Matrix exponentials; handout and solutions (no Webassign on today’s class)
L30 – Monday, November 11 – 9.6 Matrix exponentials, and Putzer’s method; handout and solutions (no Webassign on today’s class)
L31 – Wednes, November 13 – 10.1 Linearization of Autonomous Systems; handout and solutions; do Webassign 31
L32 – Friday, November 15 – 10.1 and 10.4 Linearization, and Long-time Behavior; handout and solutions; do Webassign 32
L33 – Monday, November 18 – 10.4 and 10.2 Chaos and Strange Attractors; handout and solutions and link to Lorenz simulation; do Webassign 33
L34 – Wednes, November 20 – 10.5 and 10.6 Conserved and Dissipated Energies; handout and solutions (no Webassign on today’s class)
Friday, November 22 – no class, to compensate for evening midterm
THANKSGIVING BREAK
L35 – Monday, December 2 – 10.6 Conserved and Dissipated Energies, cont.; handout and solutions (no Webassign on today’s class)
Wednes, December 4 – in-class review (optional), and evening Midterm 3
L36 – Friday, December 6 – Existence and Uniqueness Proof for Linear Systems and DEs (not examinable); handout and solutions (no Webassign on today’s class)
L37 – Monday, December 9 – Existence and Uniqueness Proof for Nonlinear Systems and DEs (not examinable); handout and solutions (no Webassign on today’s class)
L38 – Wednes, December 11 – Leeway/exam review