Lecture notes for each week should be posted over the preceding weekend, and I will bring copies to class on Mondays. After each class I will post the filled-in versions for that day. At the end of the week I'll post the entire week's filled-in notes. Week 1: January 8-12 Sections 1.1-1.3 and part of 1.4 week1.pdf Notes that include outline for entire week The daily post-notes from this week are below: jan8.pdf syllabus, 1.1. differential equations, solutions to DE's and to IVP's for DE's. jan9.pdf 1.1-1.2 differential equations of the form y'(x)=f(x). jan10.pdf 1.2 continued: position-velocity-acceleration problems jan12.pdf 1.3-1.4 slope fields and solution graphs, introduction to separable DE's. week1_post.pdf all material we covered in week 1 Week 2: January 16-19 Sections 1.3-1.5 week2.pdf Notes that include outline for entire week jan16.pdf 1.3-1.4 existence-uniqueness theorem, with separable DE examples jan17.pdf 1.4-1.5 separable DE application; introduction to linear differential equations. jan19.pdf 1.5 linear DE's continued; input-output modeling week2_post.pdf all material we covered in week 2 Week 3: January 22-26 Sections 1.5, EP 3.7, 2.1-2.3 week3.pdf Notes that include outline for entire week jan22.pdf 1.5, EP 3.7: input-output modeling example, and RLC circuits application jan23.pdf 2.1 improved population model: logistic DE. jan24.pdf 2.2 equilibrium solutions and phase diagrams for autonomous first order differential equations. jan26.pdf 2.2 phase diagram analysis; many solutions from one; harvesting logistic, and doomsday-extinction model. week3_post.pdf all material we covered in week 3 Week 4: January 29 - Feb 2 Sections 2.3-2.6, 3.1-3.2 week4.pdf Notes that include outline for entire week jan29.pdf 2.3 improved acceleration models. jan30.pdf 2.4 Euler's method for numerical approximation of solutions to first order differential equations. jan31.pdf 2.5-2.6 Improved Euler and Runge-Kutta numerical methods for first order DE's. Also, handout with Matlab functions and scripts. feb2.pdf 3.1-3.2 week4_post.pdf all material we covered in week 4 Week 5: Feb 5-9 Sections 3.1-3.5 week5.pdf Notes that include outline for entire week feb5.pdf 3.1-3.3 reduced row echelon form and solving systems of linear equations feb6.pdf 3.3 reduced row echelon form of a matrix A and how it relates to possible solutions for associated linear systems feb7.pdf 3.3 continued feb9.pdf 3.4 matrix algebra; introduction to 3.5 matrix inverses week5_post.pdf all material we covered in week 5 Week 6: Feb 12-14 Sections 3.5-3.6 week6.pdf Notes that include outline for entire week feb12.pdf 3.5 matrix inverses feb13.pdf 3.6 definition of determinants feb14.pdf 3.6 determinant properties, and review notes for exam on Friday. week6_post.pdf all material covered in week 6 Week 7: Feb 20-23 Sections 3.6, 4.1-4.3 week7.pdf Notes that include outline for entire week feb20.pdf 3.6 adjoint formula for inverse matrices; Cramer's rule. feb21.pdf 4.1 visualizing linear combinations, vector equations, and "span" in R^{2}
and R^{3}.
feb23.pdf 4.1-4.3 linear independence and span week7_post.pdf all material covered in week 7 Week 8: Feb 26 - Mar 2 Sections 4.2-4.4, 5.1 week8.pdf Notes that include outline for entire week feb26.pdf 4.2-4.4 linear independence, span, basis, dimension, for subspaces of R^{n}.
feb27.pdf 4.2-4.4 vector spaces and subspaces. feb28.pdf 4.3-4.4 sub(vector)spaces in R^{n}, and how concepts
like linear independence and span are interpreted for function "vectors".
mar2.pdf 4.4 finding bases for subspaces of R^{n}, and how reduced row echelon form of a matrix encodes
the matrix column dependencies.
week8_post.pdf all material covered in week 8 Week 9: Mar 5-9 Sections 5.1-5.3 week9.pdf Notes that include outline for entire week mar5.pdf 5.1-5.2 second (and higher order) linear differential equations mar6.pdf 5.1-5.2 continued, introduction to 5.3 mar7.pdf 5.3 part 1: solutions to homogeneous linear differential equations with constant coefficients; real roots to characteristic equation mar9.pdf 5.3 part 2: complex roots to characteristic equation week9_post.pdf all material covered in week 9 Week 10: Mar 12-16 Sections 5.4-5.6 week10.pdf Notes that include outline for entire week mar12.pdf 5.4 part 1: unforced oscillation problems without damping. mar13.pdf 5.4 part 2: unforced oscillation problems without damping. mar14.pdf 5.5 Finding particular solutions for nonhomogeneous linear differential equations, L(y)=f mar16.pdf 5.5, intro to 5.6 forced oscillations week10_post.pdf all material covered in week 10 Week 11: Mar 26-28 Sections 5.6,10.1-10.2 week11.pdf Notes that include outline for entire week mar26.pdf 5.6: forced oscillations without damping: superposition, beating, resonance. mar27.pdf 5.6: forced oscillations with damping: solutions as superposition of steady periodic and transient solutions; practical resonance. mar28.pdf 10.1-10.3 introduction to Laplace transforms week11_post.pdf all material covered in week 11 Week 12: Apr 2-6 Sections 10.2-10.5, EP7.6 week12.pdf Notes that include outline for entire week apr2.pdf 10.1-10.3 Laplace transform table entries, IVP's. apr3.pdf 10.2-10.3 continued; the linearized pendulum DE and an experiment. apr4.pdf 10.2-10.4 partial fractions, resonance table entries, step functions. apr6.pdf 10.5, EP7.6 piecewise and impulse forcing. week12_post.pdf all material covered in week 12 Week 13: Apr 9-13 Sections 10.5, EP7.6, 6.1-6.2 week13.pdf Notes that include outline for entire week apr9.pdf 10.5, EP7.6 convolutions apr10.pdf 6.1-6.2 eigenvalues and eigenvectors apr11.pdf 6.1-6.2 eigenspaces and diagonalizability apr13.pdf 7.1-7.3 introduction to systems of differential equations week13_post.pdf all material covered in week 13 Week 14: Apr 16-20 Sections 7.1-7.4 week14.pdf Notes that include outline for entire week apr16.pdf 7.1-7.2: systems of differential equations and calculus review, for differentiation rules in the matrix-vector setting. apr17.pdf 7.2-7.3: using eigendata and exponential functions to solve homogeneous first order systems of DEs. apr18.pdf 7.3: handling complex eigendata...includes finished G-H example. apr20.pdf 7.4: unforced mass-spring systems week14_post.pdf all material covered in week 14 Week 15: Apr 23-24 7.4 and reviewweek15.pdf includes 7.4 forced oscillations; review notes will be posted later. apr23.pdf 7.4: mass-spring systems apr24.pdf filled-in review notes |