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Differential Equations
2250-4 home page
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Lecture notes will be posted by 4:00 p.m. the day before class. I strongly recommend bringing a copy of these notes to class, so we can go through the concepts and fill in the details together.
Week 1: August 26-30
aug26.pdf aug26.mw Introduction to course and Chapter 1.
aug27.pdf aug27.mw 1.1-1.2: solving first order differential equations by direct and indirect anti-differerentiation techniques.
aug28.pdf aug28.mw 1.2 completed; introduction to 1.3: slope fields and graphs of solution functions to IVPs.
aug30.pdf aug30.mw 1.3-1.4: slope fields and graphs of solution functions to IVPs; separable DE's and how to solve them.
Week 2: September 3-6
sept3.pdf sept3.mw 1.3-1.4 continued
sept4.pdf sept4.mw 1.4-1.5 Toricelli DE derivation and experiment from 1.4; linear DE's from 1.5
sept6.pdf sept6.mw 1.5 linear differential equations and input-output models
Week 3: September 9-13
sept9.pdf sept9.mw 1.5, EP3.7 applications of linear DE's; begin 2.1 improved population models
sept10.pdf sept10.mw 2.1-2.2 improved population models; equilibrium solutions and stability for autonomous first order differential equations
sept11.pdf sept13.mw 2.2 autonomous differential equations and applications
sept13.pdf sept13.mw 2.3 accounting for drag forces in improved velocity-acceleration models
Week 4: September 16-20
sept16.pdf sept16.mw 2.3 escape velocity
sept17.pdf sept17.mw 2.4-2.6 numerical methods for solving DE's.
sept18.pdf sept18.mw finish numerical methods 2.4-2.6; introduction to linear systems of algebraic equations, 3.1-3.2.
numericaltemplate.pdf algorithms for Euler, improved Euler, Runge Kutta.
numerics.m Matlab code that will compute Euler, improved Euler, Runge-Kutta approximations (courtesy Prof. Hohenegger).
sept20.pdf sept20.mw 3.1-3.3 linear systems of algebraic equations
Week 5: September 23-27
September 23: We will use last Wednesday's and Friday's notes.
sept24.pdf sept24.mw 3.3 the structure of the solution sets to linear algebraic systems of equations, based on reduced row echelon form properties
sept25.pdf sept25.mw 3.4 matrix algebra
sept27.pdf sept27.mw 3.4-3.5 matrix algebra and matrix inverses
Week 6: September 30 - October 4
sept30.pdf sept30.mw 3.5-3.6 matrix inverses; determinants
oct1.pdf oct1.mw 3.6 inverse matrix formula; Cramer's rule
exam1review.pdf exam1review.mw logistical and review notes for exam 1
exam1reviewfilledin.pdf exam1reviewfilledin.mw ...filled in.
Week 7: October 7-11
oct7.pdf oct7.mw 4.1 linear combination concepts in R2 and R3
oct8.pdf oct8.mw 4.1-4.3 linear combination concepts: span, linear independence/dependence, basis, vector space, subspace.
oct9.pdf oct9.mw 4.2-4.4 linear combination concepts: span, linear independence/dependence, basis, vector space, subspace.
oct11.pdf oct11.mw 4.2-4.4 continued
Week 8: October 21-25
oct21.pdf oct21.mw 4.1-4.4 bases and dimension; homogeneous solution spaces and connection to column dependencies.
oct22.pdf oct22.mw 5.1 second order linear differential equations.
oct23.pdf oct23.mw 5.2 higher order linear differential equations.
oct25.pdf oct25.mw 5.2-5.3 discuss methods for checking linear independence for functions, then begin 5.3: how to systematically find the homogeneous solution space to constant coefficient linear DE's.
Week 9: October 28 - November 1
oct28.pdf oct28.mw 5.3 continued
oct29.pdf oct29.mw 5.3-5.4 begin applications to mechanical vibrations
oct30.pdf oct30.mw 5.4 continued, pendulum model.
nov1.pdf nov1.mw 5.4 continued: pendulum and mass-spring experiments
Week 10: November 4-8
nov4.pdf nov4.mw 5.5 finding particular solutions with the method of undetermined coefficients.
nov5.pdf nov5.mw 5.6 applications to undamped forced mechanical systems
nov6.pdf nov6.mw 5.6 applications to damped forced mechanical systems
nov8.pdf nov8.mw 10.1-10.2 Laplace transforms, and their use in solving DE IVP's.
Week 11: November 11-15
nov11.pdf nov11.mw 10.1-10.2 Laplace transform and initial value problems, continued
nov12.pdf nov12.mw 10.2-10.3 partial fractions, Laplace table entries, resonance revisited.
nov13.pdf nov13.mw 10.5 unit step function, to turn forcing on and off.
Week 12: November 18-22
nov18.pdf nov19.mw 6.1-6.2 eigenvectors, eigenvalues, eigenspaces.
nov19.pdf nov19.mw 6.1-6.2 eigenvectors, eigenspaces, and diagonalizability.
nov20.pdf nov20.mw 10.4-10.5 further Laplace transform applications.
nov22.pdf nov22.mw 10.5, EP7.6 impulse function forcing, and convolution solutions to forced oscillation problems.
EP7.6.pdf supplemental Edwards-Penney section on convolution solutions and impulse function forcing.
Week 13: November 25-27
nov25.pdf nov25.mw 7.1 introduction to first order systems of differential equations, and what they have to do with eigenvalues and eigenvectors.
nov26.pdf nov26.mw 7.1-7.3 theory and practice for solving linear first order systems of differential equations, and how this framework includes all of Chapter 5.
nov27.pdf nov27.mw 7.3: complex eigendata for solutions to x'(t)=Ax.
Week 14: December 2-6
dec2.pdf dec2.mw 7.3 solving x'(t)=Ax when A is diagonalizable, with real or complex eigendata, with applications.
dec3.pdf dec3.mw 7.3 applications, continued.
dec4.pdf dec6.mw 7.4 second order systems and mechanical applications
dec6.pdf dec6.mw 7.4 continued: train systems, transverse oscillations and buildings shaking in earthquakes.
Week 15: December 9-13
dec9.pdf dec9.mw 9.1-9.2 non-linear autonomous systems of two differential equations
dec10.pdf dec10.mw 9.2-9.3 equilibrium points and stability analysis for non-linear autonomous systems of two differential equations, with examples from population models.
dec11.pdf dec11.mw 9.4 nonlinear mechanical oscillations
Math_2250_review.pdf Math_2250_review.doc review notes