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Differential Equations
2250-1 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 20-24
aug20.pdf aug20.mw Introduction to course and Chapter 1.
aug21.pdf aug21.mw 1.2: differential equations of the form y'(x)=f(x)
aug22.pdf aug22.mw 1.2-1.3: also begin slope fields and geometric interpretation of first order DE IVPs.
aug24.pdf aug24.mw 1.3-1.4: slope fields and first order DE's; examples using separable differential equations.
Week 2: August 27-31
aug27.pdf aug27.mw More separable DE's
aug28.pdf aug28.mw and 1.5 linear differential equations
aug29.pdf aug29.mw 1.5 linear differential equations
aug31.pdf aug31.mw 1.5 applications, including EP 3.7; begin 2.1 improved population models * updated with derivation of formula for solutions to logistic differential equation IVPs that we did in class on Tuesday Sept. 4
Week 3: September 4-7
sept4.pdf sept4.mw 2.1-2.2 autonomous first order DEs
sept5.pdf sept5.mw 2.2 autonomous first order DEs and applications
sept7.pdf sept7.mw 2.3 improved velocity models
Week 4: September 10-14
sept10.pdf sept10.mw 2.3 continued, including escape velocity.
sept11.pdf sept11.mw 2.4-2.6 numerical methods for first order DE IVPs
numericaltemplate.pdf numerical algorithms template
sept12.pdf sept12.mw 2.2; 3.1-3.2: populations; simultaneous linear algebraic equations and how to find the solution sets.
sept14.pdf sept14.mw 3.1-3.3: Gaussian elimination and reduced row echelon form, for the solution set to systems of linear algebraic equations.
sept14workedexamples.pdf sept14workedexamples.mw
Week 5: September 17-21
sept17.pdf sept17.mw 3.2-3.3 Reduced row echelon form for solving linear systems of equations.
sept18.pdf sept18.mw 3.3 How the shape of the reduced row echelon form determines the structure of the solution set to linear systems of equations. sept18filledin.pdf sept18filledin.mw
sept19.pdf sept19.mw 3.4 Matrix algebra
sept21.pdf sept21.mw 3.5 Matrix inverses
Week 6: September 24-28
sept24.pdf sept24.mw 3.6 Determinants
sept25.pdf sept25.mw 3.6 Determinants
exam1review.pdf exam1review.mw review topics, for 1.1-1.5, 2.1-2.4, 3.1-3.6.
sept28.pdf sept28.mw 4.1-4.3 linear combinations of vectors
Week 7: October 1-5
oct1.pdf oct1.mw 4.1-4.3 linear combinations, span, linear independence, and how to study these questions in Rm via reduced row echelon form matrices.
oct2.pdf oct2.mw 4.1-4.3 continued
oct3.pdf oct3.mw 4.2-4.4 vector spaces, subspaces, bases, dimension. oct3filledin.pdf oct3filledin.mw lecture discussion notes filled in.
oct5.pdf oct5.mw 4.4 bases and dimension, and review.
Week 8: October 15-19
oct15.pdf oct15.mw 5.1-5.2 second order differential equations
oct16.pdf oct16.mw 5.1-5.2 second order and nth order linear differential equations
oct17.pdf oct17.mw 5.2-5.3 second order and nth order linear differential equations, with a focus on ways to test functions for linear independence.
oct19.pdf oct19.mw 5.3 algorithms for finding solution space bases, for constant coefficient homogeneous linear differential equations.
Week 9: October 22-26
oct22.pdf oct22.mw 5.4 mechanical vibrations.
oct23.pdf oct23.mw 5.4 mechanical vibrations continued
oct24.pdf oct24.mw 5.4 pendulum and mass-spring experiments. Also begin 5.5, particular solutions yP(x) for non-homogeneous linear DEs.
oct26.pdf oct26.mw 5.5 particular solutions to non-homogeneous linear differential equations
Week 10: October 29-November 2
oct29.pdf oct29.mw 5.5 particular solutions to linear DEs; 5.6 overview of forced oscillation problems, details for forced undamped oscillators
oct30.pdf oct30.mw 5.6 forced damped oscillators and applications
oct31.pdf oct31.mw 5.6 conservation of energy to find the natural frequencies for undamped mechanical and electrical configurations.
nov2.pdf nov2.mw 10.1-10.2 The Laplace transform, and why it is an amazing tool for solving linear differential equation IVPs.
Week 11: November 5-9
nov5.pdf nov5.mw 10.1-10.3 Laplace transform and initial value problems
nov6.pdf nov6.mw 10.2-10.3 Laplace transform table entries, partial fractions, and initial value problems.
exam2review.pdf exam2review.mw review outline for exam 2 exam2reviewfilledin.pdf filled-in version
nov9.pdf nov9.mw 10.4-10.5 the unit step function - to turn forcing on and off; convolution to invert products of Laplace transforms.
Week 12: November 12-16
nov12.pdf nov12.mw 10.5, EP 7.6 - periodic and impulse functions; convolution applications.
nov13.pdf nov13.mw 6.1-6.2 eigenvalues and eigenvectors
nov14.pdf nov14.mw 6.2 eigenvalues and eigenvectors, and matrix diagonalizability.
nov16.pdf nov16.mw 7.1 systems of differential equations
Week 13: November 19-21
nov19.pdf nov19.mw 7.2-7.3 first order linear systems of differential equations
nov20.pdf nov20.mw 7.3 the eigenvalue-eigenvector method for solving constant coefficient homogeneous linear systems of DE's with diagonalizable matrices; real and complex eigendata.
nov21.pdf nov21.mw 7.3 applications of first order linear systems of differential equations.
Week 14: November 26-30
nov26.pdf nov26.mw 7.4 second order linear systems of DE's for undamped mechanical systems.
nov27.pdf nov27.mw 7.4 unforced undamped mechanical systems - examples and experiment; begin forced systems.
nov28.pdf nov28.mw 7.4 forced undamped mechanical systems; earthquake shaking and (im)practical resonance.
nov30.pdf nov30.mw 9.1-9.2 autonomous first order systems of differential equations, and linearization.
Week 15: December 3-7
dec3.pdf dec3.mw 9.2-9.3 Classification of equilibria for autonomous systems via eigenvalues of the linearized system. Examples from interacting population models
dec4.pdf dec4.mw 9.2-9.4 Classification of equilibria for autonomous systems, continued. Examples from interacting population models and non-linear mechanical oscillation models.
dec5.pdf dec5.mw 9.4 non-linear autonomous mechanical oscillation models, interepreted as first order systems.
Math2250review.pdf notes for Friday