250B (Spring 2010) Class Notes
Note: Start 02.01.10, I am going to start trying to post ' lateral thinking ' problems on the overhead so to stimulate thought before class starts. Problems will be scanned and posted below when applicable. Unless noted, many problems come from the book 'Mind Benders: Adventures in Lateral Thinking' written by David J. Bodycombe. In some sense, these types of puzzles encourage the (cliched, but useful idiom) 'out of the box' thinking that is very helpful in mathematics/science/engineering (and many other places too!).
Class notes are scanned and saved as pdf (that is what the links below lead you to)
- 01.13.10 Class Overview & Evolving Philosophy
- 01.15.10 Improper Integrals
- 01.19.10 Reflections upon Infinity
- 01.20.10 Improper Integrals (cont.)
- 01.22.10 Improper Integrals (cont.)
- 01.25.10 Comparison Tests
- 01.26.10 Problems: Improper Integrals & Comparison Test
- 01.27.10 Introduction to Series
- 01.29.10 Geometric Series
- 02.01.10 Infinite series <--> Integrals, Convergence [pre-problem: pandas ]
- 02.02.10 Problems: Convergence of Infinite Series, Taking Drugs (drug problem solution 1 and solution 2 )
- 02.03.10 Convergence Tests I [pre-problem: anagrams ]
- 02.05.10 Convergence Tests II [pre-problem: playing w/ matches ]
- 02.10.10 Extending out the concept of an infinite series [pre-problem: words that start with h ]
- 02.12.10 Power Series Convergence [pre-problem: overlap? ]
- 02.15.10 Determining the Interval of Convergence [pre-problem: huh? ; Hint- consider it a play on words....]
- 02.16.10 Problems: Interval of Convergence of Infinite Series ( solutions )
- 02.17.10 Introduction to Taylor Series [pre-problem: cogs! ]
- 02.19.10 Taylor Series Basics [pre-problem: British hardware stores ]
- 02.22.10 Applications of Taylor Series: Solving Integrals & ODEs [pre-problem: Deciphering]
- 02.23.10 Problems: Applications of Taylor Series (solutions)
- 02.24.10 Applications of Taylor Series II: the binomial series/coefficients, Einstein's theory of General Relativity [pre-problem: A Cultural Divide?]
- 02.26.10 Linear Independence, the Wronskian [pre-problem: The records go round and round....]
- 03.01.10 Linear Independence (cont.) [pre-problem: A Degree of comonality (note misspelling)]
- 03.02.10 Fourier Series
- 03.03.10 Fourier Series (cont.), Auditory Biophysics [matlab code to approximate square wave via Fourier polynomial: Swave3.m]
- 03.05.10 Applications of Taylor Series: Solving Integrals & ODEs II [pre-problem: broken calculator]
- 03.10.10 Higher Order Linear ODEs (definitions), Harmonic Oscillator [pre-problem: the figure of a cube?]
- 03.12.10 Harmonic Oscillator (cont.), Imaginary #s [pre-problem: word find?]
- 03.22.10 2nd-order ODEs: Characteristic Eqn. & Eigenvalues [pre-problem: pointillism; also see this page on Georges Seurat ]
- 03.24.10 Complex #s, Fourier Revisited [pre-problem: buckets]
- 03.26.10 Harmonic Oscillator (cont.): Resonance [pre-problem: FontS....]
- 03.29.10 Harmonic Oscillator (cont.): Complex exponential solutions [pre-problem: P is to uzzle]
- 03.31.10 2nd-order (homogeneous, const. coefficients) ODEs: The Complete Story [Announcement: IS 303]
NOTE: See the following link for more info on the UofA Integrated Science Program
- 04.02.10 Systems of ODEs [pre-problem: Unique olympians?]
- 04.05.10 Systems of ODEs: General Solution [pre-problem: Arabic numerals.....]
- 04.06.10 o Chemical Reactions --> Michaelis-Menten Kinetics
o Population Dynamics --> Lotka-Volterra Eqns.
- 04.07.10 Phase Plane Analysis [pre-problem: the elusive letters are c and t, but why?]
- 04.09.10 Phase Plane Analysis cont. (w/ corrected notes) [pre-problem: little, itty bitty words]
- 04.12.10 Saddles [pre-problem: Astrological probabilities....]
- 04.14.10 Classifying Solutions for Linear Autonomous Systems [pre-problem: Painting the fence]
- Applied Math Lab Visit Summary of the student posts from D2L
- 04.14.10 Cauchy-Euler Equations [Article: from 4/19 issue of Newsweek on using computer modeling to combat malaria]
- 04.20.10 Cauchy-Euler Equations (cont.) [pre-problem: Falsity]
- 04.21.10 Method of Undetermined Coefficients (MUC) [pre-problem: More matchsticks]
- 04.23.10 MUC (cont.) [pre-problem: 3 is the magic number]
- 04.26.10 Bridges Revisted: Negative Damping in Tacoma? [pre-problem: Numerical bi-sections]
NOTE: 4/26 'notes' is really an article by K.Y. Billah & R.S. Scanlan from the American Journal of Physics (1991);
some other relevant references you are encourged to take a look at are as follows:
o Strogatz et al. (2005) on the issues of 'swaying' Millenium bridge
o Feldman (2003) further fleshing out re Tacoma Bridge
- 04.27.10 Fireflies & Synchronization
- 04.28.10 Nonlinear Systems: Linearize them! [pre-problem: Some called him Chuck]
- 04.30.10 van der Pol Oscillator: Nonlinear Systems & the Phase Plane [pre-problem: And some call him Allen Smithee]
- 05.03.10 Epidemiology: Predicting Epidemics [pre-problem: An issue of redundancy?]
- 05.05.10 250 Course Summary [pre-problem: possibly related to a diphthong?]
o An old problem revisited
o see this graphic and subsequent letter to the editor of the Daily Wildcat (entitled 'Boom goes the dynamite')
o bonus problem