250A (Fall 2009) Class Notes
Note: Class notes (hastily scrawled in-class) were scanned and saved as pdf (that is what the links below lead you to)
- 08.26.09 Review: (re-)Introduction to functions
- 08.28.09 Review: (re-)Introduction to functions (cont.)
- 08.31.09 Review: (re-)Introduction to functions (cont.)
- 09.02.09 Introduction to & Applications of ODEs
- 09.04.09 ODE Overview
- 09.08.09 Translating 'word problems' into ODEs
- 09.09.09 Solving ODEs <---> Solving Integrals
- 09.11.09 Numerical Approaches Towards Solving Integrals
- 09.11.09 Solving Autonomous ODEs, Notion of Uniqueness
- 09.14.09 Solving Integrals via Riemann Sums
- 09.15.09 Review problems for Exam I (solutions can be found here )
- 09.21.09 Methods of Integration: Substitution
- 09.22.09 Conceptual Review Problems on Integration (contact me for solutions)
- 09.22.09 Using integral to compute areas and volumes
- 09.23.09 Methods of Integration: Integration by Parts
- 09.25.09 Methods of Integration: Table of Integrals
- 09.28.09 Methods of Integration: Table of Integrals (cont.)
- 09.30.09 Methods of Integration: Algebraic Simplification
- 10.02.09 Methods of Integration: Trigonometric Substitutions
- 10.05.09 Methods of Integration: Trigonometric Substitutions (cont.)
- 10.06.09 Example Problems (note that each part builds off the former, though they are listed here out of order)
- 10.07.09 Introduction to Slope Fields
- 10.09.09 Slope Fields, Symmetry
- 10.12.09 Interpreting ODE Properties
- 10.19.09 Anchor-Point: Foundations Laid and Paths Ahead
- 10.20.09 Group Problems (& Solutions)
- 10.21.09 Existence & Uniqueness Theorem
⇒ Additional useful notes/slides on ODEs (courtesy of J. Lega): Part I , Part II , Part III
- 10.26.09 Existence & Uniqueness Theorem (cont.), Partial Derivatives
- 10.27.09 Group Problems on Existence & Uniqueness (solutions)
- 10.28.09 Phase Line Analysis
- 10.30.09 Phase Line Analysis (cont.)
- 11.02.09 Euler's Method - Solving ODEs Numerically
- 11.03.09 Euler's Method - Group Problems (solutions)
- 11.04.09 Problem Solving - Round II (see here for Polya's outline; also this link contains some of Polya's sample problems as discussed in class)
- 11.06.09 ODEs w/ Homogeneous Coefficients
- 11.09.09 ODEs w/ Homogeneous Coefficients (cont.)
- 11.13.09 Solving linear, first-order ODEs
- 11.16.09 Linear, first-order ODEs: Examples
- 11.17.09 Solving 1st Order Linear ODEs - Group Problems (solutions)
- 11.18.09 Bernoulli Differential Equations
- 11.20.09 (cont. from 11/18 notes)
- 11.23.09 Further Examples of Solving ODEs
- 11.30.09 Sequences, Interrelation Between Recursive Relationships and ODEs
- 12.01.09 Linear Regression: Least Squares Fit to a Straight Line
- 12.02.09 Sequences: Convergence/Divergence
- 12.04.09 Logistic Map &rArr CHAOS!
- 12.07.09 Generating/Visualizing (via Matlab) the Period-Doubling Cascade for the Logistic Map
[also of relevant interest might be the following on Wolfram's A New Kind of Science , as well as the following compilation of reviews critiquing it (e.g., the New York Time review presents an unbiased account of things)]
- 12.09.09 A Simple Ecological Application: Metapopulations & the Levins Model