- Ch. 5: The Laplace Transform Technique for solving linear DEs with constant coefficients
- 9.5: Fundamental Sets of Eigenvector Solutions Homogenous system
- Control of a Noisy Mechanical Rotor {sabino, gerhard}@math.colostate.edu
- Chapter 3: Modelling and Applications Principle: Develop model function f(t, x) for the rate of change of a
- Control of 1-D and 2-D Coupled Map Lattices through Reinforcement Learning
- Time series prediction by estimating Markov probabilities through topology preserving maps
- Linear Systems of Algebraic Section 1: Row operations and reduced row echelon form
- Chapter 2: First Order ODEs 2.1: ODEs and Solutions
- 2.4: Linear Equations General Form
- 2.6: Exact Equations or P(x, y)+Q(x, y)
- 2.9: Autonomous Equations and Stability Form: x = f(x)
- Chapter 3: Modelling and Applications Principle: Develop model function f(t, x) for the rate of change
- 6.2: Runge Kutta Methods (RKM) (A) 2nd Order RKM (or Improved Euler Method)
- Chapter 7: Matrix Algebra 7.1 Vectors and Matrices
- 7.2: Linear Systems with Two or Three Variables I. Geometry of Solutions
- 7.4: Homogeneous and Inhomogeneous Systems Homogeneous Systems
- 7.5 Span of a Set of Vectors Def.: Given vectors x1, . . . , xk
- 7.6 Square Matrices A: square matrix (n n)
- 9.3-4: Phase Plane Portraits Classification of 2d Systems
- 9.7: Qualitative (Stability) Analysis x = Ax, A : n n (1)
- 9.9: Inhomogeneous Systems Generalize Ch.2: x = a(t)x + f(t) xp(t) = xh(t) [f(t)/xh(t)]dt, x
- 9.8 (4.3): Higher (Second) Order Linear Equations + a1(t)y(n-1)
- 4.5-6: Inhomogeneous Higher Order Equations 4.5: Method of Undetermined Coefficients
- Fall 08, M340, Section 2 NAME: .............................. Exam 2 (each problem is worth 100 points)
- 9.6: Matrix Exponential, Repeated Eigenvalues = Ax, A : n n (1)
- 8.2-3: Geometric Interpretation and Qualitative Analysis Autonomous system
- Math 340-220 Projects, Spring 2011 Select one of the 6 projects below. Reports can be turned in by groups of at most two students.
- Computer Lab Information Location
- Fall 08, M340, Section 2 NAME: .............................. Exam 1 (each problem is worth 100 points)
- 7.3: Solving Systems of Equations a11x1 + + a1nxn = b1
- Learning to control a complex multistable system Sabino Gadaleta* and Gerhard Dangelmayr
- A Quick Introduction Sabino Gadaleta
- Reinforcement learning chaos control using value sensitive vector-quantization
- Chapter 6: Numerical Methods 6.1 Euler Method
- Ch. 9: Constant Coefficients Linear Systems 9.1 Overview of Technique: Eigenvalues/Eigenvectors
- Reinforcement learning chaos control using value sensitive vectorquantization
- Algebra and Calculus facts Note: In what follows, a, b, c, d, and
- Time series prediction by estimating Markov probabilities through topology preserving maps
- to appear in: Dynamical Systems and Applications Burst and spike synchronization of coupled neural oscillators
- 2.7: Existence and Uniqueness of Solutions Basic Existence and Uniqueness Theorem (EUT)
- 2.3: Models of Motion: Gravity Force and Air Resistance Gravity Force: Fg = -mg
- 8.4-5: Linear Systems General Form
- 7.7: Determinants For 2 2: (assume a = 0)
- 4.2: Phase Plane Portraits; 4.4: Free Harmonic Motion y + ay + by = 0 (1)
- 2.2: Solutions to Separable Equations dt = g(t)f(y)
- Sample for Exam 1 1. Consider the autonomous ODE dx
- Chapter 8: Introduction to Systems 8.1 Definitions and Examples
- 4.7: Forced Harmonic Motion Periodically forced mass-spring system: mx+x+kx = F0 cos t
- Section 9.5: Ex. 44, 52 Ex. 44: Find a fundamental set of solutions to y = Ay for
- Section 6.1: 4, 6, 8 k tk zk f(tk, zk) = 5 -zk h f(tk, zk)h
- Section 9.7, Problems 10 and 14 For the given system y = Ay, classify the equilibrium at the origin as unstable, stable or as-
- Section 4.7, Problems 7,8,16 Ex. 7: The plots below clearly show that the solution approaches a solution with linearly
