Traffic Dynamics and Control

Contents:

• Introduction
  • Abstract
  • Overview
  • Objectives
  • Modules
    • Prerequisite Modules
    • Main Modules
  • Module Details
    • Module A: Macroscopic Traffic Dynamics
    • Module B: Mesoscopic Traffic Model
    • Module C: Microscopic Traffic Dynamics
    • Module D: Architecture, Electronics, and Planning
    • Module E: Traffic Control
    • Module F: Vehicle Control
    • Module G: Pedestrian Dynamics and Control
  • Faculty
    • Pushkin Kachroo, Ph.D., Ph.D., P.E.
    • Geetam Tiwari, Ph.D.
    • K. Ramachandra Rao, Ph.D.
• Prerequisite Modules
  • Calculus Review and Real Analysis
    • Limits
      • Limit of a Sequence
        • Limit involving +Infinity
        • Limit involving -Infinity
        • Examples
        • Metric Space
        • Sequence Limit Theorems
        • Monotone Convergence Theorem
        • Cauchy Sequence
        • Complete Metric Spaces
          • \(\sqrt{2}\not\in\mathbb{Q}\)
          • \(\lim\limits_{n\to\infty}x_n=\sqrt{2}\) where \(x_n\in\mathbb{Q}\)
    • Series
      • Meaning
      • Theorem: Series convergence implies term convergence to zero
      • Theorem: Convergence of series with positive terms
    • Limit of a Function
      • One Sided Limits
        • Left side Limit
        • Right side Limit
        • Squeeze Theorem
        • Examples
          • Trigonometric Example
          • Topologist’s Sine Curve
        • Function Limit Theorems
          • + Infinite Limit
          • - Infinite Limit
          • Limit at +Infinity
          • Limit at -Infinity
    • Continuity
      • At a Point
      • On its Domain
        • Optimization Example
        • Extreme Value Theorem
        • Intermediate Value Theorem
      • Uniform Continuity
        • Example
        • Heine-Cantor Theorem
        • Example
  • Derivative
    • Table
    • Properties
    • L’Hospital’s Rule
    • Implicit Differentiation
      • Example
    • Differential
    • Inverse Functions
    • Rolle’s Theorem
    • Mean Value Theorem
    • Optimization
  • Riemann Integral
    • Fundamental Theorem of Calculus
    • Leibniz Rule
    • Mean Value Theorem for Integrals
  • Linear Algebra/Functional Analysis
    • Field
      • Axioms for \(+\) in a Field
      • Axioms for \(\cdot\) in a Field
      • Distributive Law of a Field
      • Examples
    • Vector Space
      • Axioms for \(+\) (Vector Addition) in a Vector Space
      • Axioms for \(\circ\) (Scalar Multiplication) in a Vector Space
      • Axioms for Distributivity of Operations in a Vector Space
      • Examples
        • Vector Space \((\mathbb{R}^2, \mathbb{R}, +, \circ)\)
          • Example Operations
        • Vector Space \((C[0,1], \mathbb{R}, +, \circ)\)
          • Example Operations
      • Independent Vectors
      • Span of Vectors
      • Independent Basis of a Vector Space
      • Dimension of a Vector Space
        • Examples
    • Normed Vector Space
    • Metric Space
      • Metric Space from Normed Vector Space
        • Example \(\ell_p\) Norm
        • Metric Sphere Example from \(\ell_2\) Norm
        • Example \(\ell^p\) Norm
        • Example \(L^p\) Norm

Indices and tables

• Index
• Module Index
• Search Page