http://www.math.utah.edu/~korevaar/coord2250/2250lectures.html: this page.
http://www.math.utah.edu/~korevaar/coord2250: 2250 coordinating page

Math 2250 possible lectures



There are typically 57-58 standard class meetings for the 4-credit your class. It will take at least the 51 indicated lectures to cover the core material. You can free up some extra time for optional sections by giving exams and reviews on the Thursday problem-session days.

This is only the second year we have taught the 4-credit version of 2250, and we are still working to find optimal pacing and content.

  • Chapter 1, First order differential equations: 6 lectures
    • 1.1 Mathematical modeling and differential equations
    • 1.2 Integrals as general and particular solutions
    • 1.3 Slope fields and solutions curves (1.5 lectures)
    • 1.4 Separable differential equations
    • 1.5 linear first order differential equations (1.5 lectures)
  • Chapter 2, Mathematical Models and Numerical Methods: 5 lectures
    • 2.1 Population models (1.5 lectures)
    • 2.2 Equilibrium solutions and stability (1.5 lectures)
    • 2.3 Acceleration-velocity Models
    • 2.4 and 2.6 Numerical techniques survey
  • Chapter 3, Linear Systems and Matrices: 8 lectures; in practice lectures overlap sections.
    • 3.1 Introduction to linear systems
    • 3.2 Matrices and Gaussian elimination (1.5 lectures)
    • 3.3 Reduced row-echelon matrices (1.5 lectures)
    • 3.4 Matrix operations
    • 3.5 Inverses of matrices
    • 3.6 Determinants and applications (2 lectures)
  • Chapter 4, Vector Spaces: 6 lectures
    • 4.1 The vector space {$\bf R^3$}
    • 4.2 The vector space {$\bf R^n$} and subspaces
    • 4.3 Linear combinations and independence of vectors (1.5 lectures)
    • 4.4 Bases and dimension for vector spaces (1.5 lectures)
    • 4.7 General vector spaces
  • Chapter 5, Linear Equations of Higher Order: 9 lectures
    • 5.1 Introduction: second order linear equations
    • 5.2 General solutions of linear equations
    • 5.3 Homogeneous equations with constant coefficients, including a review of Euler's formula (1.5 lectures)
    • 5.4 Mechanical vibrations, including disucssion of amplitude and phase, damping phenomena (1.5 lectures)
    • 5.5 Undetermined coefficients and variation of parameters
    • 5.6 Forced oscillations and resonance (2 lectures)
    • EP 3.7: RLC electrical circuits (2 lectures. This is a supplementary section, from DEBVP's by EP)
  • Chapter 10, Laplace transform methods: 6 lectures. It is especially important to cover sections 10.1-10.4 in detail. The remaining two sections can be covered in a less systematic manner if time is limited. We introduce Laplace transforms out of book order to make sure the students will have a protracted interval in which to learn these techniques. You are encouraged to return to these ideas to provide alternate methods of solution to systems of linear differential equations, Chapter 7.
    • 10.1 Laplace Transforms and inverse transforms
    • 10.2 Transformation of initial value problems
    • 10.3 Translation and partial fractions
    • 10.4 Derivatives, integrals and products of transforms
    • 10.5 Periodic and piecewise continuous forcing functions (possibly survey this section, if time is short)
    • EP 7.6: Impulses and Delta functions: from DEBVP's by EP. (time pressure may mean you skip this section.)
  • Chapter 6 Eigenvalues and eigenvectors: 1 lecture. Sections 6.2 and 6.3 are optional. Section 6.1 articulates well to 7.1.
    • 6.1 Introduction to eigenvalues
    • 6.2 Diagonalization of matrices
    • 6.3 Matrix powers, with applications to iteration problems, i.e. discrete dynamical systems.
  • Chapter 7, Linear systems of differential equations: 5 lectures; section 7.5 is optional
    • 7.1 First order systems and applications
    • 7.2 Matrices and linear systems
    • 7.3 The eigenvalue-eigenvector method for linear systems
    • 7.4 Second-order systems and mechanical vibrations (2 lectures)
  • Chapter 8, Matrix exponential methods: 3 optional lectures
    • 8.1 Matrix exponentials and homogeneous linear systems of DE's (1.5 lectures)
    • 8.2 Nonhomogeneous linear systems (1.5 lectures)
  • Chapter 9, Nonlinear systems and phenomena: 5 lectures
    • 9.1 Stability and the phase plane
    • 9.2 Linear and almost linear systems (2 lectures, to include a review/introduction of affine approximation from multivariable Calculus, in order to discuss linearization near equilibria)
    • 9.3 Ecological models: predators and competitors
    • 9.4 Nonlinear mechanical systems