Math 2171 Course Outline

Text

Nagle, Saff, and Snider. Fundamentals of Differential Equations, 9th Edition

Section / Topic

1.1 Background
1.2 Solutions and Initial Value Problems
1.3 Direction Fields
1.4 The approximation method of Euler
2.1 Introduction: Motion of a falling body
2.2 Separable Equations
2.3 Linear Equations
2.4 Exact Equations
2.5 omitted
2.6 Substitutions and Transformations
3.1 Mathematical Modeling
3.2 or 3.3 Compartmental Analysis or Heating and Cooling of Buildings
3.4 Newtonian Mechanics
3.5 Electrical Circuits
3.6 Numerical Methods: A Closer Look At Eulers Algorithm
3.7 Higher-Order Numerical Methods: Taylor and RungeKutta
4.1 Introduction to Second Order: The Mass-Spring Oscillator
4.2 Homogeneous Linear Equations: The General Solution
4.3 Auxiliary Equations with Complex Roots
4.4 Nonhomogeneous Equations: the Method of Undetermined Coefficients
4.5 The Superposition Principle and Undetermined Coefficients Revisited
4.6 Variation of Parameters
4.7 Variable-Coefficient Equations (optional)
4.8 omitted
4.9 A Closer Look at Free Mechanical Vibrations
4.10 A Closer Look at Forced Mechanical Vibrations
5.7 Electrical Systems (RLC circuits)
7.1 Introduction: A Mixing Problem
7.2 Definition of the Laplace Transform
7.3 Properties of the Laplace Transform
7.4 Inverse Laplace Transform
7.5 Solving Initial Value Problems
7.6 Transforms of Discontinuous Functions
7.7 Transforms of Periodic and Power Functions
7.8 omitted
7.9 Impulses and the Dirac Delta Function

Pace of the course

Complete Chapter 2 approximately one-quarter through the
term, complete Chapter 3 at midpoint, start Chapter 7 no later than three-fourths
of the way through the term (allowing for review for final exam at the end of term)

Examinations

The number and timing of the in-class term tests is the prerogitive
of the instructor. Three equally spaced in-class tests are recommended. A final
exam is required and must be a significant factor in the course grade.