Math 2070 Syllabus

Math 2070 Syllabus

Text: Ordinary Differential Equations, by William A. Adkins and Mark G. Davidson, Springer, 2012, plus a supplement on Fourier Series Methods and student solutions manual for the supplement. The student solutions manual for the text is available from the Springer website for the text.

Chapter 1: First Order Differential Equations

  • 1.1 An Introduction to Differential Equations
  • 1.2 Direction Fields
  • 1.3 Separable Differential Equations
  • 1.4 Linear First Order Equations
  • 1.5 Substitutions; Homogeneous and Bernoulli Equations
  • 1.6 Exact Equations

Chapter 2: The Laplace Transform

  • 2.1 Laplace Transform Method: Introduction
  • 2.2 Definitions, Basic Formulas, and Principles
  • 2.3 Partial Fractions: A Recursive Method for Linear Terms
  • 2.4 Partial Fractions: A Recursive Method for Irreducible Quadratics
  • 2.5 Laplace Inversion
  • 2.6 The Linear Spaces Eq: Special Cases
  • 2.7 The Linear Spaces Eq: The General Case
  • 2.8 Convolution

Chapter 3: Second Order Constant Coefficient Linear Differential Equations

  • 3.1 Notation, Definitions, and some Basic Results
  • 3.2 Linear Independence
  • 3.3 Linear Homogeneous Differential Equations
  • 3.4 The Method of Undetermined Coefficients
  • 3.6 Spring Systems or 3.7 RCL Circuits

Chapter 4: Linear Constant Coefficient Differential Equations

  • 4.1 Notation, Definitions, and Basic Results
  • 4.2 Linear Homogeneous Differential Equations
  • 4.3 Nonhomogeneous Differential Equations

Chapter 5: Second Order Linear Differential Equations

  • 5.1 The Existence and Uniqueness Theorem
  • 5.2 The Homogeneous Case
  • 5.3 The Cauchy-Euler Equations
  • 5.5 Reduction of Order
  • 5.6 Variation of Parameters

Chapter 6: Discontinuous Functions and the Laplace Transform

  • 6.1 Calculus of Discontinuous Functions
  • 6.2 The Heaviside Class
  • 6.3 Laplace Transform Method for function in the Heaviside Class
  • 6.4 The Dirac Delta Function
  • 6.5 Convolution

Chapter 8: Matrices

  • 8.1 Matrix Operations
  • 8.2 Systems of Linear Equations
  • 8.3 Invertible Matrices
  • 8.4 Determinants
  • 8.5 Eigenvectors and Eigenvalues

Chapter 9: Linear Systems of Differential Equations

  • 9.1 Introduction
  • 9.2 Linear Systems of Differential Equations
  • 9.3 The Matrix Exponential Function and its Laplace Transform
  • 9.4 Fulmer's Method
  • 9.5 Constant Coefficient Linear Systems

Supplement: Fourier Series Methods

  • 10.1 Periodic Functions and Orthogonality Relations
  • 10.2 Fourier Series
  • 10.3 Convergence of Fourier Series
  • 10.4 Fourier Sine Series and Fourier Cosine Series
  • 10.5 Operations on Fourier Series
  • 10.6 Applications of Fourier Series

William A. Adkins, August 2013. Updated January 2016.