# 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 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.