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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 available here.  The student solutions manual for the text is available from the Springer website for the text. The student solutions manual for the Fourier Series Supplement is available here.

 

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.