CHAPTER 4	Higher Order Linear Equations	(3 Lectures)
			
			4.1  General Theory of n th Order Linear Equations
			4.2  Homogeneous Equations with constant Coefficients
			4.3  The Method of Undetermined Coefficients
			4.4  The Method of Variation of Parameters

CHAPTER 6	The Laplace Transform	(7 Lectures, 1 Review)
			
			6.1  Definition of the Laplace Transform
			6.2  Solution of Initial Value Problems
			6.3  Step Functions
			6.4  Differential Equations with Discontinuous Forcing Functions 
			6.5  Impulse Functions
			6.6  The Convolution Integral

CHAPTER 7	Systems of First Order Linear Equations (10 Lectures,1 Review) 
			
			7.1  Introduction
			7.2  Review of Matrices
			7.3  Systems of Linear Algebraic Equations; Linear Independence, Eigenvalues, Eigenvectors
			7.4  Basic Theory of Systems of First Order Linear Equations
			7.5  Homogeneous Linear Systems with Constant Coefficients
			7.6  complex Eigenvalues
			7.7  Repeated Eigenvalues
			7.8  Fundamental Matrices
			7.9  Nonhomogeneous Linear Systems

CHAPTER 9	Nonlinear Differential Equations and Stability (9 Lectures, 1 											Review)
			9.1  The Phase Plane:  Linear systems
			9.2  Autonomous systems and Stability
			9.3  Almost Linear systems
			9.6  Liapunov's Second Method

CHAPTER 8	Numerical Methods
			
			8.1  The Euler or Tangent Line Method
			8.2  Errors in Numerical Procedures
			8.3  Improvements on the Euler Method

CHAPTER 10	Partial Differential Equations and Fourier Series (4 Lectures,1 											    Review)
			10.1  Separation of Variables; Heat Conduction
			10.2  Fourier Series
			10.3  The Fourier Theorem
			10.4  Even and Odd Functions
			10.5  Solution of Other Heat Conduction Problems
			10.6  The Wave Equation:  Vibrations of an Elastic String