Differential Equations 1 The Geometrical View of y\'=f(x,y): Direction Fields, Integral Curves.
(Arthur Mattuck, Haynes Miller / MIT)



Differential Equations 10 Continuation: Complex Characteristic Roots; Undamped and Damped Oscillations.
(Arthur Mattuck, Haynes Miller / MIT)



Differential Equations 11 Theory of General Secondorder Linear Homogeneous ODE\'s: Superposition, Uniqueness, Wronskians.
(Arthur Mattuck, Haynes Miller / MIT)



Differential Equations 12 Continuation: General Theory for Inhomogeneous ODE\'s. Stability Criteria for the Constantcoefficient ODE\'s.
(Arthur Mattuck, Haynes Miller / MIT)



Differential Equations 13 Finding Particular Sto Inhomogeneous ODE\'s: Operator and Solution Formulas Involving Ixponentials.
(Arthur Mattuck, Haynes Miller / MIT)



Differential Equations 14 Interpretation of the Exceptional Case: Resonance.
(Arthur Mattuck, Haynes Miller / MIT)



Differential Equations 15 Introduction to Fourier Series; Basic Formulas for Period 2(pi).
(Arthur Mattuck, Haynes Miller / MIT)



Differential Equations 16 Continuation: More General Periods; Even and Odd Functions; Periodic Extension.
(Arthur Mattuck, Haynes Miller / MIT)



Differential Equations 17 Finding Particular Solutions via Fourier Series; Resonant Terms; Hearing Musical Sounds.
(Arthur Mattuck, Haynes Miller / MIT)



Differential Equations 18 Introduction to the Laplace Transform; Basic Formulas.
(Arthur Mattuck, Haynes Miller / MIT)



Differential Equations 19 Derivative Formulas; Using the Laplace Transform to Solve Linear ODE\'s.
(Arthur Mattuck, Haynes Miller / MIT)



Differential Equations 2 Euler\'s Numerical Method for y\'=f(x,y) and its Generalizations.
(Arthur Mattuck, Haynes Miller / MIT)



Differential Equations 20 Convolution Formula: Proof, Connection with Laplace Transform, Application to Physical Problems.
(Arthur Mattuck, Haynes Miller / MIT)



Differential Equations 21 Using Laplace Transform to Solve ODE\'s with Discontinuous Inputs.
(Arthur Mattuck, Haynes Miller / MIT)



Differential Equations 22 Use with Impulse Inputs; Dirac Delta Function, Weight and Transfer Functions.
(Arthur Mattuck, Haynes Miller / MIT)



Differential Equations 23 Introduction to Firstorder Systems of ODE\'s; Solution by Elimination, Geometric Interpretation of a System.
(Arthur Mattuck, Haynes Miller / MIT)



Differential Equations 24 Homogeneous Linear Systems with Constant Coefficients: Solution via Matrix Eigenvalues (Real and Distinct Case).
(Arthur Mattuck, Haynes Miller / MIT)



Differential Equations 25 Continuation: Repeated Real Eigenvalues, Complex Eigenvalues.
(Arthur Mattuck, Haynes Miller / MIT)



Differential Equations 26 Sketching Solutions of 2x2 Homogeneous Linear System with Constant Coefficients.
(Arthur Mattuck, Haynes Miller / MIT)



Differential Equations 27 Matrix Methods for Inhomogeneous Systems: Theory, Fundamental Matrix, Variation of Parameters.
(Arthur Mattuck, Haynes Miller / MIT)



Differential Equations 28 Matrix Exponentials; Application to Solving Systems.
(Arthur Mattuck, Haynes Miller / MIT)



Differential Equations 29 Decoupling Linear Systems with Constant Coefficients.
(Arthur Mattuck, Haynes Miller / MIT)



Differential Equations 3 Solving Firstorder Linear ODE\'s; Steadystate and Transient Solutions.
(Arthur Mattuck, Haynes Miller / MIT)



Differential Equations 30 Nonlinear Autonomous Systems: Finding the Critical Points and Sketching Trajectories; the Nonlinear Pendulum.
(Arthur Mattuck, Haynes Miller / MIT)



Differential Equations 31 Limit Cycles: Existence and Nonexistence Criteria.
(Arthur Mattuck, Haynes Miller / MIT)



Differential Equations 32 Relation Between Nonlinear Systems and Firstorder ODE\'s; Structural Stability of a System, Borderline Sketching Cases; Illustrations Using Volterra\'s Equation and Principle.
(Arthur Mattuck, Haynes Miller / MIT)



Differential Equations 4 Firstorder Substitution Methods: Bernouilli and Homogeneous ODE\'s.
(Arthur Mattuck, Haynes Miller / MIT)



Differential Equations 5 Firstorder Autonomous ODE\'s: Qualitative Methods, Applications.
(Arthur Mattuck, Haynes Miller / MIT)



Differential Equations 6 Complex Numbers and Complex Exponentials.
(Arthur Mattuck, Haynes Miller / MIT)



Differential Equations 7 Firstorder Linear with Constant Coefficients: Behavior of Solutions, Use of Complex Methods.
(Arthur Mattuck, Haynes Miller / MIT)



Differential Equations 8 Continuation; Applications to Temperature, Mixing, RCcircuit, Decay, and Growth Models.
(Arthur Mattuck, Haynes Miller / MIT)



Differential Equations 9 Solving Secondorder Linear ODE\'s with Constant Coefficients: The Three Cases.
(Arthur Mattuck, Haynes Miller / MIT)



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