Introduction to Differential Equations | |
Introduction | |
Direction Fields | |
First Order Linear Differential Equations | |
Existence and Uniqueness | |
First Order Linear Homogeneous Differential Equations | |
Nonhomogeneous Differential Equations | |
Introduction to Mathematical Models | |
Mixing Problems and Cooling Problems | |
First Order Nonlinear Differential Equations | |
Existence and Uniqueness | |
Separable First Order Equations | |
Exact Differential Equations | |
Bernoulli Equations | |
The Logistic Population Model | |
One-Dimensional Motion with Air Resistance | |
One-Dimensional Dynamics with Distance as the Independent Variable | |
Euler's Method | |
Second Order Linear Differential Equations | |
Introduction | |
Existence and Uniqueness | |
The General Solution of Homogeneous Equations | |
Fundamental Sets and Linear Independence | |
Constant Coefficient Homogeneous Equations | |
Real Repeated Roots | |
Reduction of Order | |
Complex Roots | |
Unforced Mechanical Vibrations | |
The General Solution of the Linear Nonhomogeneous Equation | |
The Method of Undetermined Coefficients | |
The Method of Variation of Parameters | |
Forced Mechanical Vibrations, Electrical Networks, and Resonance | |
Higher Order Linear Differential Equations | |
Existence and Uniqueness | |
The General Solution ofnth Order Linear Homogeneous Equation | |
Fundamental Sets and Linear Independence | |
Constant Coefficient Homogeneous Equations | |
Nonhomogeneous Linear Equations | |
First Order Linear Systems | |
The Calculus of Matrix Functions | |
Existence and Uniqueness | |
Homogeneous Linear Systems | |
Fundamental Sets and Linear Independence | |
Constant Coefficient Homogeneous Systems | |
Complex Eigenvalues | |
Repeated Eigenvalues | |
Nonhomogeneous Linear Systems | |
Euler's Method for Systems of Differential Equations | |
Diagonalization | |
Functions of a Matrix and the Exponential Matrix | |
Laplace Transforms | |
The Laplace Transform | |
Lapla | |
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