## M.I.T. 18.03 Ordinary Differential Equations 18.03 Notes and Exercises

Notes
 D. Definite Integral Solutions G. Graphical and Numerical Methods C. Complex Numbers IR. Input Response Models O. Linear Differential Operators S. Stability I. Impulse Response and Convolution H. Heaviside Coverup Method LT. Laplace Transform CG. Convolution and Green's Formula LS.1. Linear Systems: Review of Linear Algebra LS.2. Homogeneous Linear Systems with Constant Coefficients LS.3. Complex and Repearted Eigenvalues LS.4. Decoupling Systems LS.5. Theory of Linear Systems LS.6. Solution Matrices GS.1-6. Graphing ODE Systems GS.7-8. Structural stability LC. Limit Cycles FR. Frequency Response P. Poles and Amplitude Response LA.1. LA.1: Phase Plane and Linear Systems LA.2. LA.2: Matrix Multiplication, Rank, Solving Linear Systems LA.3. LA.3: Complete Solutions, Nullspace, Space, Dimension, Basis LA.4. LA.4: Inverses and Determinants LA.5. LA.5: Eigenvalues and Eigenvectors LA.6. LA.6: Diagonalization and Orthogonal Matrices LA.7. LA.7: Two Dimensional Dynamics LA.8. LA.8: Trace-determinant plane, Stability LA.9. LA.9: Decoupling LA.10. LA.10: The Matrix Exponential LA.11. LA.11: Inhomogeneous Systems PDE.1. PDE.1: Fourier's Theory of Heat PDE.2. PDE.2: Decoupling; Insulated Ends PDE.3. PDE.3: The Wave Equation

Exercises and Solutions
 1 First Order ODE's Solutions 2 Higher Order ODE's Solutions 3 Laplace Transform Solutions 4 Linear Systems Solutions 5 Graphing Systems Solutions 6 Power Series Solutions 7 Fourier Series Solutions 8 Extra Problems Solutions 9 Linear Algebra Exercises Solutions 10 PDE Exercises Solutions

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