Differential Equations (Spring 2010) (M-I-T)

• Lecture 1: The Geometrical View of y'= f(x,y) (M-I-T)
• Lecture 2: Euler's Numerical Method for y'=f(x,y) (M-I-T)
• Lecture 3: Solving First-order Linear ODEs (M-I-T)
• Lecture 4: First-order Substitution Methods (M-I-T)
• Lecture 5: First-order Autonomous ODEs (M-I-T)
• Lecture 6: Complex Numbers and Complex Exponentials (M-I-T)
• Lecture 7: First-order Linear with Constant Coefficients (M-I-T)
• Lecture 8: Continuation (M-I-T)
• Lecture 9: Solving Second-order Linear ODE's with Constant Coefficients (M-I-T)
• Lecture 11: Theory of General Second-order Linear Homogeneous ODEs (M-I-T)
• Lecture 12: Continuation: General Theory for Inhomogeneous ODEs (M-I-T)
• Lecture 13: Finding Particular Solutions to Inhomogeneous ODEs (M-I-T)
• Lecture 14: Interpretation of the Exceptional Case: Resonance (M-I-T)
• Lecture 15: Introduction to Fourier Series (M-I-T)
• Lecture 16: Continuation: More General Periods (M-I-T)
• Lecture 17: Finding Particular Solutions via Fourier Series (M-I-T)
• Lecture 19: Introduction to the Laplace Transform (M-I-T)
• Lecture 20: Derivative Formulas (M-I-T)
• Lecture 21: Convolution Formula (M-I-T)
• Lecture 22: Using Laplace Transform to Solve ODEs with Discontinuous Inputs (M-I-T)
• Lecture 23: Use with Impulse Inputs (M-I-T)
• Lecture 24: Introduction to First-order Systems of ODEs (M-I-T)
• Lecture 25: Homogeneous Linear Systems with Constant Coefficients (M-I-T)
• Lecture 26: Continuation: Repeated Real Eigenvalues (M-I-T)
• Lecture 27: Sketching Solutions of 2x2 Homogeneous Linear System with Constant Coefficients (M-I-T)