Differential Equations

Differential Equations are the language in which the laws of nature are expressed. Understanding properties of solutions of differential equations is fundamental to much of contemporary science and engineering. Ordinary differential equations (ODE's) deal with functions of one variable, which can often be thought of as time.

• Lecture 1: The Geometrical View of y'= f(x,y)
• Lecture 2: Euler's Numerical Method for y'=f(x,y)
• Lecture 3: Solving First-order Linear ODEs
• Lecture 4: First-order Substitution Methods
• Lecture 5: First-order Autonomous ODEs
• Lecture 6: Complex Numbers and Complex Exponentials
• Lecture 7: First-order Linear with Constant Coefficients
• Lecture 8: Continuation
• Lecture 9: Solving Second-order Linear ODE's with Constant Coefficients
• Lecture 10: Continuation: Complex Characteristic Roots
• Lecture 11: Theory of General Second-order Linear Homogeneous ODEs
• Lecture 12: Continuation: General Theory for Inhomogeneous ODEs
• Lecture 13: Finding Particular Solutions to Inhomogeneous ODEs
• Lecture 14: Interpretation of the Exceptional Case: Resonance
• Lecture 15: Introduction to Fourier Series
• Lecture 16: Continuation: More General Periods
• Lecture 17: Finding Particular Solutions via Fourier Series
• MIT18_03S10_vlec_table.pdf
• Lecture 19: Introduction to the Laplace Transform
• Lecture 20: Derivative Formulas
• Lecture 21: Convolution Formula
• Lecture 22: Using Laplace Transform to Solve ODEs with Discontinuous Inputs
• Lecture 23: Use with Impulse Inputs
• Lecture 24: Introduction to First-order Systems of ODEs
• Lecture 25: Homogeneous Linear Systems with Constant Coefficients
• Lecture 26: Continuation: Repeated Real Eigenvalues
• Lecture 27: Sketching Solutions of 2x2 Homogeneous Linear System with Constant Coefficients
• Lecture 28: Matrix Methods for Inhomogeneous Systems
• Lecture 29: Matrix Exponentials
• Lecture 30: Decoupling Linear Systems with Constant Coefficients
• Lecture 31: Non-linear Autonomous Systems
• Lecture 32: Limit Cycles
• Lecture 33: Relation Between Non-linear Systems and First-order ODEs