001 - Review of Ax=b for Differential Equations
002 - PDEs 1- The Lay of the Land
003 - PDEs 2- Why ODEs Are Easy-They Are Just Like a Treasure Hunt!
004 - PDEs 3- A Linear ODE Is Nothing but Ax=b， and That s THE Most Important Po
005 - PDEs 4- Linear ODEs with Constant Coefficients， Finding a Particular Solut
006 - Linear ODE with Constant Coefficients- The Homogenized Equation
007 - Linear ODEs with Constant Coefficients- Distinct Roots
008 - Linear ODEs with Constant Coefficients- Matching the Initial Conditions
009 - Linear ODEs with Constant Coefficients- The Harmonic Oscillator
010 - Linear ODE with Constant Coefficients- Complex Roots with Nonzero Real Par
011 - Linear ODEs with Constant Coefficients- Repeated Roots
012 - World s Simplest ODE is Still Interesting!
013 - Linear ODEs with Constant Coefficients- Preview of Resonance
014 - Overview of Resonance Phenomena
015 - Linear ODEs with Constant Coefficients- Illustration of Resonance with Exp
016 - Linear ODEs with Constant Coefficients- Classical Resonance
017 - Intuitive Explanation of Resonance by Helmholtz
018 - Linear ODEs- Resonance and Repeated Roots
019 - A Lemma Challenge- Solve the Conundrum of Near Resonance!
020 - An Ode to the Second Derivative
021 - What Is the Laplacian?
022 - Introduction to Laplace and Poisson Equations
023 - Introduction to the Heat Equation
024 - A Further Introduction to the Wave Equation
025 - The Most Important Video in the Series- The Linear Property of the Fundame
026 - Solving the Laplace Equation in 1D
027 - Solving Poisson s equation in 1D
028 - PDEs- Separation of Variables
029 - PDEs- Separation of Variables Step 2， Which Is Putting It All Together!
030 - Solving the Heat Equation in 1D and the Need for Fourier Series
031 - Fourier Series- Preliminary Remarks
032 - Fourier Series- What to Expect
033 - Fourier Series- Determining the Coefficients
034 - Fourier Series for f(x) = x
035 - Fourier Series for f(x) = π² - x²
036 - Solving the Heat Equation in 1D by Fourier Series
037 - Solving the Wave Equation in 1D by Fourier Series
038 - Complex Fourier Series
039 - Laplace Equation on the Unit Disk
040 - Derivation of Poisson s Formula for of Laplace s Equation on the Unit Disk
041 - Laplace Eigenvalues on the Rectangle- A Complete Derivation
042 - Solution of the Poisson Equation on Unit Disk
043 - Laplace Eigenvalues on the Unit Disk- A Complete Derivation
044 - The Surprising History of Stellar Parallax
045 - Solution of the Laplace Equation on an Annulus
046 - Heat Equation with a Discontinuity
047 - Another Heat Equation with a Discontinuity
