Black Friday 2024: 25+ Ways to Save on Online Learning
Engineering Mathematics

Engineering Mathematics

Steve Brunton via YouTube Direct link

ME565 Lecture 2: Roots of unity, branch cuts, analytic functions, and the Cauchy-Riemann conditions

30 of 59
Previous
Next

30 of 59

ME565 Lecture 2: Roots of unity, branch cuts, analytic functions, and the Cauchy-Riemann conditions

Class Central Classrooms beta

YouTube videos curated by Class Central.

Classroom Contents

Engineering Mathematics

Automatically move to the next video in the Classroom when playback concludes
  1. 1 ME564 Lecture 1: Overview of engineering mathematics
  2. 2 ME564 Lecture 2: Review of calculus and first order linear ODEs
  3. 3 ME564 Lecture 3: Taylor series and solutions to first and second order linear ODEs
  4. 4 ME564 Lecture 4: Second order harmonic oscillator, characteristic equation, ode45 in Matlab
  5. 5 ME564 Lecture 5: Higher-order ODEs, characteristic equation, matrix systems of first order ODEs
  6. 6 ME564 Lecture 6: Matrix systems of first order equations using eigenvectors and eigenvalues
  7. 7 ME564 Lecture 7: Eigenvalues, eigenvectors, and dynamical systems
  8. 8 ME564 Lecture 8: 2x2 systems of ODEs (with eigenvalues and eigenvectors), phase portraits
  9. 9 ME564 Lecture 9: Linearization of nonlinear ODEs, 2x2 systems, phase portraits
  10. 10 ME564 Lecture 10: Examples of nonlinear systems: particle in a potential well
  11. 11 ME564 Lecture 11: Degenerate systems of equations and non-normal energy growth
  12. 12 ME564 Lecture 12: ODEs with external forcing (inhomogeneous ODEs)
  13. 13 ME564 Lecture 13: ODEs with external forcing (inhomogeneous ODEs) and the convolution integral
  14. 14 ME564 Lecture 14: Numerical differentiation using finite difference
  15. 15 ME564 Lecture 15: Numerical differentiation and numerical integration
  16. 16 ME564 Lecture 16: Numerical integration and numerical solutions to ODEs
  17. 17 ME564 Lecture 17: Numerical solutions to ODEs (Forward and Backward Euler)
  18. 18 ME564 Lecture 18: Runge-Kutta integration of ODEs and the Lorenz equation
  19. 19 ME564 Lecture 19: Vectorized integration and the Lorenz equation
  20. 20 ME564 Lecture 20: Chaos in ODEs (Lorenz and the double pendulum)
  21. 21 ME564 Lecture 21: Linear algebra in 2D and 3D: inner product, norm of a vector, and cross product
  22. 22 ME564 Lecture 22: Div, Grad, and Curl
  23. 23 ME564 Lecture 23: Gauss's Divergence Theorem
  24. 24 ME564 Lecture 24: Directional derivative, continuity equation, and examples of vector fields
  25. 25 ME564 Lecture 25: Stokes' theorem and conservative vector fields
  26. 26 ME564 Lecture 26: Potential flow and Laplace's equation
  27. 27 ME564 Lecture 27: Potential flow, stream functions, and examples
  28. 28 ME564 Lecture 28: ODE for particle trajectories in a time-varying vector field
  29. 29 ME565 Lecture 1: Complex numbers and functions
  30. 30 ME565 Lecture 2: Roots of unity, branch cuts, analytic functions, and the Cauchy-Riemann conditions
  31. 31 ME565 Lecture 3: Integration in the complex plane (Cauchy-Goursat Integral Theorem)
  32. 32 ME565 Lecture 4: Cauchy Integral Formula
  33. 33 ME565 Lecture 5: ML Bounds and examples of complex integration
  34. 34 ME565 Lecture 6: Inverse Laplace Transform and the Bromwich Integral
  35. 35 ME565 Lecture 7: Canonical Linear PDEs: Wave equation, Heat equation, and Laplace's equation
  36. 36 ME565 Lecture 8: Heat Equation: derivation and equilibrium solution in 1D (i.e., Laplace's equation)
  37. 37 ME565 Lecture 9: Heat Equation in 2D and 3D. 2D Laplace Equation (on rectangle)
  38. 38 ME565 Lecture 10: Analytic Solution to Laplace's Equation in 2D (on rectangle)
  39. 39 ME565 Lecture 11: Numerical Solution to Laplace's Equation in Matlab. Intro to Fourier Series
  40. 40 ME565 Lecture 12: Fourier Series
  41. 41 ME565 Lecture 13: Infinite Dimensional Function Spaces and Fourier Series
  42. 42 ME565 Lecture 14: Fourier Transforms
  43. 43 ME565 Lecture 15: Properties of Fourier Transforms and Examples
  44. 44 ME565 Lecture 16 Bonus: DFT in Matlab
  45. 45 ME565 Lecture 17: Fast Fourier Transforms (FFT) and Audio
  46. 46 ME565 Lecture 16: Discrete Fourier Transforms (DFT)
  47. 47 ME565 Lecture 18: FFT and Image Compression
  48. 48 ME565 Lecture 19: Fourier Transform to Solve PDEs: 1D Heat Equation on Infinite Domain
  49. 49 ME565 Lecture 20: Numerical Solutions to PDEs Using FFT
  50. 50 ME565 Lecture 21: The Laplace Transform
  51. 51 ME565 Lecture 22: Laplace Transform and ODEs
  52. 52 ME565 Lecture 23: Laplace Transform and ODEs with Forcing and Transfer Functions
  53. 53 ME565 Lecture 24: Convolution integrals, impulse and step responses
  54. 54 ME565 Lecture 25: Laplace transform solutions to PDEs
  55. 55 ME565 Lecture 26: Solving PDEs in Matlab using FFT
  56. 56 ME 565 Lecture 27: SVD Part 1
  57. 57 ME565 Lecture 28: SVD Part 2
  58. 58 ME565 Lecture 29: SVD Part 3
  59. 59 The Laplace Transform: A Generalized Fourier Transform

Never Stop Learning.

Get personalized course recommendations, track subjects and courses with reminders, and more.

Sign up for free
Someone learning on their laptop while sitting on the floor.