Schedule:

START OF CLASSES

• September 24: Lecture 1 [Slides] [Notes]
  Introduction. Ordinary differential equations (ODEs), and initial and boundary conditions. Solution of homogeneous and inhomogeneous ODEs. Eigenvalue and eigenvector analysis, and multimode analysis. Linear time-invariant systems, impulse response, and transfer function.
  
  
• September 25: Lecture 2, tutorial and problem solving session [Slides] [Notes] [Matlab code]
  Introduction to Matlab for linear systems, ODEs and PDEs. Analytical and numerical techniques. Solution to example problems, using paper and pencil, and verified by numerical simulation.

WEEK 1

• September 29: Lecture 3 [Notes]
  Introduction to PDEs. One-dimensional heat equation, and its equivalents in electrical and chemical transport with applications to biomedical engineering. Flux through membranes. One-dimensional wave equation in an electrical transmission line, with open and short circuit termination. Finite difference PDE approximations.
  
  
• October 1: Lecture 4 [Notes]
  Solutions to PDEs over bounded and unbounded domains. Separation of variables. Boundary value problem and solution of the x dependent equation. Product solution of the PDEs with specified boundary conditions. Solutions over infinite domains using Fourier transforms, and Green's functions. Finite difference and finite element numerical analysis.
  
  
• October 2: Problem solving session--student presentations

WEEK 2

• October 6: Lecture 5 [Notes]
  Review of vector calculus. Gradients, divergence, curl, and Laplacian. Transformation between Cartesian, cylindrical, and radial coordinates. Fields and potentials. Divergence theorem, and Stokes theorem.
  
  
• October 8: Lecture 6 [Notes]
  Electrostatics. Coulomb's law. Electric field and potential. Work and moving charge. Equivalence of surface/field product and enclosed charge. Gauss's law, and Poisson's and Laplace's equation. Electric field near and in conductors. Dielectric phenomena. Capacitance.
  
  
• October 9: Problem solving session--student presentations

WEEK 3

• October 13: Lecture 7 [Notes]
  Magnetic effects and fields. The Biot-Savart law and units. Magnetostatics and the role of electric current. Solutions by vector integration, and integral solution of the magnetic field from a conducting loop. The divergence and curl of the magnetic field, and Ampere's law.
  
  
• October 15: Lecture 8 [Notes]
  Maxwell's equations, and electromagnetism. Faraday's law of induction, and Ampere's law with Maxwell's correction. Electromagnetic waves.
  
  
• October 16: Problem solving session--student presentations

WEEK 4

• October 20: Lecture 9 [Notes]
  Wave propagation in homogeneous and inhomogeneous media. Far and near field. RF telemetry and power delivery. Tissue absorption.
  
  
• October 22: Lecture 10 [Notes] [Sample midterm] [Solutions]
  Review and sample midterm
  
  
• October 23: Problem solving session--student presentations

WEEK 5

• October 27: Midterm [Midterm] [Solutions]
  
  
• October 29: Lecture 11 [Notes]
  Brownian motion, and diffusion. Theory for one-dimensional displacement. Solutions for the diffusion equation. Diffusion coefficient, and Reynolds number. Chemical reactions.
  
  
• October 30: Problem solving session--student presentations

WEEK 6

• November 3: Lecture 12 [Notes]
  Derivation of the diffusion equation. Solution for constant diffusion coefficient from a plane source. Diffusion from a finite region consisting of a volume source. Diffusion from and in confined regions. Dimensionless formulation and solution of the diffusion equation.
  
  
• November 5: Lecture 13 [Notes]
  Additional considerations on diffusion. Alternative interpretations of the diffusion process. Flux as velocity times concentration. Thermodynamic interpretation of diffusion. Application of Gauss' theorem in deriving the diffusion equation.
  
  
• November 6: Problem solving session--student presentations

WEEK 7

• November 10: Lecture 14 [Notes]
  Heat equation. Temperature, thermal energy, and flux. Diffusion of thermal energy, and boundary conditions on temperature and flux. Thermal equilibrium.
  
  
• November 12: Lecture 15 [Notes]
  Analytical solution to the diffusion equation. Separation of variables revisited, with Fourier series expansions of initial conditions.
  
  
• November 13: Problem solving session--student presentations

WEEK 8

• November 17: Lecture 16 [Notes]
  Solutions of partial differential equations with stochastic boundary conditions.
  
  
• November 19: Lecture 17
  Review. Methods for solving partial differential equations using Fourier series, the Fourier transform, and the Laplace transform.
  
  
• November 20: Problem solving session--student presentations

WEEK 9

• November 24: Lecture 18 [Notes]
  The one dimensional wave equation. The vibrating string as a boundary value problem. Vibrating string clamped at both ends. Standing waves and summation of traveling waves.
  
  
• November 26-27: Thanksgiving

WEEK 10

• December 1: Lecture 19 [Notes]
  Sound. Transmission of waves in gases. Pressure variation in a sound wave.
  
  
• December 3: Lecture 20
  Course review and sample final exam.
  
  
• December 4: Problem solving session--student presentations

FINAL EXAM

• December 9: 11:30am-2:30pm

Reading and reference materials:

• Richard Haberman, Applied Partial Differential Equations (4th Edition), Pearson-Prentice Hall, 2004.
• H. M. Schey, Div, Grad, Curl, and All That: An Informal Text on Vector Calculus (4th Edition), Norton Press, 2005.
• David J. Griffiths, Introduction to Electrodynamics (3rd Edition), Benjamin Cummings Press, 1999.
• John D. Jackson, Classical Electrodynamics (3rd Edition), John Wiley, 1998.
• Richard Fitzpatrick, Classical Electromagnetism: An intermediate level course, Univ. Texas, 2006.
• Wikipedia, the free encyclopedia:
  • Ordinary differential equations
  • Partial differential equations
  • Vector calculus
  • Classical electrodynamics
• Gerard Michon, Final Answers on Maxwell's Equations, Numericana, 2009.