Advanced Mathematics (MSE 298D)

Materials Science and Engineering 298D
Advanced Mathematics for Material Scientist

Course Outline

  1. Introduction to the Use of a Mathematical Software
    1. Basic: Plotting Data, 2 – Dimensional Plotting, Graphics, Primitives, Formatting
    2. Symbolic and Numeric Calculations, Linear Algebra, Roots of Equation
    3. Functional Programming Packages and File Input/Output
  2. Probability and Statistics
    1. Introduction to probability, random variables, expectation values
    2. Moments and generating functions
    3. Central limit theorem
    4. Sampling and averaging
    5. Confidence levels
    6. Geometric mean, arithmetic mean, harmonic mean, median, mode
  3. Vectors, tensors and matrices
    1. Introduction to vectors and tensors
    2. Operations with vectors and tensors
    3. Application to mechanics of anisotropic media, light propagation
    4. Inverse, diagonalization, linear regression
    5. Eigenvalues, eigenfunctions
    6. Linear equations
    7. Non-linear equations and approximations
  4. Fourier and Laplace Transforms
    1. Introduction to transforms
    2. Structure factors. Gases, liquids, crystals
    3. Applications:
      1. spectroscopy
      2. electron diffraction
      3. x-ray and neutron scattering
      4. nucleation and growth
      5. interfacial segregation and spinodal decomposition
  5. Ordinary Differential Equations
    1. First order ODE (reaction kinetics)
    2. ODE of higher orders
    3. Series solutions and asymptotics
    4. Numerical solutions
  6. Partial Differential Equations
    1. Introduction to PDE. Examples (diffusion, transport, wave phenomena)
    2. Separation of variables
    3. Laplace transform
    4. Numerical methods
    5. Applications to mechanics, diffusion, sound propagation