UASLP Mathematical Methods

In this course, students should develop the mathematical skills required to understand ans develop engineering models. This is an Master and PhD level course. The full syllabus can be found here. I have taught the following contents:

Multivariable Calculus

Objective: Evaluate multivariable functions and comput their extreme values

  1. Differentiable transformations
  2. Inverse and Implicit function theorems
  3. Extreme values of multivariable functions
  4. Extreme value of a functional

Vectors and Tensors

Objective: Apply theorems regarding line, surface and volume integrals in multivariable functions

  1. Algebra of Cartesian tensors
  2. Differential operators
  3. Green’s Theorem
  4. Gauss’s Theorem
  5. Stokes’s Theorem
  6. Leibnitz’s integral rule
  7. Orthogonal curvilinear coordinates (cylindrical, spherical, etc)

Complex Variable Functions

Objective: Introduce complex variables and their use in solving important problems in physics and engineering

  1. Analytic functions
  2. Cauchy’s Theorem
  3. Power series and analytic functions
  4. Residual calculation
  5. Partial fraction expansion
  6. Conformal maps