Introduction:  This course provides an accelerated review of mathematical tools for scientific applications and analysis. See its description on the catalog

 

Books:  I am planning to use my own notes. For the first part of the course I will base my notes on the book by Francis B. Hildebrand "Methods of Applied Mathematics"  Dover (1992). On the second part, I am planning to cover "Sensitivity and perturbation analysis of nonlinear matrix models".  For this part of the course will base my lectures on the book "Applied Mathematical Demography" by N. Keyfitz and H. Caswell (3rd edition) Springer (2005). In addition we will review some research papers on these topics.

 

Syllabus  MS-Word document  PDF format  

Lectures:

  • Part I: Matrices and Linear Algebra.
    1.  Introduction(1.1), Linear Equations(1.2), Matrices and Determinants(1.3-4). lecture-PDF
    2.  Special Matrices(1.5), The inverse matrix(1.6), Rank of a matrix(1.7), Elementary operations(1.8). lecture-PDF.  Homework 2 (courtesy of Tom Tiahrt).
    3.  Solvability of Linear Systems(1.9), Linear vector Space(1.10), Linear equations and vector space(1.11). lecture-PDF. Homework 3 (courtesy of Tom Tiahrt).
    4.  Eigenvalue-value problems(1.12), Google Search Engine, Orthogonalization(1.13).  lecture-PDF. Homework 4 (courtesy of Tom Tiahrt).
    5. Equivalent matrices and transformations(1.16), Multiples eigenvalues of symmetric matrices(1.18), Numerical solution of eigenvalue problems(1.23). lecture-PDF
    6. Test on the Part I material (1-5). Homework 5 (courtesy of Tom Tiahrt).
  • Part II Nonlinear Matrix Models and Stability Analysis
    1. Matrix model framework. lecture-PDF, Homework # 6
    2. The Leslie Matrix and the Life Table, lecture-PDF,  Homework #7
    3. Birth and Population Increase  from Matrix Population Models.  lecture-PDF,  Homework #8.
    4. Continued
    5. Reproductive Value from Matrix Models lecture-PDF, Homework #9.
    6. Perturbation Analysis of Matrix Models (Sensitivity Analysis) lecture-PDF, Homework # 10
    7. Continued (Elasticity Analysis) lecture-PDF  homework # 11
    8. LTRE's lecture-PDF, homework#12 ----you will need this data.
    9. Markov Chains for Individual Life Histories (if time permitted)