Self-Paced Online Mathematical Modeling and Parameter Estimation Certificate Course

Register and Enroll

CLICK HERE to Register for Mathematical Modeling and Parameter Estimation

Cost: $2,500
Discounted Student Rate: $1,250 (Proof of student ID required)
Current MSU students, email Dr. Kirk Dolan (dolank@msu.edu)

Group discount: 20% discount for ≥ 3 participants from the same organization/institution.

Start your enrollment by first creating an MSU guest account, sign in with your email/password, and complete the enrollment process. See “Enrollment Instructions – Self-Paced Mathematical Modeling and Parameter Estimation” for step-by-step instructions for completing your enrollment.

Duration

180 Days (60-day extension allowed, if needed to suit a learner’s pace)

What This Course Offers

Nearly 40 hours of instruction
Hands-on assignments and a final project with real data and a model
Instructor’s template MATLAB codes so you can solve any parameter estimation problem

Target Audience

Engineering graduate students and engineers and scientists working in the industry or research, who:

Want to learn MATLAB;
Collect experimental data to which a mathematical model will be fit;
Want to learn to estimate 1-10 parameters from observed data and a linear or nonlinear mathematical model;
Need to use numerical techniques to solve integrals and ordinary and partial differential equations;
Want to do a thorough statistical analysis for comparison of models;
Are preparing a research presentation for work or a conference

Topics Covered

Numerical methods, parameter estimation, and statistical analysis for mathematical models used in engineering. Theory will be illustrated with examples from various engineering disciplines. MATLAB will be taught and is required to be used for assignments. Course Director will supply template codes for inverse problems.

Learning Objectives

Upon completion of this course, you will be able to:

Compute the area integral by trapezoidal, Simpson, and Gauss-Legendre Quadrature, and know when each method should be used;
Determine whether a model is linear or nonlinear with respect to each parameter;
Know when to use a forward or an inverse problem, and what the difference is;
Plot scaled sensitivity coefficients (SSCs);
Determine whether any parameter in the model can be estimated and which parameters will be most accurate;
Solve numerically the forward problem of coupled ordinary differential equations (ODEs) or single partial differential equations (PDEs) with a time and a space variable;
Estimate parameters by Ordinary Least Squares and sequentially in systems of coupled ODEs, a single PDE, or in explicit equations;
Compute all statistical results for parameters and the dependent variable;
Determine whether all eight standard statistical assumptions are met;
Use bootstrap and Monte Carlo methods;
Set up an optimal experimental design based on the model and parameter values;
Give insight into the estimation process based on examination of SSCs and residual analysis;
Use MATLAB for a variety of engineering and other problem-solving purposes.
Give a research presentation on the forward and inverse problems, as if you were at a conference.

COURSE MODULES:

1. The Forward Problem

MATLAB basics (Chapter 2 Reading). Do examples in Chapters 2 and 3.
Types of error (Chapter 4 Reading). Roots bracketed and open.
Review of matrices. Numerical Differentiation. Boundary-value (BV) problems: Finite-difference (FD) method for ordinary differential equations (ODEs).
Finite-difference for BV problems for ODEs and partial differential equations (PDEs)
Numerical solution to initial-value problems—Runge-Kutta (RK) methods. Adaptive methods and stiff systems—using ode45. Solving BV problems using shooting method. Nonlinear ODEs.
Numerical integration: trapezoidal, Simpson, Numerical integration of functions: Gauss-Legendre Quadrature.

2. The Inverse Problem

Parameter estimation intro; linear regression
Matrix formulation for linear models; standard statistical assumptions; confidence intervals CIs) for linear regression; Matrix formulation for nonlinear models
Plotting scaled sensitivity coefficients, Parameter estimation examples, multi-response models.
Sequential estimation for linear and nonlinear models
Sequential Estimation for nonlinear estimation
Bootstrap and Monte Carlo methods
Model discrimination using Akaike info criterion (AICc) criterion; Optimal experimental design; cftool in MATLAB; Parameter joint confidence regions
Project Presentation via Zoom. (NOTE: Submit PowerPoint and MATLAB codes in advance of the presentation)

Assignments & Grading

Eight coding assignments that are auto-graded in MATLAB Grader.
Project presentation via Zoom. Rubric is given separately.
To obtain certification, must obtain at least 80% score total on the eight coding assignments and on the project presentation.

Access to MATLAB

If you do not already have access to MATLAB, the Basic version is available free at mathworks.com after registering a free account. The “Statistics and Machine Learning” Toolbox (free) must be accessed for many of the assignments.

Required Texts

Chapra, S.C. Applied Numerical Methods with MATLAB for Engineers and Scientists, 2012 3^rd edition (I will use this one) or 2008, 2^nd edition or, McGraw-Hill, NY. Can check addall.com for used copies. Not included in the course fee. Used copies run about $20, including shipping at Amazon.
Beck, J.V. and Arnold, K.J. Parameter Estimation in Engineering and Science. John Wiley & Sons, Inc. Out of print, but available electronically from the instructor for free.
Beck, J.V. and Arnold, K.J. Parameter Estimation in Engineering and Science, Chapter 6, revised in 2007 for MATLAB applications, and available electronically from the instructor for free.

Other useful text:

Motulsky, H., and Christopoulos, A. Fitting Biological Data Using Linear and Nonlinear Regression. A Practical Guide to Curve Fitting. 2004. Oxford University Press, NY.

Course Director

Dr. Kirk Dolan, Professor, Biosystems & Agri Engineering and Food Science & Human Nutrition, Michigan State University, East Lansing, MI 48824. Email: dolank@msu.edu