Ordinary and Partial Dierential Equations
Lab 1. Direction elds and numerical solutions of rst-order DEs
Bibliography: Nagle, Sna, Sieder - Fundamentals of DEs and BVPs (6th ed.) - section 1.3.
Objectives:
1. To learn how to use Mathematica to create the
Ordinary and Partial Dierential Equations
Lecture 7. Higher order linear dierential equations
Bibliography: Nagle, Sna, Sieder - Fundamentals of DEs and BVPs (6th ed.) - chapter 6
INTRODUCTION
A linear dierential equation of order n is of the form
an (x)y
Ordinary and Partial Dierential Equations
Lecture 5. Linear second-order dierential equations with variable coecients
Homogeneous and nonhomogeneous equations. Cauchy-Euler equations.
Bibliography: Nagle, Sna, Sieder - Fundamentals of DEs and BVPs (6th ed
Ordinary and Partial Dierential Equations
Lecture 6. Introduction to systems and phase plane analysis
Bibliography: Nagle, Sna, Sieder - Fundamentals of DEs and BVPs (6th ed.) - chapter 5
DIFFERENTIAL OPERATORS
We dene the dierential operator D which acts
Ordinary and Partial Dierential Equations
Lecture 3. First-order dierential equations - Part 2.
Exact equations. Special integrating factors. Substitutions and transformations.
Bibliography: Nagle, Sna, Sieder - Fundamentals of DEs and BVPs (6th ed.) - se
Ordinary and Partial Dierential Equations
Lab 4. Mathematical Modeling: Consecutive Reactions for Batch Reactors
Bibliography:
[1] Nagle, Sna, Sieder - Fundamentals of DEs and BVPs (6th ed.) - chapter 5;
[2] Holland, C.D., Anthony R.G. - Fundamentals of C
Ordinary and Partial Dierential Equations
Lab 3. Analytical and graphical analysis of systems
Bibliography:
[1] Nagle, Sna, Sieder - Fundamentals of DEs and BVPs (6th ed.) - chapter 5;
[2] Perelson, Kerschner, DeBoer - Dynamics of HIV Infections of CD4+ T
Ordinary and Partial Dierential Equations
Lecture 1. Introduction
Bibliography: Nagle, Sna, Sieder - Fundamentals of DEs and BVPs (6th ed.) - sections 1.1, 1.2, 1.3
BACKGROUND
In the sciences and engineering, mathematical models are developed to aid in th
Ordinary and Partial Dierential Equations
Lab 2. Numerical solutions: Eulers method
Bibliography: Nagle, Sna, Sieder - Fundamentals of DEs and BVPs (6th ed.) - sections 1.4; 3.6.
Objectives:
1. To learn how to numerically approximate solutions using Euler
Ordinary and Partial Dierential Equations
Lecture 8. Linear systems of dierential equations
Bibliography: Nagle, Sna, Sieder - Fundamentals of DEs and BVPs (6th ed.) - chapter 9
LINEAR SYSTEMS IN NORMAL FORM
A linear system of dierential equations can be