APMA 0330: Methods of Applied Mathematics - I
Mathematical techniques involving differential equations used in the analysis of physical, biological and economic phenomena. Emphasis is placed on the use of established methods, rather than rigorous foundations.
- First and second order differential equations.
- Variable coefficient second order linear differential equations.
- The Laplace transform.
- Numerical methods.
Software as a Learning Resource for DiffEqs
This course in elementary differential equations is designed to introduce the student for displaying the interrelations between mathematics and physical sciences or engineering. The principal attention is given to those methods that are capable of broad applications and that can be extended to various problems.
The methods discussed here include not only elementary analytical techniques that lead to exact solutions of certain classes of problems, but also include approximations based on numerical algorithms or series expansions, as well as qualitative or geometrical methods. The problem sets will be assigned and discussed in subsequent class sessions. A student is expected to learn how to use a software package (commercial or free) in solving ordinary differential equations. Workload:
| Hours per week | Number of weeks | Hours (total) | |
| Class meetings | 3 | 13 | 39 |
| Recitations | 1 | 13 | 13 |
| Reviewing material | 3 | 13 | 39 |
| Homework | 4 | 13 | 52 |
| Midterms exams | 8 | 2 | 16 |
| Project | 2 | 1 | 2 |
| Final exam | 22 | 1 | 22 |
| TOTAL | 183 |
Prerequisite: Elementary Calculus.
While previous knowledge of any computational solver is not a requirement for APMA 0330, students are expected to learn one or more of available either free (Octave, wxMaxima/Maxima, Sage, R, Julia, or SymPy/Python) or commercial (Matlab/Live Editor, Mathematica, or Maple) software in some applications during the semester. Therefore, students without software experience may need to take initiative in learning simple software techniques (click on "Computing" button on this page) to ensure success in the course. TA's and the instructor are usually available to provide mathematical software help for all students.
Nasser M. Abbasi prepared a solution solver for many ODEs problems:
Вместе с этим читают:
- APMA 2550: Finite Difference SchemesThe course intended for students who desire a rigorous development of the mathematical foundations of the methods used. This course provides further techniques of ordinary and partial differential equations, which are not covered by APMA 0330 and are of great importance in practice. Here are the main topics to be covered (syllabus): Topics from matrix algebra. Systems of linear ordinary differenti...
- APMA 1180: Numerical Solution of DifferentialThe course intended for students who desire a rigorous development of the mathematical foundations of the methods used. This course provides further techniques of ordinary and partial differential equations, which are not covered by APMA 0330 and are of great importance in practice. Here are the main topics to be covered (syllabus): Basic concepts. Root finding. Solutions of nonlinear systems of e...
- APMA 0360: Partial Differential EquationsThe course APMA0360 intended for students who desire a rigorous development of the mathematical foundations of the methods used. This course provides further techniques of partial differential equations, which are not covered by APMA 0340 and are of great importance in practice. Here are the main topics to be covered: Basic partial differential equations. Sturm--Liuville problems and orthogonal ex...
- APMA 0340: Methods of Applied Mathematics - IIThe course intended for students who desire a rigorous development of the mathematical foundations of the methods used. This course provides further techniques of ordinary and partial differential equations, which are not covered by APMA 0330 and are of great importance in practice. Here are the main topics to be covered (syllabus): Topics from matrix algebra. Systems of linear ordinary differenti...
- Computing InformationThe following links will lead you to applications of differential equations using particular software It should be pointed out from the very beginning that any software is only a tool. As a very important tool, it is more useful if its user has thought through the details of the task for which the tool is designed. Once you have learned the concepts behind the differential equations (which is the ...
- Linear Algebra with MathematicaThis website provides two things: One is comprised of equations and proofs which together constitute the bedrock of mathematics. The other is Wolfram software code which automates processing and reduces the tedium of solving many mathematical problems. The second, and the use of computers in general, must be viewed as a "black box" which may be specifically and completely understood only in terms ...