The 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 differential equations. Nonlinear ordinary differential equations. Qualitative theory of ordinary differential...

The 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 equations. Initial value problems. Boundary value problems. Finite difference schemes. Adomian decomp...

The 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 expansions. Integral transformations. Heat equations. Wave equations. Elliptic equations. Elements of ...

The 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 differential equations. Nonlinear ordinary differential equations. Qualitative theory of ordinary differential...

The 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 topic of the course) and know how to set up a specific problem, software will be of great help in un...

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 fo...

This 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 of the equations and proofs contained therein. Permission is granted to copy, distribute and/or modi...

The cybernetic revolution that occured on the eve of twenty-one century effected our life in all demeanors. The collection, organization, transformation, and interpretation of information are the cornerstones of science, inductry, business, and goverment. Each of these aspects of information management uses mathematics as a tool. Linear algebra has undergone a real metamorphosis during this century, partly due to the birth and development of computers. It is so active that entire periodical maga...

The cybernetic revolution that occurred on the eve of the twenty–first century affected our life in all demeanors. The collection, organization, transformation, and interpretation of information are the cornerstones of science, industry, business, and government. Each of these aspects of information management uses mathematics as a tool. Linear algebra has undergone a real metamorphosis during this century, partly due to the birth and development of computers. It is so active that entire p...

The cybernetic revolution that began on the eve of twenty-first century effected our life in all dimensions. The collection, organization, transformation, and interpretation of information are cornerstones of science, industry, business, and government. Each aspect of information management uses mathematics as a tool. Applied Mathematics (APMA for short) has undergone a real metamorphosis during this century, partly due to the birth and development of computers. It is so active that entire perio...