Designed for an undergraduate course on mathematical modeling or differential equations, this text provides students with an understanding of the practical and theoretical aspects of mathematical models involving ODEs and PDEs. It develops students' intuition by building the theory from the ground up and illustrates the analysis of more than 20 distinct models through concrete applications in physics, engineering, finance, and many other areas. The book also uses MATLAB® GUIs that enable students to discover patterns and make conjectures.
Designed for an undergraduate course on mathematical modeling or differential equations, this text provides students with an understanding of the practical and theoretical aspects of mathematical models involving ODEs and PDEs. It develops students' intuition by building the theory from the ground up and illustrates the analysis of more than 20 distinct models through concrete applications in physics, engineering, finance, and many other areas. The book also uses MATLAB® GUIs that enable students to discover patterns and make conjectures.
ORDINARY DIFFERENTIAL EQUATIONS: Welcome! A Basic Analysis Toolbox. A First Wave of Mathematical Models. Finite Dimensional Theory Ground Zero: The Homogenous Case. Finite Dimensional Theory Next Step: The Non Homogenous Case. A Second Wave of Mathematical Models Now, with Nonlinear Interactions. Finite Dimensional Theory Last Step: The Semi Linear Case. ABSTRACT ORDINARY DIFFERENTIAL EQUATIONS: Getting the Lay of a New Land. Three New Mathematical Models. Formulating a Theory for (A HCP). The Next Wave of Mathematical Models With Forcing. Remaining Mathematical Models. Formulating a Theory for (A NonCP). A Final Wave of Models Accounting for Semilinear Effects. Appendix. Bibliography. Index.
ORDINARY DIFFERENTIAL EQUATIONS: Welcome! A Basic Analysis Toolbox. A First Wave of Mathematical Models. Finite Dimensional Theory Ground Zero: The Homogenous Case. Finite Dimensional Theory Next Step: The Non Homogenous Case. A Second Wave of Mathematical Models Now, with Nonlinear Interactions. Finite Dimensional Theory Last Step: The Semi Linear Case. ABSTRACT ORDINARY DIFFERENTIAL EQUATIONS: Getting the Lay of a New Land. Three New Mathematical Models. Formulating a Theory for (A HCP). The Next Wave of Mathematical Models With Forcing. Remaining Mathematical Models. Formulating a Theory for (A NonCP). A Final Wave of Models Accounting for Semilinear Effects. Appendix. Bibliography. Index.
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