Mathematical Modeling: A Chemical Engineer's PerspectiveMathematical modeling is the art and craft of building a system of equations that is both sufficiently complex to do justice to physical reality and sufficiently simple to give real insight into the situation. Mathematical Modeling: A Chemical Engineer's Perspective provides an elementary introduction to the craft by one of the century's most distinguished practitioners. Though the book is written from a chemical engineering viewpoint, the principles and pitfalls are common to all mathematical modeling of physical systems. Seventeen of the author's frequently cited papers are reprinted to illustrate applications to convective diffusion, formal chemical kinetics, heat and mass transfer, and the philosophy of modeling. An essay of acknowledgments, asides, and footnotes captures personal reflections on academic life and personalities.
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From inside the book
Results 1-5 of 42
... unstable. However, the broken line B = 0 can be reached in a finite time by a solution starting above A = 0 in the lower part of the phase plane and below A = 0 in the upper part. If the value at the singularity, B = 0, which is ...
... exists, there exists also an optimal adjoint vector p"(t) satisfying dp/dt = x: temperature FIGURE 18 Structure of the optimal control of a batch reactor. FIGURE 19 Phase-plane of a C* controlled about the unstable. OBSERVING CONDITIONS 7|
... unstable. The value of having a plane diagram on which one could impose one's geometrical imagination was proved in the subsequent problem that Amundson took up just at the time I went to Minnesota. This problem was to try to control ...
... 20 variation of the limit-cycle with increasing control. FIGURE 19 Phase-plane of a C* controlled about the unstable steady state (initially a saddle-point) by cooling proportional to the temperature. i t I 1.8 2.0 2.2. THE PHASE PLANE 77.
... UNSTABLE s.s. IIIb. ----'T. Md -L---------- .......STABLE LIMIT CYCLE S|- 5d *------ 5e •- - - - - UNSTABLE LIMIT CYCLEmi- > m; ... --> m or a EWAPORATION --- --0. "H: *>00 A || C F || 3 || A A C E J D G B |\ . *s, IIIC B I ...
Contents
MATTER | 105 |
MISCELLANEA | 417 |
BIBLIOGRAPHY | 455 |
INDEX OF GRADUATE STUDENTS AND COAUTHORS | 467 |
SUBJECT INDEX TO THE PAPERS IN THE BIBLIOGRAPHY | 469 |
INDEX | 473 |