A First Course in Mathematical Modeling
Cengage Learning, 2008. júl. 3. - 640 oldal
Offering a solid introduction to the entire modeling process, A FIRST COURSE IN MATHEMATICAL MODELING, 4th Edition delivers an excellent balance of theory and practice, giving students hands-on experience developing and sharpening their skills in the modeling process. Throughout the book, students practice key facets of modeling, including creative and empirical model construction, model analysis, and model research. The authors apply a proven six-step problem-solving process to enhance students' problem-solving capabilities -- whatever their level. Rather than simply emphasizing the calculation step, the authors first ensure that students learn how to identify problems, construct or select models, and figure out what data needs to be collected. By involving students in the mathematical process as early as possible -- beginning with short projects -- the book facilitates their progressive development and confidence in mathematics and modeling.
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The Modeling Process Proportionality and Geometric Similarity
Discrete Probabilistic Modeling
Optimization of Discrete Models
Modeling Using Graph Theory
Modeling with a Differential Equation
Modeling with Systems of Differential Equations
Optimization of Continuous Models
Problems from the Mathematics Contest in Modeling 19852008
An Elevator Simulation Algorithm
The Revised Simplex Method
Brief Review of Integration Techniques
Answers to Selected Problems
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½ Figure absolute deviations algorithm amount approximate ASSO ASST assume assumptions average baleen whales behavior Calculate coefﬁcients consider constant constraint construct cost Country criterion cubic spline data points deﬁne density dependent variable depicted in Figure derivative determine difference equations differential equation dimensional analysis dimensionless products discussion divided difference dynamical system edge elevator equilibrium value estimate Euler’s example extreme point factors ﬁnd ﬁnding ﬁrst ﬁsh ﬁt ﬂoor ﬂow ﬂuid geometrically similar given Golden Section Search graph graphical increases initial integration intersection point interval krill least-squares length Let’s linear program mathematical model maximize maximum method minimize missiles objective function obtain optimal solution phase plane plot polynomial predict problem proﬁt proportionality random numbers represents rest point satisﬁed Section ships simulation slope solution curve solve speciﬁc Step submodel Suppose Table trajectory UMAP velocity vertex vertices weight Y force zero