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This text demonstrates the process of comprehensive applied mathematical modeling through the introduction of various case studies. The case studies are arranged in increasing order of complexity based on the mathematical methods required to analyze the models, providing a self-contained presentation. To reinforce and supplement the material introduced, original problem sets are assigned involving case studies closely related to the ones presented. With this style, the text's perspective, scope, and completeness of the subject matter are considered unique. Having grown out of four self-contained courses taught by the author, this text will be of use for a two-semester sequence for advanced undergraduate and beginning graduate students, requiring rudimentary knowledge of advances calculus and differential equations, along with a basic understanding of some simple physical and biological scientific principles.