![]() ![]() For example, notice the difference between Mathematica's "Simplify" function expects an expression as a parameter, which it simplifies. Feel free to skip over examples if you don't have the necessary background. The material that we will be covering here requires varying levels of mathematical expertise. In this notebook we will explore this support in more depth. IntroductionĬhapter 6 only hints at the support for symbolic mathematics provided by Mathematica. ![]() In it we will explore the idea of symblic computing further. This notebook is designed to accompany Chapter 6 of Introduction to Scientific Programming: Computational Problem Solving Using Mathematica and C by Joseph L. You can look at theĪppended non-interactive HTML version of the notebook to learn what We can model the amount of salt in the tank using differential equations.Click below to download a Mathematica notebook. We will assume that the water in the tank is constantly stirred so that the mixture of salt and water is uniform in the tank. If the tank is also draining at a rate of 4 liters per minute, the water level in the tank will remain constant. Suppose that we have a large tank containing 4000 liters of water and that water containing 0.01 kg of salt per liter flows into the tank at a rate of 4 liters per minute. For example, we might wish to model how chemicals are mixed together in a refinery, how pollutants are mixed together in a pond or a lake, how ingredients are mixed together when brewing beer, or even how various greenhouse gases mix together across different layers of the atmosphere. These problems refer to situations where two are more substances are mixed together in a container or containers. There is a large class of problems in modeling known as mixing problems. ![]() Newton's law of cooling can be easily stated as a differential equation, The answer to our forensic question can be found by using Newton's law of cooling, which tells us that the rate of change of the temperature of a object is proportional to the difference between the temperature of the object and the temperature of the surrounding medium. The liquid will cool quite quickly during the first few minutes but will remain relatively warm for quite a long period. Think of how a hot cup of coffee or tea cools. We should not expect the body to cool at a constant rate either. Eventually, the temperature of the body will match the temperature of the environment. If the surrounding temperature is cooler, then the body will cool down after death. How does a forensic scientist or a medicalĮxaminer determine the time of death? Human beings have a temperature of 98.6 ○F orģ6.6 ○C. Important question on many popular movies and television programs. The time of death of a murder victim is an Separable equations arise in a wide range of application problems. Return to the main page for the course APMA0340 Return to the main page for the course APMA0330 Return to Mathematica tutorial for the second course APMA0340 Return to computing page for the second course APMA0340 Return to computing page for the first course APMA0330
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