Only $299/month A mathematical representation of an object or event is a model Any factor in an experiment that can change or change the outcome is referred to as a variable

Explanation: A scientific law is the statement which includes the facts about the cause of natural phenomena, events and processes occurring all over the worl

A model is a simplified representation of a system at some particular point in time or space intended to promote understanding of the real system As an abstraction of a system, it offers insight about one or more of the system’s aspects, such as its function, structure, properties, performance, behavior, or cos

model anything that provides a partial representation of something else inductive reasoning

By looking and “reading” illustrations, we can make hypotheses about living conditions of the poor among many other factors of underclass life Art is a very important form of representation, as you can see, and makes up for a great deal of the knowledge we have about history

n the derivative of a function of two or more variables with respect to one of the variables, the other or others being considered constant

Linear equations are an important tool in science and many everyday applications They allow scientist to describe relationships between two variables in the physical world, make predictions, calculate rates, and make conversions, among other things Graphing linear equations helps make trends visible

Almost any situation where there is an unknown quantity can be represented by a linear equation, like figuring out income over time, calculating mileage rates, or predicting profit Many people use linear equations every day, even if they do the calculations in their head without drawing a line grap

Scientists use mathematical models to create amazing, as well as useful images Scientists use the models to relate the amount of energy reflected from objects to the objects’ physical condition

Mathematical and computational models are increasingly used to help interpret biomedical data produced by high-throughput genomics and proteomics projects The application of advanced computer models enabling the simulation of complex biological processes generates hypotheses and suggests experiment

Example: An ice cream company keeps track of how many ice creams get sold on different days By comparing this to the weather on each day they can make a mathematical model of sales versus weather They can then predict future sales based on the weather forecast, and decide how many ice creams they need to make

1. Step 1: Specify the Problem •
2. Step 2: Set up a metaphor •
3. Step 2: Set up a metaphor •
4. Step 3: Formulate Mathematical Model
5. Step 4: Solve Mathematical Model • Analytically
6. Step 5: Interprete Solution
7. Step 6: Compare with Reality • Validation of model
8. Step 7: Use Model to Explain, Predict, Decide, Design • Determine:

A mathematical model is a description of a system using mathematical concepts and language The process of developing a mathematical model is termed mathematical modeling A model may help to explain a system and to study the effects of different components, and to make predictions about behavior

Advantages

• They are quick and easy to produce
• They can simplify a more complex situation
• They can help us improve our understanding of the real world as certain variables can readily be changed
• They enable predictions to be made
• They can help provide control – as in aircraft scheduling

Mathematical models can help students understand and explore the meaning of equations or functional relationships After developing a conceptual model of a physical system it is natural to develop a mathematical model that will allow one to estimate the quantitative behavior of the syste

Disadvantages of modelling and simulation Mistakes may be made in the programming or rules of the simulation or model The cost of a simulation model can be high The cost of running several different simulations may be high Time may be needed to make sense of the results

Key Takeaways

• A function can be represented verbally For example, the circumference of a square is four times one of its sides
• A function can be represented algebraically For example, 3x+6 3 x + 6
• A function can be represented numerically
• A function can be represented graphically

Mathematical techniques can explain how the world works and make it better Mathematical modelling is capable of saving lives, assisting in policy and decision-making, and optimising economic growth It can also be exploited to help understand the Universe and the conditions needed to sustain lif

Abstract: Mathematical modelling is commonly regarded as the art of applying mathematics to a real world problem with a view to better understand the problem As such, mathematical modelling is obviously related to problem solving

ie; the conversion of a physical situation into mathematics using suitable conditions  Mathematical modeling is an activity in which we make model to describe the behavior of various phenomenal activities of our interest in many ways using words, drawings or sketches, computer programs, mathematical formulae etc… 3

The control systems can be represented with a set of mathematical equations known as mathematical model These models are useful for analysis and design of control systems Analysis of control system means finding the output when we know the input and mathematical model

Definition of State-Space Models State variables x(t) can be reconstructed from the measured input-output data, but are not themselves measured during an experiment The state-space model structure is a good choice for quick estimation because it requires you to specify only one input, the model order, n

1 Which among the following is a unique model of a system? Explanation: Transfer Function is defined as the ratio of the Laplace output to the Laplace input with the zero initial conditions and is a unique model of the system

In engineering, a transfer function (also known as system function or network function) of an electronic or control system component is a mathematical function which theoretically models the device’s output for each possible input