Page Of 3 Zoom Programming With MATLAB In This Exercise

Pageof 3zoomprogramming With Matlabin This Exercise You Are Provided

Pageof 3zoomprogramming With Matlabin This Exercise You Are Provided

In this exercise, you are provided with an example problem and a practice problem involving programming with MATLAB. You are expected to run the example problem in MATLAB to understand how it works then complete the practice problem. The assignment includes evaluating mathematical expressions, writing simple MATLAB scripts for calculating geometric areas and volumes, plotting functions, prompting user input, and applying the Bisection method to find roots of equations.

The exercise emphasizes understanding the significance of variable assignment, mathematical operations, plotting functions, user interaction, and numerical methods within MATLAB. You should demonstrate competence in using MATLAB commands such as arithmetic operators, plotting functions such as sin() and abs(), string concatenation, and implementing algorithms like the Bisection method.

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Programming with MATLAB is a fundamental skill for engineers and scientists, especially when performing scientific computations, data visualization, and algorithm development. This exercise aims to familiarize students with MATLAB's core functionalities through practical applications such as evaluating expressions, calculating geometric quantities, plotting functions, and implementing numerical methods like the Bisection technique.

Understanding variable assignment in MATLAB is essential because it enables effective data manipulation and computation. For example, the statement z = 10 creates a variable named z and assigns it the value of 10. This process is fundamental as it stores data in MATLAB's workspace, allowing for subsequent calculations and operations. Variables act as containers that facilitate computational workflows, and understanding how to assign and manipulate them is critical.

Evaluating mathematical expressions is core to MATLAB's functionality. In the example problem, the expression (x^2*y^3)/(x-y)^2 was evaluated with specific values for x=3 and y=4. MATLAB efficiently computes results using arithmetic operators and standard functions. The result, 576, exemplifies MATLAB’s capability to handle complex algebraic calculations seamlessly. The practice problem asked to evaluate an expression with x=2 and y=-1, which can be achieved similarly, reinforcing the importance of understanding precedence and syntax in MATLAB expressions.

Calculating geometrical quantities such as the area of a circle or the volume of a cylinder involves applying mathematical formulas within MATLAB. For instance, the area of a circle is computed as πr^2. The MATLAB script captures this via the statement area = pi radius^2, then creates a message string that concatenates explanatory text with the numerical result using num2str(). Displaying the message with disp() enhances user understanding. The practice problem extends this concept by calculating the volume of a cylinder, which involves computing the base area and multiplying it by the height, illustrating MATLAB's flexibility in handling multiple related calculations within scripts.

Plotting functions is an important MATLAB feature used widely in data analysis and visualization. The example demonstrates plotting sin(x) over the interval [0, 6], with x ranging from 0 to 6 in increments of 0.1. The plot() function visualizes the sine wave, allowing for graphical interpretation of mathematical functions. For practice, students are asked to graph the absolute value of sin(t) over [-2π, 2π] with an increment of π/10. This involves using abs() for absolute value and setting the range appropriately, demonstrating how MATLAB’s plotting tools facilitate understanding complex functions visually.

User input functions in MATLAB are used to gather data interactively. The example program prompts the user for their name using input() with a string option ('s'), and then constructs a response string concatenating fixed text with the user input. The practice problem involves creating a mailing address format by prompting for the user’s name and address, then formatting and displaying them similarly. This illustrates how MATLAB can handle string inputs and produce formatted output suitable for various applications such as mailing, data entry, or personalized messages.

Applying numerical methods like the Bisection method to find roots of functions demonstrates MATLAB’s capabilities in simulation and problem-solving. For the function f(x) = x^3 - 9, the goal is to find the root near a specific interval that contains the solution. Selecting an initial interval, such as [1, 3], which brackets a root, and then iteratively reducing the interval until a desired tolerance is achieved, exemplifies MATLAB's utility in numerical analysis. Implementing this method manually in MATLAB involves repetitive calculations, convergence checks, and interval updates, providing practical experience with algorithms used widely in scientific computing.

This collection of MATLAB exercises encapsulates essential skills for computational tasks: variable management, expression evaluation, plotting, user interaction, and root-finding algorithms. Mastery of these concepts enables students to effectively model, analyze, and visualize mathematical problems, forming a foundation for more advanced computations in engineering and science fields.

References

  • Matlab Documentation. (2023). MATLAB Arithmetic Operations. MathWorks. https://www.mathworks.com/help/matlab/arithmetic-operations.html
  • Matlab Documentation. (2023). Plotting Data. MathWorks. https://www.mathworks.com/help/matlab/creating_plots.html
  • Matlab Documentation. (2023). String Concatenation and Display. MathWorks. https://www.mathworks.com/help/matlab/matlab_prog/creating-and-using-strings.html
  • Kiusalaas, J. (2013). Numerical Methods in Engineering with MATLAB. Cambridge University Press.
  • Matlab Central. (2023). Implementing the Bisection Method. MathWorks Community Forums. https://www.mathworks.com/matlabcentral/fileexchange/
  • Chapra, S. C., & Canale, R. P. (2010). Numerical Methods for Engineers. McGraw-Hill Education.
  • Press, W. H., Teukolsky, S. A., Vetterling, W. T., & Flannery, B. P. (2007). Numerical Recipes: The Art of Scientific Computing. Cambridge University Press.
  • Hughes-Hallet, D., et al. (2011). Calculus: Single Variable. OpenStax. https://openstax.org/books/calculus-volume-1
  • Kaiser, P. S., & Staehler, T. (2011). MATLAB for Beginners: A Gentle Approach. Springer.
  • MathWorks. (2023). Numerical Methods Overview. https://www.mathworks.com/solutions/numerical-analysis.html

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