Evaluate The Following Scilab Expression

Evaluate The Following Scilab Expr

Engr 112 homework assignment requiring evaluation of various expressions without using the software directly, focusing on understanding operator precedence, mathematical functions, vector operations, temperature conversions, and plotting graphs. The assignment includes calculations by hand and verification with Scilab, involving both pure arithmetic and vectorized operations, as well as plotting exponential functions.

Paper For Above instruction

The assignment tasks students with evaluating a series of mathematical expressions manually to emphasize an understanding of operator precedence and mathematical hierarchy, then verifying their results with Scilab to reinforce computational validation. Additionally, students are required to perform operations involving mathematical functions, scientific notation, vector manipulation, temperature conversions, and graphical plotting, integrating theoretical concepts with computational practice.

Evaluation of Mathematical Expressions

The first set of expressions centers on the evaluation of basic arithmetic expressions respecting operator precedence, where multiplication and division take precedence over addition and subtraction, and parentheses modify order of operations. For example, the expression 2 / 2 3 involves division and multiplication, which share the same precedence and are evaluated from left to right: (2 / 2) 3 = 1 * 3 = 3. Similarly, 2 / 3 ^ 2 involves exponentiation with higher precedence: 3 ^ 2 = 9, then 2 / 9 ≈ 0.2222. Expression (2 / 3) ^ 2 modifies division with parentheses, leading to (2 / 3) ≈ 0.6667, then squared: (0.6667)^2 ≈ 0.4444.

Further expressions, such as 2 + 3 4 – 4, evaluate multiplication first: 3 4 = 12, then addition and subtraction from left to right: 2 + 12 – 4 = 10. The expression 2 ^ 2 3 / 4 + 3 involves exponentiation, multiplication, division, and addition. Evaluate exponent first: 2 ^ 2 = 4. Then, multiply: 4 3 = 12. Divide: 12 / 4 = 3. Finally, add 3: 3 + 3 = 6. For 2 ^ (2 3) / (4 + 3), evaluate parentheses: 2 3 = 6 and 4 + 3 = 7. Then, compute exponential: 2 ^ 6 = 64. Divide: 64 / 7 ≈ 9.1429. The remaining expressions follow similar logical steps based on operator precedence and parentheses.

Mathematical Functions and Scientific Notation

Next, students are instructed to evaluate functions such as square roots, powers, and scientific notation expressions without computational aid initially, then verify with Scilab. For instance, the square root of 2 is approximately 1.4142. The expression 3 + 4 / (5 + 6) computes the denominator first: 5 + 6 = 11. Then, division: 4 / 11 ≈ 0.3636. Sum with 3 yields approximately 3.3636. Calculations involving scientific notation, such as (0. + 5.678 x 10^-3) x 0.4567 x 10^-4, require careful handling of exponents, resulting in very small values.

Vector Operations and Hand Computations

Given empty vectors 'a' and 'b', the student must evaluate a set of vector expressions such as c = a – b, which results in an empty vector, and more complex operations like c = 2 * a + a .^ b. These require understanding component-wise operations, scalar-vector products, and the implications of vector size and initialization. Calculations by hand can be verified with Scilab to ensure the correct application of vectorized operations, element-wise operators, and matrix calculations.

Temperature Conversion Between Celsius and Fahrenheit

The temperature conversion task involves defining arrays in Scilab for Fahrenheit and Celsius, then applying the conversion formula F = 9 / 5 C + 32. For example, converting 37°C results in F = 9 / 5 37 + 32 = 66.6 + 32 = 98.6°F. This demonstrates array-based computation and functional application commonly used in scientific data processing.

Graphical Representation Using Semilogy

The assignment concludes with plotting several functions over the interval 0 to 4 using semilogy, which plots the logarithm of the y-values. Functions such as x^2, x^3, x^4, and e^{x^2} are used to visualize growth and exponential behavior. Proper graphing techniques include setting appropriate axes, labels, and legends for clarity and interpretability, illustrating the functions' behavior over the specified domain efficiently with logarithmic scales.

Conclusion

This assignment blends manual computation and software validation to deepen understanding of operator precedence, mathematical functions, vector operations, temperature conversion, and graphical plotting. Mastering these fundamental concepts enhances the ability to analyze and interpret mathematical models and datasets in engineering and scientific contexts, preparing students for more complex analytical tasks.

References

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