| Learning Outcomes | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |
|---|
| Define multiple integrals and explain the concept of zero-measure sets. | 3 | 3 | 3 | 2 | 3 | - | - | - | - | - | - |
| Compute double and triple integrals and apply them to geometric and physical problems. | 3 | 3 | 3 | 2 | 3 | - | - | - | - | - | - |
| Explain the fundamental properties of multiple integrals and use the Fubini\'s Theorem to evaluate integrals iteratively. | 3 | 3 | 3 | 2 | 3 | - | - | - | - | - | - |
| Apply the change of variables technique and reformulate integrals using coordinate transformations. | 3 | 3 | 3 | 2 | 3 | - | - | - | - | - | - |
| Perform integral calculations in polar, cylindrical, and spherical coordinate systems. | 3 | 3 | 3 | 2 | 3 | - | - | - | - | - | - |
| Use multiple integrals to compute area and volume, and derive the volume of an n-dimensional sphere. | 3 | 3 | 3 | 2 | 3 | - | - | - | - | - | - |
| Analyze the convergence of improper multiple integrals. | 3 | 3 | 3 | 2 | 3 | - | - | - | - | - | - |
| Evaluate parametric integrals and explain the relationship between the Gamma Function and the Beta Function. | 3 | 3 | 3 | 2 | 3 | - | - | - | - | - | - |
| Interpret applications of multiple integrals in physics, engineering, and probability theory. | 3 | 3 | 3 | 2 | 3 | - | - | - | - | - | - |
| Define vector fields and analyze integral curves. | 3 | 3 | 3 | 2 | 3 | - | - | - | - | - | - |
| Compute gradient, divergence, and curl, and explain their physical meanings. | 3 | 3 | 3 | 2 | 3 | - | - | - | - | - | - |
| Evaluate line integrals over parametric curves and apply the fundamental theorem. | 3 | 3 | 3 | 2 | 3 | - | - | - | - | - | - |
| Compute line integrals of vector fields and apply Green\'s Theorem. | 3 | 3 | 3 | 2 | 3 | - | - | - | - | - | - |
| Define parametric surfaces, compute surface area, and evaluate surface integrals of scalar functions. | 3 | 3 | 3 | 2 | 3 | - | - | - | - | - | - |
| Explain oriented surfaces and compute surface integrals of vector fields. | 3 | 3 | 3 | 2 | 3 | - | - | - | - | - | - |
| Apply Stokes\' Theorem and the Divergence Theorem to relate different types of integrals. | 3 | 3 | 3 | 2 | 3 | - | - | - | - | - | - |
| Use the fundamental theorems of vector calculus to produce analytical solutions to multivariable problems. | 3 | 3 | 3 | 2 | 3 | - | - | - | - | - | - |