| Learning Outcomes | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |
|---|
| Define and analyze the geometric and topological properties of n-dimensional Euclidean spaces. | 3 | 3 | 3 | 2 | 3 | - | - | - | - | - | - |
| Explain real-valued multivariable functions defined on Euclidean spaces and interpret their graphs. | 3 | 3 | 3 | 2 | 3 | - | - | - | - | - | - |
| Use level curves and level surfaces to provide geometric interpretations of functions. | 3 | 3 | 3 | 2 | 3 | - | - | - | - | - | - |
| Define single-variable and multivariable vector-valued functions and analyze their graphical representations. | 3 | 3 | 3 | 2 | 3 | - | - | - | - | - | - |
| Explain the concept of limits for multivariable functions and compute directional and sequential limits. | 3 | 3 | 3 | 2 | 3 | - | - | - | - | - | - |
| Describe pointwise and global continuity of multivariable functions and apply continuity theorems | 3 | 3 | 3 | 2 | 3 | - | - | - | - | - | - |
| Analyze convergence of sequences in Euclidean spaces and explain the concept of sequential continuity. | 3 | 3 | 3 | 2 | 3 | - | - | - | - | - | - |
| Apply concepts of sequential compactness, uniform continuity, and the Extreme Value Theorem. | 3 | 3 | 3 | 2 | 3 | - | - | - | - | - | - |
| Distinguish between connected and path-connected subsets of Euclidean space and illustrate them with examples. | 3 | 3 | 3 | 2 | 3 | - | - | - | - | - | - |
| Define the concept of differentiation for multivariable functions and interpret derivative mappings. | 3 | 3 | 3 | 2 | 3 | - | - | - | - | - | - |
| Compute partial derivatives, construct the Jacobian Matrix, and apply the Chain Rule. | 3 | 3 | 3 | 2 | 3 | - | - | - | - | - | - |
| Compute the Gradient and directional derivatives; determine tangent lines and tangent planes. | 3 | 3 | 3 | 2 | 3 | - | - | - | - | - | - |
| Compute higher-order derivatives and apply the Clairaut\'s Theorem, Taylor\'s Theorem, Implicit Function Theorem, and Inverse Function Theorem. | 3 | 3 | 3 | 2 | 3 | - | - | - | - | - | - |
| Analyze local and global extrema of multivariable functions; use the Hessian Matrix and Lagrange Multipliers to solve optimization problems. | 3 | 3 | 3 | 2 | 3 | - | - | - | - | - | - |