IIT M DIPLOMA AN2 EXAM QDD2 25 Feb 2024 - 25 Feb 2024

Concepts this paper tests

Auto-generated summary from the source site. Handy as a checklist; the lessons above explain each idea from scratch.

Summary of Core Topics, Concepts, Principles, and Equations

1. Linear Algebra

• Matrix Operations: Inverse, multiplication, diagonalization.
• Vector Spaces: Row space, column space, span.
• Eigenvalues and Eigenvectors: Calculation and properties.
• Diagonalization: Finding matrix $P$ such that $P^{-1}AP$ is diagonal.

Equations:

• $A = \begin{pmatrix} a & b \\ c & d \end{pmatrix}$, $P^{-1}AP = D$ (diagonal matrix)
• Row space and column space: $\text{span}\{v_1, v_2, \ldots, v_n\}$

2. Calculus

• Linear Approximation: Approximating function values using derivatives.
• Multivariable Calculus: Partial derivatives, directional derivatives.
• Limits and Continuity: Evaluating limits and checking continuity.

Equations:

• Linear approximation: $f(x) \approx f(a) + f'(a)(x-a)$
• Directional derivative: $D_{\mathbf{u}} f(a, b) = \nabla f(a, b) \cdot \mathbf{u}$

3. Machine Learning

• Supervised Learning: Tasks like prediction, classification.
• Dimensionality Reduction: Techniques like PCA, encoders, and decoders.
• Least Squares Method: Finding the best fit line.

Equations:

• Least squares method: $y = mx + c$
• Reconstruction error: $R(f, g) = \frac{1}{n} \sum_{i=1}^{n} \| X_i - g(f(X_i)) \|^2$

4. Differential Equations and Functions

• Differentiability and Continuity: Checking differentiability and continuity of functions.
• Second Derivatives: Calculating and interpreting second derivatives.

Equations:

• Differentiability: $f'(x)$
• Continuity: $\lim_{x \to a} f(x) = f(a)$