APPLIED MATHS UNIT 3+4 | IMPORTANT TOPICS + PYQs | SURESHOT TOPICS | IPUNEX | NEXERA | GGSIPU

for notes:
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[03:00] - Introduction to Unit 3: Overview of important topics.
[04:44] - Rank of a Matrix: Definition and concept of linearly independent rows.
[06:34] - Determining Rank: Understanding the range of rank based on matrix dimensions.
[07:39] - Method to Find Rank: Using the determinant method and step-by-step calculation.
[08:00] - Determinant Calculation: A quick refresher on how to calculate the determinant of a matrix.
[15:00] (approx) - Linear Equations: Solving systems of linear equations (Consistent vs. Inconsistent).
[30:00] (approx) - Eigenvalues and Eigenvectors: Concept and calculation of characteristic equations.
[45:00] (approx) - Cayley-Hamilton Theorem: Statement, verification, and using it to find the inverse of a matrix.
Unit 4: Vector Calculus
[01:10:00] (approx) - Introduction to Unit 4: Overview of vector differentiation and integration.
[01:20:00] (approx) - Gradient, Divergence, and Curl: Physical interpretation and mathematical operations.
[01:35:00] (approx) - Directional Derivatives: Finding the rate of change of a scalar field in a specific direction.
[01:45:00] (approx) - Vector Integral Theorems: Brief on Gauss Divergence Theorem, Green's Theorem, and Stokes' Theorem.
[01:50:21] - Important Problems: Discussion on Curvature and Torsion of the Helix (frequently asked).