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Week - 1 |
Euclidean Spaces: Geometric and topological properties of n-dimensional Euclidean spaces |
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Week - 2 |
Functions defined between Euclidean spaces: Multivariable real-valued functions, Level curves, Level surfaces, Graphs of functions |
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Week - 3 |
Functions defined between Euclidean spaces: Single-variable vector-valued functions, Curves and their graphs |
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Week - 4 |
Functions defined between Euclidean spaces: Multivariable vector-valued functions |
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Week - 5 |
Limit: Limits of multivariable functions, Directional limits, Iterated limits |
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Week - 6 |
Continuity: Pointwise and global continuity of multivariable functions, Continuity theorems |
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Week - 7 |
Sequences in Euclidean spaces: Sequences in Euclidean spaces and convergence, Sequential continuity |
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Week - 8 |
Sequences in Euclidean spaces: Sequential compactness, Uniform continuity, Extreme Value Theorem |
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Week - 9 |
Connectedness: Connected and path-connected subsets of Euclidean space |
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Week - 10 |
The Concept of Derivative in Multivariable Functions: Derivative as linear transformation and its properties. |
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Week - 11 |
The Concept of Derivative in Multivariable Functions: Partial derivatives, Jacobian Matrix, Chain Rule |
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Week - 12 |
The Concept of Derivative in Multivariable Functions: Gradient vector and Directional Derivative, Tangent lines, Tangent Planes |
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Week - 13 |
The Concept of Derivative in Multivariable Functions: Gradient vector and Directional Derivative, Tangent lines, Tangent Planes |
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Week - 14 |
Extrema of multivariable functions, Hessian Matrix, Method of Lagrange Multipliers |