MATH: P-6 Calculus of Several Variables(e-PGP) (English)

   Wednesday, January 11, 2023   

Starting a new Lecture Notes Series on MATH: P-6 Calculus of Several Variables(e-PGP)

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MATH: P-6 Calculus of Several Variables(e-PGP)
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Lecture Description of this above Topic:

Lecture 1: On Equality of Mixed Partial Derivatives

Lecture 2: Taylor Series for Scalar Fields

Lecture 3: Limits and Continuity of Vector Fields

Lecture 4: Vector Derivative of a Vector Field

Lecture 5: Discussions on Differentiability of a Vector Field

Lecture 6: Jacobian Matrix of a Differentiable Vector Field

Lecture 7: Mean Value Theorem for a Differentiable Vector Field

Lecture 8: Introduction to Integration

Lecture 9: On Curves and Their Lengths

Lecture 10: On Line Integrals

Lecture 11: Fundamental Theorems of Calculus on Line Integrals

Lecture 12: Necessary and Sufficient Conditions for a Vector Field to be Gradient

Lecture 13: Double Integrals I

Lecture 14: Double Integrals II

Lecture 15: Green's Theorem

Lecture 16: Change of Variables in Double Integral

Lecture 17: Multiple Integrals

Lecture 18: Introduction to Surfaces

Lecture 19: Surface Integrals

Lecture 20: Stokes' Theorem and Divergence Theorem

Lecture 21: Inverse Function Theorem and Implicit Function Theorem