Multivariable Calculus (2022)

[LeeAndro]

Published 06/2022MP4 | Video: h264, 1280x720 | Audio: AAC, 44.1 KHz, 2 ChGenre: eLearning | Language: English + srt | Duration: 32 lectures (9h 49m) | Size: 2 GB

Calculus in 3-space
Partial Differentiation
Multiple Integration
Vector Calculus

Single Variable Calculus

This is a complete course in Multivariable calculus.​

Multivariable calculus is an extension of single variable calculus to calculus with functions of two or more variables. It is expected that anyone taking this course has already knows the basics from single variable calculus: limits and continuity, differentiation and integration.

In this course you will learn how to perform calculus on functions of two or more variables, as well as vector-valued functions. In particular, the topics covered include the basics of three dimensional space and vectors, vector-valued functions including the calculus of vector-valued functions (limits, differentiation, and integration), differentiation of functions of two or more variables, integration of functions of two or more variables, and vector calculus.

Single variable Calculus is a prerequisite for this course.

Here is a complete list of the topics that will be covered

Three-dimensional Space and Vectors

Rectangular Coordinates in 3-space

Vectors

Dot Product

Cross Product

Equations of Lines

Equations of Planes

Quadric Surfaces

Vector-valued Functions

Arc Length and the TNB-Frame

Curvature

Functions of Multiple Variables and Partial Differentiation

Functions of Two or More Variables

Limits and Continuity

Partial Derivatives

Differentiability

Chain Rule

Directional Derivatives

Maxima and Minima of Functions of Two Variables

Multiple Integrals

Double Integrals

Double Integrals over Nonrectangular Regions

Double Integrals over Polar Regions

Triple Integrals

Cylindrical and Spherical Coordinates

Triple Integrals in Cylindrical and Spherical Coordinates

Vector Calculus

Vector Fields

Line Integrals

Independence of Path

Green's Theorem

Parametric Surfaces

Surface Integrals

Orientable Surfaces and Flux

Stoke's Theorem

Divergence Theorem

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