What you'll learn

Line integrals with applications, Path independence, important theorems
Double integrals, Triple Integrals, Surface integrals
Green's Theorem, Stokes Theorem, Divergence Theorem with Proofs and Applications
70+ solved examples, 50+ homework assessments, lecture pdfs and eBooks
Derivation of Basic PDEs, including The Continuity Equation, Heat Equation, Wave Equation, Laplace Equation, etc.

Requirements

Precalculus, basic knowledge of computing derivatives and integrals is enough.
A few lectures require the concept of continuity of a function. Otherwise the course is mostly self contained
A little bit of MATLAB knowledge will be needed in a few lectures.

Description

Vector Calculus is one of the most important subject for advanced studies in applied mathematics, physics or engineering. The core of the subject contains the "Integral Theorems" as they have a wide range of applications to these disciplines. Keeping in view the course outlines of most of the (local) institutes and universities, the following topics are included in this course:Line Integrals (of both scalar and vector fields) Work done as a Line integralPath Independent Line integralsConservative FieldsSimply Connected and Multiply Connected Domains (with Animations for illustration)Theorems (with proofs) on Path independence of Line Integrals and Conservative Fields (five theorems)Applications of Line integrals (Calculating the area of fence whose base is a curve C in space, calculating the Mass, the Center of Mass, and Moment of inertia of a wire)The Double Integrals with applications (calculating mass, c.o.m, moment of inertia of a lamina)Parametric Representation of SurfacesSurface area (with alternative formulas)Tangent Plane and Normal to a Surface Surface Integrals (of vector and scalar fields)Integral Theorems (Green's Theorem, Stokes's Theorem, Gauss's (Divergence) Theorem)Applications of Integral Theorems Derivation of Heat equation, Wave Equation, Laplace Equation, Continuity Equation etc. More than 70 worked examples are included to illustrate these topics. Most of the topics are illustrated with Slides and Animations (where needed), and a few examples are worked on digital white board (One Note) using Tablet.PDFs of lectures are also attached with the video lectures, Student Practice Material is also included with necessary hints. Most of the lectures are in the form of slides so that the learners time is marginally saved as compared to the white board lectures. More examples will be included (some examples can be included on demand of the learners).Hopes the students may learn and enjoy from this course.There may be mistakes and I will be extremely thankful to those who point out mistakes in any lecture (Check out the

Description

of each video for corrections). Suggestions are always welcomed because we always need improvements.

Who this course is for

This course is for Undergraduate students of Mathematics, Physics, Computer, Engineering etc.
Graduate Students and Instructors may also profit from this course
Homepage:

https://www.udemy.com/course/vector-calculus-with-applications/

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