The Complete Guide to Vector & Multivariable Calculus
Vector Calculus (Calculus 3) Made Clear: Solve Complex Problems with Visual Aids & Step-by-Step Computations.
The Complete Guide to Vector & Multivariable Calculus free download
Vector Calculus (Calculus 3) Made Clear: Solve Complex Problems with Visual Aids & Step-by-Step Computations.
Multivariable Calculus or Vector Calculus (also some times called as Calculus 3) 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 Multivariable Calculus or Vector Calculus or Calculus-3 by most of the (local) institutes and universities, the following topics are included in this course Multivariable Calculus or Vector Calculus or Calculus-3:
Line Integrals (of both scalar and vector fields)
Work done as a Line integral
Path Independent Line integrals
Conservative Fields
Simply 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 Surfaces
Surface 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 in this course Multivariable Calculus or Vector Calculus or Calculus-3 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 Multivariable Calculus or Vector Calculus or Calculus-3.
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.
#Multivariable Calculus
#Vector Calculus
#Calculus-3
