Calculus 3 Made Easy (Multivariable or Vector Calculus)

Multivariable Calculus, also known as Vector Calculus or Calculus 3, is a fundamental subject for advanced studies in applied mathematics, physics, and engineering. At the heart of this subject lie the integral theorems, which have broad applications across these disciplines. This course is designed based on the standard outlines followed by many universities and institutes.

It covers all major topics commonly included in Multivariable Calculus / Vector Calculus / Calculus 3 courses, such as:Topics Covered:Line Integrals (of scalar and vector fields)Work done as a line integralPath Independence and Conservative FieldsSimply Connected vs Multiply Connected Domains (illustrated with animations)Theorems on Path Independence and Conservativity (Five key theorems with proofs)Applications of Line Integrals:Area of a fence with curved baseMass, center of mass, and moment of inertia of a wireDouble Integrals with applications:Mass, center of mass, and moment of inertia of a laminaParametric Representation of SurfacesSurface Area (with alternate formulas)Tangent Plane and Normal to a SurfaceSurface Integrals (of vector and scalar fields)Integral Theorems:Green's TheoremStokes's TheoremGauss's (Divergence) TheoremApplications of Integral TheoremsDerivations of major equations:Heat EquationWave EquationLaplace's EquationContinuity EquationWhat's Inside: Over 70 worked examples covering major concepts Most topics explained using PowerPoint slides and animations Select problems solved on digital whiteboard (OneNote + tablet) Downloadable PDFs of lectures included Practice material with helpful hints More examples may be added based on student requestsThis course emphasizes clarity and time-saving. Instead of lengthy blackboard-style lectures, most content is taught through structured slides, allowing for better focus and efficient learning. Note: Despite best efforts, small mistakes may occur.

I genuinely appreciate students who help identify them (check video descriptions for any corrections). Your feedback and suggestions are always welcome - we grow through continuous improvement. /////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////Multivariable Calculus Vector Calculus Calculus 3 Advanced Mathematics Engineering Math Mathematics Course.