Vector Calculus Lecture Sheet 1 MATHEMATICS

Description

Vector calculus, also known as multivariable calculus, is the study of vector fields and functions involving multiple variables. It extends the concepts of single-variable calculus to higher dimensions and includes operations like gradient (which measures the rate and direction of change), divergence (which measures how much a field spreads out), and curl (which measures rotation in a field). Vector calculus plays a critical role in describing and analyzing physical systems in electromagnetism, fluid flow, and gravitational fields. Key theorems, such as Green’s theorem, Stokes’ theorem, and the Divergence theorem, provide powerful tools for transforming and solving complex integrals in vector fields.

Topics Covered

• Vectors and Vector Fields

• Gradient, Divergence, and Curl

• Line Integrals and Surface Integrals

• Green’s Theorem

• Stokes’ Theorem

• Divergence Theorem

• Applications in Physics and Engineering

🔹 Prerequisites

• Calculus (single-variable)

• Basic linear algebra concepts

🔹 Applications

• Electromagnetism

• Fluid Mechanics

• Thermodynamics

• Computer Graphics

• Engineering Design