ESTR1006 Multivariable Calculus for Engineers

What is this course about?

This course is an introduction to multivariable calculus for engineering students. The course covers the following topics:

1. Matrix Operations and Vector Spaces

• inverse of a matrix
• Gauss-Jordan elimination
• LU decomposition
• vector spaces
• inner product spaces
• linear transformations

2. Vectors and Vector Products

• vectors in 2D/3D space
• inner product
• vector product

3. Vector Fields and Curves

• vector field
• curves
• arc length
• torsion
• chain rule

4. Vector Calculus

• gradient
• directional derivative
• potential function
• divergence of a vector field
• Laplacian
• curl of a vector field

5. Integration

• line integrals
• path independence of line integrals
• double integrals
• Green's theorem in the plane
• Stokes' theorem

6. Surface Geometry and Integrals

• representation of surfaces
• cylinder/sphere/cone
• tangent plane and surface normal
• surface integrals
• orientation of surfaces

7. Triple Integrals

• divergence theorem of Gauss

What is multivariable calculus?

Multivariable calculus is the extension of calculus in one variable to calculus in more than one variable. It is a branch of calculus that studies functions of more than one variable. It is used in many fields of science and engineering, especially in physics and engineering. Multivariable calculus is also known as vector calculus, as it deals with vectors and vector functions.