MAS2104/3104 - Introduction to Vector Calculus

Graeme Sarson

This page contains (or will contain) the following material related to this course:

• Course information.
• Handouts.
• Exercises.
• Solutions to the exercises.
• Problems for the Problems Classes.
• Exams from previous years.

The relevant material will be added as the semester progresses.

Course Information

Here is the basic course Plan. An extract from the School Handbook gives a more detailed Syllabus, and a separate sheet give a more detailed breakdown of the course Structure (with links to one of the course books).

The schedule of Student Presentations (for Single Honours students taking MAS2213) is also available.

As I had to rush through the example calculation of a surface flux integral slightly (in the lecture on Wednesday, December 7th), a scan of the solution is also available.

Handouts

Handouts issued to date.

• Handout 1 (Tangent and length of a curve in parametric form; Intersection of curves).
• Handout 2 (Curves in three dimensions).
• Handout 3 (Two-parameter families of curves).
• Handout 4 (Gradient, divergence and curl in Cartesian coordinates).
• Handout 5 (The meaning of grad, div and curl).
• Handout 6 (Subscript notation).
• Handout 7 (Grad, div and curl in cylindrical and spherical coordinates).
• Handout 8 (Volume elements in cylindrical and spherical coordinates).
• Handout 9 (Change of variables in double and triple integrals).
• Handout 10 (Review of line integrals).
• Handout 11 (Verification of Gauss's Theorem).
• Handout 12 (Verification of Stokes' Theorem).
• Handout 13 (Relations between integral theorems).

Exercises

Exercise sheets issued to date.

• Exercises 1 (Curves in two dimensions).
• Exercises 2 (Curves in two and three dimensions, and families of curves).
• Exercises 3 (Surfaces and normal vectors, and the gradient).
• Exercises 4 (Gradient, divergence and curl).
• Exercises 5 (Volume and surface integrals, and nabla in polar coordinates).

Solutions

Solution sheets available to date.

• Solutions to Exercises 1.
• Solutions to Exercises 2.
• Solutions to Exercises 3.
• Solutions to Exercises 4.
• Solutions to Exercises 5.

Problems

Problems sheets issued to date.

• Problems 1 (Vectors, and curves in two dimensions).
• Problems 2 (Curves in two and three dimensions, and families of curves).
• Problems 3 (Surfaces and normal vectors, and the gradient).
• Problems 4 (Gradient, divergence and curl).
• Problems 5 (Volume and surface integrals, and nabla in polar coordinates).
• Problems 6 (Gauss's Theorem, Stokes' Theorem, and more line, double and volume integrals).

Exams

Some exam papers from previous years.

• 2010-11 papers for MAS2104 and MAS3104.
• 2009-10 papers for MAS2104 and MAS3104.
• 2008-09 papers for MAS2104 and MAS3104.

I worked through the 2010-11 paper for MAS3104 in the revision lectures. For the questions where I skipped parts of the solutions, scans of the solutions are available here.

Contact Details

Last updated: January 11, 2012.