Isaac Vikram Chenchiah University of Bristol

Main Page Calculus 2 & Multivariable Calculus:
Official unit websites, Prerequisites, Syllabus,
Table of contents, Miscellaneous points 		Textbooks Lectures Homework Exam


"The attention I gave them was my question and their response was their beauty."
- Aurelius Augustine, Confessions


Official unit websites

  1. Math 20900 Calculus 2
  2. Math 20901 Multivariable Calculus

Prerequisites

  1. MATH 11005 Linear Algebra and Geometry:
    1. Rn as an inner product space; the cross product in R3.
    2. Linear functions (transformations) from Rn to Rm and their relationship to matrices in Rm*n.

  2. MATH 11006 Analysis 1:
    1. Continuity for functions from R to R.
    2. Differentiability for functions from R to R.

  3. MATH 11007 Calculus 1:
    1. Partial derivatives and directional derivative.
    2. Tangent to a curve and normal to a surface.
    3. Double integrals in Cartesian and polar coordinates.

Syllabus

  1. Multivariable Calculus (for both Math 20900 Calculus 2 & Math 20901 Multivariable calculus):
    1. Vector-valued functions of several variables: continuity and differentiability. The derivative, curl and divergence.
    2. Curves and line integrals. Two-dimensional integration (review) and Green's theorem. Surfaces, surface integrals and Stokes' Theorem.
    3. Three-dimensional integration and the divergence Theorem.

  2. Functions of a complex variable (only for Math 20900 Calculus 2):
    1. Functions of a complex variable: continuity, analyticity, the Cauchy-Riemann equations, harmonic functions.
    2. Holomorphic functions. Cauchy's theorem and formula. Differentiable implies infinitely differentiable. Liouville's theorem. Taylor Series.
    3. Laurent series. Isolated singularities. Residues.


Table of contents with schedule

  1. Multivariable calculus (Version 2009-11-16/23:34)
  2. Functions of a complex variable (Version 2009-12-10/20:10)

Miscellaneous points

  1. After every class I stay behind to answer questions; this is a very good time to talk to me. Alternatively you may email me (address above). Please do not drop by my office without prior appointment.
  2. If you're unhappy with any aspect of the course please talk to me in the first instance. I welcome feedback (good or bad) and constructive criticism.
  3. If you're falling behind or otherwise find the class difficult you're welcome to request help from me.

Main Page Calculus 2 & Multivariable Calculus:
Official unit websites, Prerequisites, Syllabus,
Table of contents, Miscellaneous points 		Textbooks Lectures Homework Exam


Email: Isaac.Chenchiah, Phone: +44 117 928 7984, Room 2.15
Updated: Thursday 10 December 2009
University of Bristol