Unit name | Multivariable Calculus and Complex Functions |
---|---|
Unit code | MATH20015 |
Credit points | 20 |
Level of study | I/5 |
Teaching block(s) |
Teaching Block 1 (weeks 1 - 12) |
Unit director | Dr. Wiesner |
Open unit status | Not open |
Pre-requisites |
MATH10011 Analysis, MATH10012 ODEs, Curves and Dynamics, MATH11005 Linear Algebra and Geometry |
Co-requisites |
None |
School/department | School of Mathematics |
Faculty | Faculty of Science |
Unit Description
The emphasis is on basic ideas and methods; theorems will be stated, but the emphasis is on methods rather than proofs. The first half develops an understanding of multivariable calculus including the major theorems of vector calculus. The main focus is on developing differential vector calculus, tools for changing coordinate systems and major theorems of integral calculus for functions of more than one variable. This material is fundamental to physical applied mathematics and it is also relevant to the second half of the course which introduces functions of a complex variable, with a focus on holomorphic functions. It introduces differentiation and integration of functions of one complex variable, goes through the main theorems of integration, leading up to Cauchy’s Residue theorem, and contains a final part on using theorems of complex functions to solve real-valued integrals
Relation to Other Units
This unit extends elementary calculus as seen in ODEs, Curves and Dynamics.
This unit feeds into pure and applied mathematics, such as Complex Function Theory (which develops the material) and Fluid Dynamics. Applied Partial Differential Equations and Mathematical Methods also use the material.
At the end of the course the student should be able to:
Three lectures and one problems class per week.
Formative assessment:
Summative assessment:
Raw scores on the examinations will be determined according to the marking scheme written on the examination paper. The marking scheme, indicating the maximum score per question, is a guide to the relative weighting of the questions. Raw scores are moderated as described in the Undergraduate Handbook.
If you fail this unit and are required to resit, reassessment is by a written examination in the August/September Resit and Supplementary exam period
Recommended