Complex Analysis & Applications
3203NSC
Week 1
Complex Analysis and Applications
Welcome!
Convenor: Juan Carlos Ponce Campuzano
Housekeeping
-
Time commitment - 150 hr
-
About 7-8 hr/wk on regular course material
- 2 hr to read/watch core material, "Check Your Understanding"
- 3-4 hr on workshop problems and reviewing core material
- 2 hr session to reinforce ideas (quizzes and other exercises)
-
About 50 hours on
- reviewing progress, focus on difficult areas
- assessment tasks, exam prep
-
About 7-8 hr/wk on regular course material
-
Assessment
-
Student-negotiated assessment [40%]:
- reinforcement/feedback on core knowledge/skills
- exam skills development: maths communication
- Assignment [20%]: assesses ability to present solutions
- Oral Exam [40%]: assesses understanding
-
Student-negotiated assessment [40%]:
In-class assessment
-
What?
- 4 activities through trimester (10% of course mark each)
- In-class quizzes
- Running tutorials
- Presentations of solutions to (tutorial) problems
- ... open to other suggestions
-
When?
- Fit around other assessment ...
- No class in Wk 5 (GC) / Wk 9 (NA)
- 20% assignment due end Wk 10
- 40% exam in Wks 13-14
- We will finalise assessments and dates next week
Working together
The point of this (and any) course is
to know more than when you started ...
-
What you should do?
- help each other understand (maths, applications, context)
- share ideas for what to do
-
What you should not do?
- tell each other the answer (defeats the educative purpose)
- do the work for one another
- copy one another's work
What is Complex Analysis?
1. Complex Numbers
What is Complex Analysis?
2. Complex Functions
$f(z) = u(x,y) + i v(x,y)$
What is Complex Analysis?
3. Differentiation
What is Complex Analysis?
4. Integration
$ \ds \int_C f(z)\,dz = \int_a^bf\left(z(t)\right)z'(t)\,dt$
What is Complex Analysis?
5. Complex Series
$ \ds \sum_{n=1}^{\infty}z_n=z_1+z_2+z_3+\cdots$
What is Complex Analysis?
6. Residues (integration revisited)
$ \ds \int_C f(z)\,dz =2\pi i \sum_{z_k\text{ inside }C}\text{Res}_{z=z_k}f(z)$
What is Complex Analysis?
7. Applications: Real integrals
$ \ds \int_{0}^{\infty}\frac{\sin x}{x}dx$
What is Complex Analysis?
8. Applications: Inverse Laplace problems
|
$ \ds \mathcal{L}\left\{f\right\}=F(x) =\int_0^{\infty} e^{-st}f(t)\,dt$ |
|
What is Complex Analysis?
9. Applications: Laplace's equation
$ \ds \nabla ^2 \phi(x,y)=0$
What is Complex Analysis?
10. Applications: Series, Number Theory, Geometry, etc.
For the rest of today
-
Check your understanding
- How to use these sheets
- Answers for this week
-
Tutorial problems
- Answers for this week
