# Team:UANL Mty-Mexico/math course

### From 2012.igem.org

**Math Modelling Course**

This year, the iGEM UANL team decided to establish an introductory course called 'Mathematical Modeling in Systems Biology', with the idea of preparing our faculty students in the mathematical area of biology.

This course is made up of three phases, each one demanding a different knowledge level.

**Phase I ** Has the intention of teaching the students
theoretical and applicable aspects of differential
and integral calculus as a fundamental part in
solving and distinguishing differential equations.

**Phase II** Was designed with the aim of making the
students able to understand the applications of
linear transformation of vector spaces for the
solution of differential equations that can be
applied in systems biology.

**Phase III.** The objective of this part of the course
is that students come to understand the general concepts
of systems biology and become familiar with its theoretical
basis, having as purpose increasing the student's critical awareness on this area.

**Description**

This program is based on the UNAM Genomic Sciences career's syllabus, which is an internationally-recognised career by many other universities and prestigious investigation centers in the world.

The first phase of the course was successfully imparted along June and July of this year by M.Sc. Jesús Botello González, professor of the Chemistry School of our University (UANL). It had a duration of 6 weeks and took place in our faculty; approximately 40 students enrolled this course.

M.Sc. Botello will impart phase II as well, but the program has still to be dated.

We think this course is a great step toward the learning of advanced knowledge in the field of molecular biology and genomics that has to be made use of, and it is really important for the UANL students, so that we are well-educated in this field.

**The subjects that are included in the first phase (Phase I) of this course
are:**

**1.** Precalculus

1.1Elementary algebra

1.2Understanding of the behavior of functions through their graphs.

1.3Functions, dependent and independent variables, domain and range.

1.4Function composition

1.5Inverse functions

**2.**Differential calculus

2.1Limits

2.2Lateral limits

2.3Infinite limits

2.4Limits tending to infinite

2.5Behavior of asymptotic rational functions applying limits

2.6Continuity

2.7Definition of derivatives

2.8Derivation rules

2.9Derivative of a composite function

2.10Chain rule

2.11Change rate in relation to time

2.12Optimization

2.13Function graphing using derivatives

**3.**Integral calculus

3.1Sigma notation

3.2Riemann sums (Definite integral definition)

3.3Calculation of the area under a curve with definite integrals

3.4Integral calculus theorems, including the Fundamental Theorem of Calculus

3.5Definition of indefinite integrals (anti-derivatives)

3.6Polynomial function integration

3.7Integration by substitution

3.8Calculation of the area between functions

3.9Calculation of volume by slices

3.10Calculation of the volume of solids of revolution with discs and cylindric layers

3.11Integration techniques