Mathematical Biology. 01: Introduction to the Course

UCI Math 113B: Intro to Mathematical Modeling in Biology (Fall 2014)
Lec 01. Intro to Mathematical Modeling in Biology: Introduction to the Course
View the complete course: ocw.uci.edu/courses/math_113b_...
Instructor: German A. Enciso, Ph.D.
Textbook: Mathematical Models in Biology by Leah Edelstein-Keshet, SIAM, 2005
License: Creative Commons CC-BY-SA
Terms of Use: ocw.uci.edu/info
More courses at ocw.uci.edu
Description: UCI Math 113B is intended for both mathematics and biology undergrads with a basic mathematics background, and it consists of an introduction to modeling biological problems using continuous ODE methods (rather than discrete methods as used in 113A). We describe the basic qualitative behavior of dynamical systems in the context of a simple population model. As time allows, we will then discuss other types of models such as chemical reactions inside the cell, or excitable systems leading to oscillations and neuronal signals. The necessary linear algebra is also discussed to avoid including additional requirements for this course.
Recorded on January 6, 2014
Required attribution: Enciso, German A. Math 113B (UCI OpenCourseWare: University of California, Irvine), ocw.uci.edu/courses/math_113b_.... [Access date]. License: Creative Commons Attribution-ShareAlike 3.0 United States License. (creativecommons.org/licenses/b...)

[@raquelcardoso8149]

Thank you a lot. These videos helped me to finish my Master.

[@CataM1988]

Awesome teacher. Thank you for sharing

[@iulianamihaela7968]

Thank you for this course

[@sodiqyusuff8013]

really love this...thanks

[@ahmetyucel8328]

Thanks. This is so beatiful

[@cityuuniversity1365]

Love this lectures !! Helped me out a ton!! would love to study at UCI one day!

[@topvisuals7513]

Search for QUADRATIC EQUATIONS by Crunching Numbers

[@biswarupmandal9788]

sir, can you tell me which book you are following? and which is the best book for "Chemotaxis".

[@karanhiwrale459]

Actually it was so helpful, for biologycal students

[@karanhiwrale459]

@Nirbhay Saluja thanks about rectify my spelling

[@qaisarbadshah3909]

please mention the name of book for the beginner in this field

[@user-bq9nt3im6h]

شكراً حبيبي♥️

[@wahyudiusman4753]

First, I appreciate videos like this because it would be very good for the development of applied mathematics. There is something I want to ask. Is there a way to determine or find the point of equilibrium of a dynamic system with n-dimensions? I just made a mathematical model of the immune response, where my model is a nonlinear system of differential equation And it dimension 9, I have trouble finding the equilibrium point either manually or by using mathematical applications such as maple or matlab

[@ayeshaansari7726]

A.o.a

[@deconfinedQPT]

Great Professor!

[@RubenR-du3hg]

pH.. balance is the titration of the acidity of skin with alkaline cologne at equivalent point. Henderson hasselbach eq

[@Betonoszlop]

Temperature can also affect bacteria growth rates

[@gabriellabourboulia8788]

what is the A ? I understand that is a constant but what is describes? The same with the small k (kappa) what it describes? can anyone help me?

[@hamzehabuabed6333]

Thanks so much

[@hassanamer6875]

Could u pls explain more about (alpha) which describe the food consumption by one bacterium. how can i get the value of alpha? is it coming from the biology test?

[@topvisuals7513]

Search for QUADRATIC EQUATIONS by Crunching Numbers

[@qurratulainaslam1018]

Thanks for such well explained lecture. Kindly tell name of reference book?

[@yankumar5280]

thanks for sharing UCIrvineOCW

[@raheemibraheem1903]

which books can one read to follow

[@dmaninthewall]

(At 4:05) d*n/d*t what does the "d" and "n" mean here ?

[@SuperCarottesRapees]

"d" refers to "an infinitesimally small increment in" the variable mentioned after "d". So dt means an infinitesimally small increment in time and dN refers to an an infinitesimally small increment in bacteria population.

[@theshreyansjain]

Reference book- leah edelstein-keshet: mathematical models in biology

[@ilhamazad]

This guy is actually really good

[@aventura1266]

What are the prerequisites for this course? University level calculus?

[@the_unstopable3958]

sir i am a high school past out. i had taken admission in course of BSc biotechnology(honours). will you kindly suggest me the best book for this course to learn biomaths.

[@m35926]

I suggest you first become very strong in differential equations and learn modeling in different programs such as XPPaut, Python, MATLAB, etc. This will give you a very strong foundation to enter biomaths.

[@hassan010012]

Awesome!

[@19Ronin95]

What does it mean that the number of bacteria is discreet? 2:31

[@theAkashMurthy]

Measurement of bacteria in a medium of sorts taken over a period of time wouldn't be 1.5, 2.3 or 2.2. It would be 222 or 22 or 23 or 12. It is discrete, thumbrule, something you can count.

[@sarcastic4694]

Consider human population for example. It can't be in fractions like someone can't have 2.5 members in their family. It's either 2 or 3 (whole number not fraction) that's why it's discrete 😂

[@giovag.996]

What is the time constant? How I can calculate it from differential equations such as dx/dt = -0.5x + 12

[@nisacelik2590]

x(t)=24+Ce^(-t/2)

[@giovag.996]

@@nisacelik2590 Oh thank you. Is there a specific rule that I have to follow? I mean, how we suppose to arrive to Ce^(-t/2)?

[@TheNaikas]

​@@giovag.996 So starting from dx/dt = -0.5x + 12, this can be written like dx/dt = (-1/2)x + 12 or dx/dt = (24-x)/2 when we add them like fractions. Bringing the x polynomial to the derivative we get, (dx/dt) (1/(24-x)) = 1/2. Both sides can be multiplied by dt such that (1/(24-x)) dx/dt * dt = 1/2 dt which is 1/(24-x) dx = 1/2 dt. Integrating both sides, int(1/(24-x) dx) = int(1/2 dt),, we have ln|24-x| = t/2 + C. I combined both constants on the right side to get C. Removing the log, 24-x = e^(t/2 + C). We can rewrite the right using our exponent properties, 24-x = e^(t/c) * e^(C). The e^(C) part is what we define as the "time constant" you mentioned if that makes sense. We can define an arbitrary constant since our constant before is just e getting raised to it, creating another arbitrary constant. Some people define e^(C) to be K. I've seen A. I've also seen C as @Nisa Çelik did. It's up to you. Let's just call it C for continuity's sake. 24-x = e^(t/2) *C 24-x =Ce^(t/2) -x = Ce^(t/2) - 24 x(t) = -Ce^(t/2) + 24 Again since C is an arbitrary constant we do not know what negative C would be so we can just also make that C : x(t) = Ce^(t/2) + 24 As for how we can calculate C. You would need more information like a point. Typically you are given an initial value, which says when t is 0 x(t) will be a certain value. Say we have the initial value x(0) = 5, we can calculate C using basic substitutions. 5 = Ce^(0/2) + 24 5 = C(1) + 24 C = 5-24 C = -19 This gives us the final solution of x(t) = -19e^(t/2) + 24, given that x(5) = 0. Hope that clears up some confusion!

[@giovag.996]

@@TheNaikas god, thank you very much

[@TheNaikas]

@@giovag.996 ha no problem. I’m glad struggling in my differential equations class amounted to something

[@akshitsood8496]

Respected sir I'm from India and i have done my masters in Mathematics for further research studies i'm quite interested in particular this branch of mathematics. As both biology and mathematics are best combination for me. Because in grade 12 studies i have both subjects simultaneously (math+ additional biology). I wanted to know that is this branch of mathematics has any further scope in future and what will be the job opportunities after doing my research degree in this field. This would be so helpful for me if you give me your little reply.

[@jackyjack9660]

Is it branch of maths or biology... Because maths is used in economics, physics.. So can say maths is a different thing... And this thing in the video is mathematical science and mathematical biology is sub field of this ... Means it's part of science...

[@vlogjk6404]

Could u please tell me about some books to be followed for mathematical biology as a beginner. I am also interested in studying mathematical biology 😇Suggest some books for both basic and then to higher level😇

[@vlogjk6404]

@@jackyjack9660 Suggest some books to be followed for mathematical biology 😇

[@ayeshaansari7726]

Listen plz i am from Pakistan i need your help plz listen to me

[@convenios22]

❤️

[@homeshhirwani8750]

Subtitles plz

[@anubhavgupta6873]

Which book to Follow?

[@biomathematics]

+Anubhav Gupta Hi, you can follow several books, one example is Murray J.D. Mathematical Biology: an introduction. Third edition. Interdisciplinary Applied Mathematics. Mathematical Biology. Spring: 2002. Best, Jorge Pires,

[@Kpop_stole_foids_fromcurrycell]

I didnt think there is math in biology untill i watch this video

[@navjotsingh2251]

There is a lot of math and chemistry in biology, depending on how deep you go.

[@jackyjack9660]

@@navjotsingh2251 but isn't biology just advance chemistry and mathematics is used for modelling those molecular structures...

[@TheReck12]

@@jackyjack9660 in the video he literally shows you how math is used in biology...it's more than just modeling molecules

[@jackyjack9660]

@@TheReck12 ikr... I'm in masters...ms biophysics...

[@mostlysunny582]

@@jackyjack9660 haha biology is not advance chemistry.

[@racquelsabesaje4562]

family is the smallest unit of society

[@sandipmishra261]

is mathematics imp for doing bio science

[@SuperCarottesRapees]

Not necessarily (I'm a PhD student in the field)

[@TheJereeeeee]

what field?

[@SuperCarottesRapees]

bioscience

[@SuperCarottesRapees]

To expand on my answer, you can do experiments in the wetlab and know very little maths

[@reecemolloy7106]

It depends. I have worked with researchers regarding metabolism for instance and on the team we have a former civil engineer, physicist, applied mathematician and two biologists. Both biologists don't have maths backgrounds and just provide experimental data, where the maths they need isn't too advanced at all, so I'd say maths helps a lot and you should do it with any science, but it isn't a huge bottle neck if you aren't so solid with it, just be hold with data analysis

[@James-wg8mn]

Complex

[@hamishmccreight6639]

THere is a bit more to it than this. This is just about rates of change and of course you use differential equations. There is also the other area of simulating how cells work by creating a mathematical model. Isn't maths great !!!!

[@ottonormalverbraucher9004]

Is dat doods name really "German"?

[@vincent10kd]

lmao, I think it's "latin american" for Herman(n).

[@kristynguyen1508]

Otto Normalverbraucher n

[@racquelsabesaje4562]

group of people

[@racquelsabesaje4562]

population

[@racquelsabesaje4562]

biology study life

[@racquelsabesaje4562]

math

[@maaan8494]

his face at 07:44 XD

[@rider2731]

It is such a waste of time and distraction to write those words on the board. He should have used slides. It is much more time-efficient to use slides with color illustrations and easy to read texts. He can create the slides once, and use them many times. The instructor may be an expert in his field, but he needs to improve his communication skills.

[@potassiumlanthanium5655]

Must be because he is either INTP or ENTP.

[@aeroscience9834]

Agus Widjaja I actually hate sides, they’re so much harder to follow then writing on the blackboard. And most of my fellow physics students agree, which is why the good professors don’t use slides for math/theory lectures

[@ilhamazad]

Aeroscience Thank you!! I despise slides too! My brain is incapable of grasping contents from slides. I wish the good old methods come back. Blackboard writing works best for me. The chalk noise, the friction of the board etc all contribute in some bizarre way. I guess our brains are all wired differently that some people have more absorption when specific techniques are incorporated.

[@saubaral]

@@potassiumlanthanium5655 lol, writing this here

[@diff2587]

Slides fucking suck. I will not elaborate.

[@lennycarlson1178]

Biology is getting hot and therefore mathematical. Girls about to get left behind it seems.

[@1234s6]

What do you mean? That they are not as good in math?

[@bluebullets8023]

shut up, incel