In this video we will see the beginning of a topic that has revolutionized the way we understand the world. Key minutes by topic 0:00 Intro 2:06 Classification of DEs 3:21 ODEs 4:35 Order of an ODE 4:48 Solving a DE 5:21 DE in partial derivatives 9:56 Work approach 14:50 1st Order ODE of Separable Variables 24:47 Example 1 29:36 Homogeneous ODE 43:39 Example 2 50:59 1st Order Linear ODE 59:39 Example 3 1:21:01 Special cases To understand, you should see the previous videos: Functions: • FUNCTIONS OF ONE VARIABLE: Class Comp... Derivatives: • DERIVATIVES: Complete Class from Scratch Integrals: • INTEGRALS - Complete Class from Scratch You can support the development of more material like this by donating through Patreon: / eltraductordeingenieria Some recommended books: To get started to understand calculus topics, you may find useful: Michael Spivak, Calculus, 3rd Edition George Thomas, Calculus: One Variable, 12th Edition, Pearson Publishing James Stewart, Calculus: Early Transcendental, 6th Edition, Cengage Learning Publishing. Claudio Pita Ruiz, Calculus of One Variable, 1st Edition, Prentice Hall Publishing. Ron Larson, Bruce H. Edwards, Calculus 1 of One Variable, 9th Edition, Mc Graw Hill Publishing. Recommended book on differential equations (used to produce this video): George G. Simmons - Differential Equations with Applications and Historical Notes-McGraw-Hill (1993) Some YT channels that I recommend: lasmatematicas.es / juanmemol MateFacil / @matefacilyt 3Blue1Brown / @3blue1brown blackpenredpen / blackpenredpen MIT OpenCourseWare / @mitocw Álgebra Para Todos / @algebraparatodos ----------------------------------------------------------------------------------------------------------------- Observations/Errata: In 7-50 T(x,y,x,t) appears, it should be T(x,y,z,t). Editing error. The model for the growth of bacteria presented is a real variable. Models usually reduce reality by simplifying the treatment and considering only some aspects and not others. The results are usually approximations to reality. In this case, P(t) takes real values ​​that could approximate the amount of bacteria at time t. How well it approximates depends on the type of experiment and the type of model. If the integer part of each value that P(t) takes were considered, that could, under certain hypotheses, represent the amount in question. 49-42 the constant k1 is strictly positive 1-01-24 that amount of salt, in practice, does not reach dilution. I consider that the incoming solution enters with salt precipitate and comes out in a homogeneous form. This problem invites you to investigate about saturation of solutions, it invites you to think. Also the output flow in practice is impossible to be constant. We will assume it is constant to simplify the model. It will end up being an approximation, like any model. In 1-12-08 dt was still used, when du should have been used. Have you found an error in the video? Let me know in the comments, and I will give you feedback! ----------------------------------------------------------------------------------------------------------------- As a cameraman this time I have been helped by: Santiago Müller Images of the presentation used for educational/illustrative purposes, credits to: • VIAJEROS CIENCIA ADENTRO - 26º de lat... • Engineering to avoid tragedies... • Mathematics applied to biological problems... • Mathematics - UNLP • Physics - UNLP Everything is there! Now it only depends on you! (or you ;) ) We are changing the classroom. We are showing that you can teach differently. #DifferentialEquations