1 00:00:00,270 --> 00:00:04,560 Natalie, welcome you in this course, and I'm very thankful for your participants. 2 00:00:05,010 --> 00:00:07,500 Let us first discuss about the structure. 3 00:00:08,650 --> 00:00:13,360 In the beginning, we will learn how to use Python and Jupyter notebooks. 4 00:00:13,390 --> 00:00:19,300 We will discover how you can install the Python programming language and how you can set up your first 5 00:00:19,450 --> 00:00:20,470 Jupyter notebook. 6 00:00:21,310 --> 00:00:27,520 And then I have added a two hour crash course where we will discuss concepts like Nampai functions, 7 00:00:27,520 --> 00:00:29,470 arrays and the visualization. 8 00:00:29,980 --> 00:00:35,710 So this is especially for the students that are new to Python or that don't have so much experience 9 00:00:35,710 --> 00:00:36,100 with it. 10 00:00:36,640 --> 00:00:43,360 If you are unsure if you should watch these videos, then I have prepared some quizzes, coding exercises 11 00:00:43,360 --> 00:00:49,840 and solutions so you could just jump right into these quizzes and challenges and see if you manage or 12 00:00:49,840 --> 00:00:50,140 not. 13 00:00:50,620 --> 00:00:53,830 And then with the third section, the actual course starts. 14 00:00:53,860 --> 00:01:01,000 We will begin by discussing series expansion and interpolation, and this also contains topics such 15 00:01:01,000 --> 00:01:06,280 as Blind's solving linear equations systems and also filling data. 16 00:01:07,090 --> 00:01:13,630 Then we will turn to two very important concepts derivatives and integrals, and in both cases, we 17 00:01:13,630 --> 00:01:17,650 will first discuss different methods with different accuracy. 18 00:01:18,220 --> 00:01:23,350 So there exist different methods to calculate numerically a derivative or also an integral. 19 00:01:24,160 --> 00:01:29,650 And then we will really turn to actual physical examples, such as calculating the velocity and the 20 00:01:29,650 --> 00:01:31,390 acceleration from a data file. 21 00:01:31,900 --> 00:01:39,010 And then we will calculate the rotational motion or rotational energy and the corresponding moment of 22 00:01:39,010 --> 00:01:43,240 inertia, and we will also calculate the magnetic field of a wire. 23 00:01:43,750 --> 00:01:49,510 For this, we even need the derivative concepts in multiple dimensions, such as gradients, divergences 24 00:01:49,510 --> 00:01:50,170 and kernels. 25 00:01:50,920 --> 00:01:52,090 And then for the integrals. 26 00:01:52,480 --> 00:01:57,580 As the last lecture, we will discuss future transforms that we will need later on. 27 00:01:58,060 --> 00:02:03,430 So then come Sections six and seven, which are actually the longest and most important sections of 28 00:02:03,430 --> 00:02:03,970 this course. 29 00:02:04,220 --> 00:02:08,289 Here we will discover all the properties of differential equations. 30 00:02:09,039 --> 00:02:16,360 We will begin very mathematical and we will really program an Euler method and a quarter for five method 31 00:02:16,360 --> 00:02:17,110 ourselves. 32 00:02:17,890 --> 00:02:23,410 And of course, we will also discover the methods are provided by Nampai and by Python in general to 33 00:02:23,410 --> 00:02:28,390 solve problems such as the radioactive decay, the fall and pendulum motion. 34 00:02:29,020 --> 00:02:32,500 So these are all pretty basic and in one dimension. 35 00:02:32,800 --> 00:02:38,350 But then we will make things more difficult and go to multiple dimensions, and we will simulate a rolling 36 00:02:38,350 --> 00:02:38,740 ball. 37 00:02:39,100 --> 00:02:44,350 We will simulate a chaotic Lorence system and we will discover the butterfly effect. 38 00:02:44,830 --> 00:02:50,770 We will solve the heat equation where we will investigate how temperature propagates over time in the 39 00:02:50,770 --> 00:02:57,220 sample, and we will then solve the famous three body problem at the example of Sun, Earth and Moon. 40 00:02:57,220 --> 00:03:02,620 And we will actually even add a fourth body, which will be a rocket ship with which we fly to the Moon. 41 00:03:03,670 --> 00:03:08,200 Then in section eight, we will solve and discuss an eigenvalue problem. 42 00:03:08,920 --> 00:03:11,800 The coupled motion of harmonic oscillators. 43 00:03:11,950 --> 00:03:16,480 So for example, you have several pendulums and you a couple of them, and this gives rise to a very 44 00:03:16,480 --> 00:03:19,450 complicated type of motion, which is hard to understand. 45 00:03:20,350 --> 00:03:26,200 However, we actually have three tools at our hands from the previous lectures, so these are calculating 46 00:03:26,200 --> 00:03:33,340 the eigenvalues of a matrix using a fit of procedure and calculating to fully transform it. 47 00:03:33,340 --> 00:03:39,760 In all cases, we will get very similar solutions, and we will really be able to understand the complicated 48 00:03:39,760 --> 00:03:40,420 behavior. 49 00:03:40,990 --> 00:03:44,980 And then the last real section of this course is about Monte-Carlo methods. 50 00:03:45,130 --> 00:03:48,730 This is where we exploit randomness to get extra results. 51 00:03:49,420 --> 00:03:52,060 And first, we will test this at a mathematical example. 52 00:03:52,060 --> 00:03:59,590 We will calculate the numerical value of PI, and then we will actually simulate the collective magnetism 53 00:03:59,590 --> 00:04:05,560 of many small individual magnets that form a ferromagnetic and also an antifa magnet. 54 00:04:06,130 --> 00:04:07,990 So that's the main part of the course. 55 00:04:07,990 --> 00:04:14,080 And then I have two additional add on sections, which are for the advanced students that want to see 56 00:04:14,080 --> 00:04:17,740 what is even beyond these previous topics that I have just explained. 57 00:04:18,100 --> 00:04:22,120 So this is about quantum physics, where I have actually a whole course here on Udemy. 58 00:04:22,300 --> 00:04:27,460 So this is just a teaser on how to solve the Schrodinger equation, which is the differential equation 59 00:04:27,460 --> 00:04:31,300 that describes the quantum behavior of electrons, for example. 60 00:04:32,270 --> 00:04:39,230 And then section 11 is really state of the art research here, we will discuss the electronic properties 61 00:04:39,230 --> 00:04:44,630 of graphene and for this topic, the Nobel Prize was awarded quite recently. 62 00:04:44,990 --> 00:04:50,300 So you see, it's really a difficult topic and state of the art research, but with our tools that we 63 00:04:50,300 --> 00:04:55,460 have employed so far, we can really tackle these problems and understand what is going on. 64 00:04:56,240 --> 00:04:57,440 So I hope you are excited. 65 00:04:57,710 --> 00:04:59,630 And let's jump right into the topic. 66 00:04:59,870 --> 00:05:05,120 And in the next lecture, I will explain to you how you can install Python and Jupyter Notebook to get 67 00:05:05,120 --> 00:05:05,630 started.