【Stanford engineering】Applied mathematics (16/20): Heat eqn: cylindrical Bessel functions скачать в хорошем качестве

【Stanford engineering】Applied mathematics (16/20): Heat eqn: cylindrical Bessel functions

Applied Mathematics Lecture Series These videos were inspired in part from my applied mathematics course at Stanford University, taught to undergraduate engineering students. I’m sharing them here in case they’re helpful to students, educators, or just anyone who enjoys a good Laplace / Fourier approach to transform the world towards a hope of an even better future. What You'll Learn (20 lectures): • Classification, first- and second-order differential equations (L1 - L3) • Power series and Frobenius methods (L4 - L5) • Laplace transforms (L6 - L8) • Fourier series (L9 - L10) • Derivations of the heat, diffusion, and reaction equations (L11, L17, L20) • Cylindrical Bessel functions (yes, really) (L16) • Separation of variables (and a whole lecture on how not to do it) (L12 - L14) • PDEs in different dimensions and coordinate systems (L15) • Similarity transforms (L18 - L19) • ... plus a bonus final lecture with my parting advice to students (Bonus) Why This Course Matters: Applied math is the language we use to describe physical systems—from heat conduction in a rocket engine to diffusion in a living cell. Being fluent in these mathematical tools will change the way you see the natural world and tackle important engineering challenges of today and the future. About Me: I’m Sho Takatori, a professor of Chemical Engineering at Stanford. I post videos on engineering, soft matter physics, data-driven models, and the art of science communication. Think of this as my way of opening the classroom to a wider audience. Outside of research, I have had a strong passion for public speaking since high school, taking speech courses in college and competing in speech contests in Toastmasters International (a professional organization to improve public speaking and leadership skills) for several years as a PhD student. More recently, as a professor and educator, I have channeled my passion for speaking towards science education and technical communication. I have always believed that effective science communication can make broad impacts to society by building public trust in science, promoting data-driven decisions in government and industry, and improving the accessibility of science to all communities. I look forward to continue working on effective science communication skills and storytelling techniques with students and researchers in my career. My contents are personal and do not represent Stanford University.