Applied Math 105: ordinary & partial differential equations Course web: http://isites.harvard.edu/icb/icb.do?keyword=k80051 Eli Tziperman, eli@seas.harvard.edu; Museum Bldg, Oxford 24, room 456; 617-384-8381; John Crowley, jcrowley@fas.harvard.edu office hours: see course web page. TFs: Aaron Kuan, Manish Gupta, Marianna Linz, Matthew Newman, Nathan Arnold, Phillip Yao, Preya Shah Course requirements: weekly HW (30%, 0th HW already posted), three mid-terms (during evening time, 30%), final (40%) Matlab intro sessions: this week! See course web page Required preparation: APM 21a,b/ Math 21a,b; no programming preparation expected, Matlab will be introduced & used in HW Times of sections, logistics: see course web page.

Textbook & extended syllabus Page numbers from relevant textbook for each lecture given in detailed syllabus: http://www.seas.harvard.edu/climate/eli/ Courses/APM105/2012spring/detailed-syllabus-apm105.pdf; linked from course web page, requires VPN outside campus. Greenberg, Advanced Engineering Mathematics: main textbook. Any course material not from this textbook is posted to course web page. Also: Erwin Kreyszig, Advanced Engineering Mathematics: similar to Greenberg, a bit more concise, used occasionally. Strogatz, Nonlinear dynamics and chaos: will be used for just a few lectures about linear and nonlinear dynamics. Francis B. Hildebrand, Advanced Calculus for Applications

What is this about? You should come out of this course having an idea of Ordinary differential equations (ODEs): 1st order, 2nd order, and motivation using examples from different applications. Initial value problems vs boundary value problems How to solve them analytically, brief into to numerical solution Introduction to special functions (Bessel, Legendre, Hermit, …) Geometric approach to ODEs Partial differential equations (PDEs): elementary introduction Diffusion; Waves; Laplace (e.g., steady diffusion) With applications and examples; again both analytic solutions and a brief intro to numerical solutions. Time permitting: Introduction to nonlinear dynamics & chaos What not to expect? Not too many rigorous proofs, focus on applied

What to expect… Material gets somewhat more complicated later in the course. Nothing you cannot deal with after taking APM21ab, but does require a sustained effort. Useful student feedback: “This is a challenging class, [...] Problem sets take a long time, and they are very difficult [...] Just be ready to put in a few late nights.” “learnt a lot from the problem sets and although hard and long was worth it!” “[homeworks were] Generally too long. But wouldn't learn the material otherwise […]” Start working on HW early, come to sections, do not fall behind, please come and seek help if needed…!

APM105 before Danica McKellar, actress, proved Chayes-McKellar-Winn Theorem: "Percolation & Gibbs states multiplicity …”. after

Let the fun begin…