Multivariable Calculus Math 21a,Oliver Knill, Spring 2006All the course information is on the Math 21a website. Here is asummary of the most crucial information.Key inform ation• URL: http://www.courses.fas.harvard.edu/˜math21a/• Classes: MWF 10-11, 11-12, 12-1 (*), TTh 10-11:30, 11:30-1• Sections: regular, biochem and physics (with s ufficient e nrollment)• Course head: Oliver Knill, 434 Science Center, [email protected]• Office hours: TBA• Book: J. Stewart, Multivariable calculus, Third edition• Additional Biochem Book: Y.Z. Rozanov, Probability theory, Dover• Math question center: Science Center 309, Su-Th 8-10PM• Course assistants:, TBA• Problem sessions: will be organized by CA• Homework:, weekly HW will be ass igned in three parts, one in each lecture. No homeworkextensions. Lowest HW score of 1 week HW is discarded.• Homework: is due at the be ginning o f each lecture.• First hourl y: March 14, Hall D, 7-8:30 PM• Second hourly: April 18, Hall D, 7-8:30 PM• Final: or ganized by registrar, time to be anno unced• Mathematica: program and project will be available on the website• Grades:Midterm 1: 15Midterm 2: 15Homework : 25Project : 5Final : 40Calendar:Su Mo Tu We Th Fr Sa | week special dates month---------------------+---------------------------------------Su Mo Tu We Th Fr Sa Week1 2 3 4 Feb5 6 7 8 9 10 11 1 6/7 start of lectures12 13 14 15 16 17 18 219 20 21 22 23 24 25 3 20.Feb Presidents day26 27 28 1 2 3 4 4 Mar5 6 7 8 9 10 11 512 13 14 15 16 17 18 6 March 14. First hourly19 20 21 22 23 24 25 726 27 28 29 30 31 1 Spring recess Apr2 3 4 5 6 7 8 89 10 11 12 13 14 15 916 17 18 19 20 21 22 10 April 18. Second hourly23 24 25 26 27 28 29 1130 1 2 3 4 5 6 12 Mai7 8 9 10 11 12 13 Reading period14 15 16 17 18 19 20 17. end reading period21 22 23 24 25 26 27 26. End exam period---------------------+---------------------------------------Sectioning:• From a Windows computer, open the SecureCRT application. Use the ”Quickconnect” menuto open a connection with protocol ssh2, hostname: ulam.fas.harvard.edu and username:section.• From a Macintosh with OS X start the ”Terminal” application located under Applica-tions/Utilities. At the shell prompt, type ”ssh [email protected]” and typereturn.• Using any terminal on a Linux or any other computer running a Unix flavour, login intoyour FAS account. At the shell prompt, type ”ssh [email protected]” and typereturn.Daily SyllabusHour Topic Book section Tue Thu1. Geometry of Space 2/6-2/111 - coordinates 9.1 | 1- distance |2 - vectors 9.2 -+- dot product 9.3 | 23 - cross product and planes 9.4 |2. Functions and Graphs 2/13-2/181 - lines and planes 9.5 |- distance formulas | 12 - functions 9.6 -+graphs |3 - level curves | 2- quadrics |3. Curves 2/20-2/25- Presidents day, no class1 - curves in space 10.1 | 1- velocity |- acceleration 10.2 |2 - arc length 10.3 -+ 2- curvature 10.4 |4. Surfaces 2/27-3/31 - cylindrical coordinates 9.7 | 1- spherical coordinates |2 - parametric surfaces 10.5 -+ 23 - functions 11.1 |- continuity 11.2 |5. Functions 3/6-3/101 - partial derivatives 11.3 |Solutions to PDE’s | 12 - linear approximation 11.4 +tangent planes3 - chain rule 11.5 | 2implicit differentiation |6. Gradient 3/13-3/171 - review for first hourly | 12 - gradient 11.6 -+gradient and level curves | 23 - directional derivative 11.6 |direction of steepest decent |7. Extrema 4/3-4/71 - maxima, minima, saddle points 11.7 | 12 - Lagrange multipliers 11.8 -+3 - Combined problems 11.8 | 2Spring recess8. Double Integrals 4/10-4/141 - double integrals 12.1/2 | 12 - general regions 12.3 +3 - polar coordinates 12.4 | 29. Surface Area 4/17-4/211 - review for second hourly | 12 - surface area 12.6 |3 - triple integrals 12.7 | 210. Triple and line Integrals 4/24-4/281 - cylinder, spherical coordinates 12.8 -+ 12 - vector fields 13.1 +3 - line integrals 13.2 | 2This is the syllabus for the regular and physics sections.11. Integral Theorems I 5/1-5/51 - fundamental thm line integrals 13.3 | 12 - Greens theorem 13.4 -+3 - curl and divergence 13.5 | 212. Integral Theorems II 5/8-5/121 - flux integrals 13.6 | 12 - Stokes theorem 13.7 -+3 - Gauss theorem 13.8 | 2- Applications 13.9 |Mathematica project due!The Biochem section roughly part of the fist 5 chapters in Rozanov.11. Probability theory I (5/1-5/5) biochem1 - discrete random variables 1-4 | 12 - continuous random variables 7 |distributions + 23 - expectation, variance etc 8-9|12. Probability theory II (5/8-5/12) biochem1 - independence, conditional probab. 5+6| 12 - binomial and Poisson distributions 10 +3 - normal distributions 11 | 2Mathematica project
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