Mathematics 23b Spring 2006 Theoretical Linear Algebra and Multivariable Calculus II Catalog Number 8571 Exam Group 4 COURSE INFORMATION Instructor Alberto De Sole contact info Sc Ctr 331 617 496 5211 desole math harvard edu Course Assistants Gerardo Con Diaz condiaz fas harvard edu Samuel Cross cross fas harvard edu Robert Furrow rfurrow fas harvard edu Andrew Laitman laitman fas harvard edu Alexandra Kjuchukova akjuchuk fas harvard edu Textbooks C H Edwards Jr Advances calculus of several variables Other suggested readings W Rudin Principles of mathematical analysis 3rd edition T Apostol Calculus A N Kolmogorov and S V Fomin Elements of the theory of functions and functional analysis Meeting times Lectures M W F 11 12 am in Science Center E Instructor s office hours M 12 1 W 6 7 Problem sessions TBA Course Web Page http www courses fas harvard edu math23a Course announcements homework assignments and homework solution sets will all be posted here Grading policy Problem sets 30 mid term exams 30 final exam 40 1 SYLLABUS Metric and topological spaces Limits and continuity Wednesday February 1 1 Subject Course overview Friday February 3 2 Subject Completeness axiom of R Reading Rudin 1 4 Monday February 6 3 Subject Countable and uncountable sets Reading Rudin 2 1 Wednesday February 8 4 Subject Metric spaces Reading Rudin 2 2 Friday February 10 5 Subject Topology of metric spaces Reading Rudin 2 2 Problem Set 1 due Monday February 13 6 Subject Sequences and limits Reading Rudin 3 1 3 2 Wednesday February 15 7 Subject Definition of limit and continuity Reading Rudin 4 2 4 2 Edwards 1 7 2 Friday February 17 Class cancelled Problem Set 2 due Monday February 20 President s day no class 8 Wednesday February 22 Subject Continuous functions Reading Rudin 4 2 4 2 Edwards 1 7 9 Wednesday February 22 afternoon make up class Subject Examples and properties of continuous functions Reading Rudin 4 2 4 2 Edwards 1 7 10 Friday February 24 Subject Compact sets Reading Rudin 2 3 Edwards 1 8 Problem Set 3 due 11 Monday February 27 Subject Bolzano Weierstrass Theorem and Heine Borel Theorem for compact sets in Rn Reading Edwards 1 8 Appendix Multivariable differential calculus 12 Wednesday March 1 Subject Curves in Rn Reading Edwards 2 1 13 Friday March 3 Subject Directional derivatives and the differential Reading Edwards 2 2 3 Problem Set 4 due Monday March 6 Midterm Exam 1 14 Wednesday March 8 Subject Directional derivatives and tangent planes Reading Edwards 2 2 15 Friday March 10 Subject Continuously differentiable functions Reading Edwards 2 2 Problem Set 5 due 16 Monday March 13 Subject Chain rule Reading Edwards 2 3 17 Wednesday March 15 Subject Mixed second order partial derivatives Reading Edwards 2 3 18 Friday March 17 Subject Taylor s formula in one variable Reading Edwards 2 6 Problem Set 6 due 19 Monday March 20 Subject Taylor s formula in several variables Reading Edwards 2 7 20 Wednesday March 22 Subject Maximum minimum problems Reading Edwards 2 4 2 5 2 8 4 21 Friday March 24 Subject Second derivative test Reading Edwards 2 4 2 5 2 8 Problem Set 7 due Monday March 27 Friday March 31 Spring Break no class 22 Monday April 3 Subject Lagrange multipliers Reading Edwards 2 4 2 5 2 8 Multivariable integral calculus 23 Wednesday April 5 Subject Area and the 1 dimensional integral Reading Edwards 4 1 24 Friday April 7 Subject Volume and the n dimensional integral Reading Edwards 4 2 Problem Set 8 due 25 Monday April 10 Subject Step functions and Riemann Sums Reading Edwards 4 3 26 Wednesday April 12 Subject Iterated integrals and Fubini s Theorem Reading Edwards 4 4 27 Friday April 14 Subject Change of variables Reading Edwards 4 5 5 Problem Set 9 due Monday April 17 Midterm Exam 2 28 Wednesday April 19 Subject Improper integrals Reading Edwards 4 6 29 Friday April 21 Subject Path length Line integrals Reading Edwards 5 1 Problem Set 10 due 30 Monday April 24 Subject Green s Theorem Reading Edwards 5 2 31 Wednesday April 26 Subject Multilinear functions Area of a parallelopiped Reading Edwards 5 3 32 Friday April 28 Subject Surface area Reading Edwards 5 4 Problem Set 11 due 33 Monday May 1 Subject Differential forms Reading Edwards 5 5 34 Wednesday May 3 Subject Stokes Theorem Reading Edwards 5 6 6 35 Friday May 5 Subject The classical theorems of vector analysis Reading Edwards 5 7 Problem Set 12 due Reading Period May 6 May 17 Final Examination Period May 18 May 26 The final exam is scheduled on Saturday May 20 7