Second semester of a one year honors course in calculus, linear algebra and analysis. Assuming a good background in one variable calculus and a strong interest in mathematics, the course is devoted to a rigorous, modern presentation of multivariable calculus and linear algebra. There will be a greater emphasis on understanding the mathematical details of the theorems and proofs than would be found in a standard course, but intuition and applications will not be neglected.
Vector Calculus, Linear Algebra and Differential Forms, by John and Barbara Hubbard. We will cover most of chapters 3, 4, 6 in the second semester.
There will be grades for homework, two midterm exams and a final exam. All exams and quizzes are open book/notes, calculators allowed.
Quizzes 20 % Midterm Exams (20% each) 40 % Final Exam 40 %
For general policy statements about grades and academic honesty, go to: Policy Statements .
Midterm I Tuesday, February 16 Midterm II Tuesday, March 30 Final Exam Monday, May 10, 1:30-4:30 pm, Vincent Hall 311
Homework will be assigned but not collected. Instead there will be weekly quizzes consisting of problems very similar to the homework problems. If you can do the homework problems you should have no trouble with the quizzes. One quiz score will be dropped to allow for an absence or just a "bad day." To see the assignments, click on the link above.
Week Topic Reading 1/20-1/22 Manifolds, Tangent Spaces 3.1-3.2 1/25-1/29 Higher derivatives 3.3-3.4 2/1-2.5 Quadratic forms, critical points 3.5-3.6 2/8-2/12 Lagrange multipliers 3.7 2/15-2/19 Midterm I, Integration 4.1 2/22-2/26 Integrable functions, measure zero 4.3-4.4 3/1-3/5 Fubini's theorem, iterated integrals 4.5 3/8-3/12 Linear change of variables 4.7, 4.9 3/15-3/19 Spring Break 3/22-3/26 Nonlinear change of variables 4.10 3/29-4/2 Midterm II, Forms on R^n 6.1 4/5-4/9 Integrating forms, orientation 6.2-6.3 4/19-4/23 Work, flux, mass, boundaries 6.5-6.6 4/26-4/30 Exterior derivative, div, grad, curl 6.7-6.9 5/3-5/7 Stokes' theorem 6.10-6.11