MA 411. Advanced Calculus

General Information

• Time: Tue & Thu. 9:30 AM - 10:45 AM

• Place: CAS 216

• Prerequisite: MA 225 or 230, MA 242 or 442

• Text book: R. Wrede, M. Spiegel, Advanced Calculus (Schaums Outline Series), 3rd Ed. McGraw-Hill. ISBN:978-0-07-162366-7.

• Course description

• Syllabus
  
  
  

Instructor: Yoosik Kim

• Email: yoosik (at) bu (dot) edu

• Office hours (MCS 237B): Mon. 3 PM - 5 PM , Thu 11 AM - 12 PM, or by appointment

Supplementary

• Lecture Note (Sep. 5th) - Review of Taylor series and Trig identities.

• Lecture Note (Sep. 7th) - Fourier series

• Lecture Note (Sep. 12th) - Fourier sine and cosine series

• Lecture Note (Sep. 14th) - Convergence theorem of Fourier series, Parseval's identity

• Lecture Note (Sep. 19th) - Review of sequences and series of numbers

• Lecture Note (Sep. 21st) - Review of tests for convergence/divergence of series

• Lecture Note (Sep. 26th) - Sequences and series of functions

• Lecture Note (Sep. 28th) - Pointwise convergence

• Lecture Note (Oct. 3rd) - Uniform convergence

• Lecture Note (Oct. 5th) - Why uniform convergence

• Lecture Note (Oct. 12th) - Weierstrass M-test

• Lecture Note (Oct. 17th) - Pointwise/uniform convergence of power series

• Lecture Note (Oct. 26th) - Pointwise/uniform convergence of Fourier series

• Lecture Note (Oct. 31st) - Integration and differentiation of Fourier series

• Lecture Note (Nov. 2nd) - Complex form of Fourier series

• Lecture Note (Nov. 7th) - Fourier transforms, Fourier integral theorem

• Lecture Note (Nov. 9th) - Parseval's identities, Gamma functions

• Lecture Note (Nov. 14th) - Gamma and beta functions

• Lecture Note (Nov. 16th) - Differentiation of several variable functions

• Lecture Note (Nov. 21st) - Jacobian matrices, linear approximation, chain rule

• Lecture Note (Nov. 28th) - Inverse function theorem

• Lecture Note (Nov. 30th) - Implicit function theorem

• Lecture Note (Dec. 5th) - Hessian matrices

• Lecture Note (Dec. 7th) - (The last example is Corrected!) Change of variables and Jacobians
  
  
  

Exams

• The midterm exam (Oct. 24th in class) - Prob/Sol

• The cumulative final exam (Dec. 19th, 9 - 11 AM, CAS 216) - Prob/Sol