MA 411. Advanced Calculus

General Information

• Time: Tue. & Thu. 9:30 AM - 10:45 AM

• Place: KCB 106

• 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

Lecture notes - The handwritten notes might be incomplete.

• Lecture 1 - Review of Taylor series

• Lecture 2 - Fourier series

• Lecture 3 - Fourier cosine and sine series

• Lecture 4 - Fourier convergence theorem

• Lecture 5 - Parseval's identity, mathematical definition of limits of sequences

• Lecture 6, 7 - Review of sequence and series of numbers.

• Lecture 8 - Pointwise convergence of sequences and series of functions

• Lecture 9 - Uniform convergence of sequences of functions

• Lecture 10 - Properties of uniform convergences

• Lecture 11 - Weierstrass M-test, Power series

• Lecture 12 - Pointwise convergence and uniform convergence of Fourier series

• Supplementary notes - Proof of pointwise convergence of Fourier series

• Lecture 13 - Integration and differentiation of Fourier series

• Lecture 14 - Complex form of Fourier series

• Lecture 16 - Fourier transforms, Fourier integral theorem, Parseval's identity

• Lecture 15 - Gamma and beta functions

• Lecture 17 - Differentiation of functions of several variables

• Lecture 18 - Jacobian matrices, Chain rule

• Lecture 19 - Inverse and implicit function theorem

• Lecture 20 - Review of eigenvalues, positive and negative definite matrices

• Lecture 21 - Hessian matrices, local maxima and minima

• Lecture 22 - Multiple integrals, change of variables and Jacobians
  
  
  

Exams

• The midterm exam (Oct. 30th) - Prob/Sol

• The final exam - Dec. 18th from 9 am to 11 am - Prob/Sol