This Spring, I shall be the recitation instructor for the Advanced Calculus II (MATH 1540-graduate version). This course is designed to prepare the 1st and 2nd year graduate students for the Preliminary examination in real analysis. This exam is offered twice a year (May and August) by the department. My teaching page is the following: https://lupucezar.wordpress.com/teaching/.
- Homework (30% of your final grade!) will be assigned and collected weekly by Dr. DeBlois and you can find it on his webpage here. The homework will be graded and returned the following week. Late homework is accepted only with the instructor’s permission.
- The homework assigned last Spring’16 semester by Dr. Xu and me were the following:
- HW 1-LINEAR MAPS, LIMITS, CONTINUITY AND DIFFERENTIABILITY OF FUNCTIONS OF SEVERAL VARIABLES
- HW 2-THE INVERSE AND IMPLICIT FUNCTION THEOREMS; EXTREMUM PROBLEMS AND LAGRANGE MULTIPLIERS
- HW 3-INTEGRAL CALCULUS FOR FUNCTIONS OF SEVERAL VARIABLES
- HW4-SETS OF MEASURE ZERO AND LEBESGUE INTEGRATION
- I encourage you to solve as many problems as you can from this last year’s homework. All of them have the same caliber as prelim problems from previous years.
- Moreover, I shall assign four WORKSHEETS for this semester as follows:
- LINEAR MAPS, LIMITS, CONTINUITY AND DIFFERENTIABILITY OF FUNCTIONS OF SEVERAL VARIABLES.
- THE INVERSE AND IMPLICIT FUNCTION THEOREMS; EXTREMUM PROBLEMS AND RELATED TOPICS.
- INTEGRAL CALCULUS FOR FUNCTIONS OF SEVERAL VARIABLES.
- LEBESGUE INTEGRATION AND SETS OF MEASURE ZERO.
- My office hours are Tuesday (5-6 PM) & Wednesday (12-2 PM) in the POSVAR LAB and Tuesday (6-7 PM) in the MAC. My office is Thackeray 711.
- I invite you to join our Facebook group. The purpose of this group is to discuss problems from your homework or from previous preliminary exams. Moreover, I shall also post some notes from the recitation as a substitute for review sessions. Maybe, from time to time I shall upload some videos with solved prelim-type problems.
- Last but not least, you should also start working on problems from the famous Berkeley Problems in Mathematics by P. Ney de Souza and J-N. Silva. This book is a must for every graduate student! If you feel discouraged by the difficulty of the problems in the book, please remember to take into account Polya’s advice on how to approach a problem. Other resources can be found on my teaching page (look for Advanced Calculus-undergraduate & graduate 2014, 2015, 2016).
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