Math 121 – Differential Calculus, Fall 2016

Instructor: Anatolii Grinshpan
Office hours: MTR 12-1,  Korman 249.

Calendar    Main page    Tutoring center    Greg Naber    MIT OCW

Sept 19. Introduction to the course. The idea of a limit. 

Sept 20. One-sided approach. Calculation of limits. Problems.

Sept 21. Calculation of limits. Problems. Handout.

Sept 23. Quiz 1: 1.1, 1.2.

 

Sept 26. Limits at infinity. Leading terms. Problems.

Sept 27. Limits at infinity. Oscillation. Hyperbolic functions.

Sept 28. The number e. Continuity. Problems.

Sept 30. Quiz 2: 1.3, 1.5. Bolzano’s theorem.

 

Oct   3.  Trigonometric limits. Problems.

Oct   4.  Trigonometric limits. Handout.

Oct   5.  The slope of the tangent line. Problems.

Oct   7.  Quiz 3: 1.6, 2.1.

 

Oct 10.  Columbus day.

Oct 11.  The derivative function. Problems.

Oct 12.  Properties and rules of differentiation. Problems.

Oct 14.  Quiz 4: 2.2-2.4.

 

Oct  17. Derivatives of trigonometric functions. Problems.

Oct  18. Chain rule. Problems.

Oct  19. Examples and practice.

Oct  21. Midterm 1: 8-8:50AM, Main Auditorium.

 

Oct  24. Implicit differentiation. Problems.

Oct  25. Implicit equationsExample. Derivatives of  logarithmic functions.

Oct  26. Logarithmic differentiation. Problems.

Oct  28. Quiz 5: 3.1, 3.2.

 

Oct  31. Derivatives of exponential and inverse trigonometric functions. Problems.

Nov  1.  No class.

Nov  2.  Related rates. Aircraft and observer. Problems.

Nov  4.  Quiz 6: 3.3, 3.4.

 

Nov  7.  Sliding ladder. Spherical vial.

Nov  8.  Local linear approximation. Problems.

Nov  9.  Indeterminacies. Examples. Bernoulli’s rule. Problems.

Nov 11. Quiz 7: 3.5, 3.6.  Differentials. Area ratio. L’Hôpital’s book.

 

Nov 14.  Analysis of functions. Critical points. Inflections.

Nov 15.  Points of local extremum. Problems.

Nov 16.  Examples and practice.

Nov 18.  Midterm 2: 8-8:50AM, Main Auditorium.

 

Nov 21. Analysis of functions. Vertical tangents and cusps. Problems.

Nov 22. Points of absolute extremum. Problems. Quiz.

Nov 23. Thanksgiving break.

Nov 25. Thanksgiving break.

 

Nov 28. Points of absolute extremum.

Nov 29. Optimization. Problems.

Nov 30. Optimization.

Dec  2.  Quiz 9: 4.5.

 

Office hours: Dec 6, 1-2PM, and Dec 8, 1-3 PM

Old exams: Fall 2015, Fall 2010.

 

Dec  9.   Final exam: 10:30-12:30, Nesbitt 125.