Math 121 – Differential Calculus, Winter 2016

Instructor: Anatolii Grinshpan
Office hours:  Tuesday 12-1 & Thursday 12-2,  Korman 249.

Syllabus    Calendar    Tutoring center    Greg Naber    MIT OCW    Fall 2015

Jan 4.   The idea of a limit. One-sided approach. Example.

Jan 5.   Calculation of limits.

Jan 6.   Calculation of limits. Handout.

Jan 7.   Quiz 1: 1.1, 1.2.

Reading and exercises: 1.1, 1.2.

 

Jan 11. Limits at infinity. Leading terms.

Jan 12. Limits at infinity. The number e.

Jan 13. Continuity.

Jan 14. Quiz 2: 1.3, 1.5.

Reading and exercises: 1.3, 1.5.

 

Jan 18.  MLK day.

Jan 19.  Bolzano’s theorem. Trigonometric limits.

Jan 20.  Trigonometric limits. Handout. Slope of the tangent line.

Jan 21.  Quiz 3: 1.6, 2.1.

Reading and exercises: 1.6, 2.1.

 

Jan 25.  Average vs instantaneous. The derivative function.

Jan 26.  Properties and rules of differentiation.

Jan 27.  Derivatives of trigonometric functions.

Jan 28.  Examples and practice.

Reading and exercises: 2.2-2.5.

 

Feb 1.  Midterm 1: Chapters 1 and 2 (1.4 and 2.6 excepted).

Feb 2.  Chain rule.

Feb 3.  Implicit differentiation. Implicit equations. Example.

Feb 4.  Quiz 4: 2.6, 3.1.

Reading and exercises: 2.6, 3.1.

 

Feb 8.   Derivatives of  logarithmic functions. Logarithmic differentiation.

Feb 9.   Derivatives of exponential functions.

Feb 10. Derivatives of inverse trigonometric functions.

Feb 11. Quiz 5: 3.2, 3.3.

Reading and exercises: 3.2, 3.3.

 

Feb 15. Related rates.

Feb 16. Related rates. Aircraft problem.

Feb 17. Local linear approximation. Differentials.

Feb 18. Quiz 6: 3.4, 3.5.

Reading and exercises: 3.4, 3.5.

 

Feb 22. Bernoulli’s rule. L’Hôpital’s book.

Feb 23. Analysis of indeterminacies. Examples.

Feb 24. Analysis of indeterminacies. Area ratio.

Feb 25. Examples and practice.

Reading and exercises: 3.6.

 

Feb 29. Midterm 2: 2.6, Chapter 3.

Mar   1. Intervals of monotony and concavity. Critical points. Inflections.

Mar   2. Points of local extremum. Polynomials and rational functions.

Mar   3. Quiz 7: 4.1, 4.2. 

Reading and exercises: 4.1, 4.2.

 

Mar  7.  Vertical tangents and cusps. Points of absolute extremum.

Mar  8Optimization. 

Mar  9.  Optimization.

Mar 10. Quiz 8: 4.4, 4.5.

Reading and exercises: 4.3-4.5.

 

Mar 11. Office hours 2-4, Korman 249.

 

Mar 16. Final exam: 10:30-12:30, Randell 121.