Math 121 – Differential Calculus, Spring 2015

Instructor: Anatolii Grinshpan
Office hours:  Mon 2-3 & Wed 1-3,  Korman 249.

Syllabus    Calendar    Tutoring center    Greg Naber    MIT OCW    Fall 2014

Mar 30.   Introduction to the course.  The idea of a limit.

Mar 31.   Evaluation of limits. Example.

Apr   1.   Evaluation of limits. Handout. Example.

Apr   2.   Quiz 1: 1.1, 1.2.

 

Apr   6.   Limits at infinity. Leading terms. Hyperbolic functions.

Apr   7.   Limits at infinity. The number e.

Apr   8.   Continuity. Classification of discontinuities. Bolzano’s theorem.

Apr   9.   Quiz 2: 1.3, 1.5.

 

Apr 13.  Trigonometric limits. Handout. The slope of the tangent line.

Apr 14.  Calculation of slopes. Tangent line equation. Power rule.

Apr 15.  The derivative function.

Apr 16.  Quiz 3: 1.6, 2.1.

 

Apr 20.  Product and quotient rules.

Apr 21.  Techniques of differentiation.

Apr 22.  Examples and practice. Example.

Apr 23.  Midterm 1: Chapters 1 and 2 (1.4 and 2.6 excepted).

 

Apr 27.  Chain rule.

Apr 28.  Implicit differentiation.

Apr 29.  Working with implicit equations. Example.

Apr 30.  Quiz 4: 2.6, 3.1.

 

May 4.   Derivatives of logarithmic functions. Logarithmic differentiation.

May 5.   Derivatives of exponential functions.

May 6.   Derivatives of inverse trigonometric functions.

May 7.   Quiz 5: 3.2, 3.3.

 

May 11. Related rates.

May 12. Related rates. Aircraft problem.

May 13. Local linear approximation.

May 14. Quiz 6: 3.4, 3.5. Differentials.

 

May 18. Bernoulli’s rule.

May 19. Evaluation of indeterminacies. Question.

May 20. Examples and practice.

May 21. Midterm 2: 2.6, Chapter 3.

 

May 26. Intervals of monotony and concavity. Critical points. Inflections.

May 27. Points of local extremum.

May 28. Quiz 7: 4.1, 4.2. Vertical tangents and cusps.

 

June  1.  Points of absolute extremum.

June  2.  Optimization.

June  3.  Optimization.

June  4.  Quiz 8: 4.4, 4.5.

 

June 11. Final exam: 6-8PM, Randell 326.