MATH – 10B.      Calculus

August, Summer 2017

 MWF, 2:00pm-3:50pm, HSS 1330.  

NEWS      HOMEWORK     HANDOUTS

Instructor:      Professor Vladimir Rotar; office: APM-6353,  e-mail: vrotar@ucsd.edu.

Office hours:  MWF, 4:15-5:15. If it is needed, office hours may be extended.  Some short questions may be answered right after the lectures.

 Text:   Hughes-Hallet et ai, Calculus: Single Variable,  6th  edition. 

Examinations: There will be several quizzes, and a final exam. Homework will be assigned each lecture and posted on the HW site. 

 

SYLLABUS

The list below is rather one of topics than of lectures: the real experience may dictate a slower or faster pace. A slight change of the order of exposition is also possible.

  1. Sec. 5.1-5.2: How do we measure distance travelled? Definite integral.
  2. Sec. 5.3-5.4: The fundamental theorem and interpretations. Theorems about definite integrals. 
  3. Sec. 6.1-6.2: Antiderivatives graphically and numerically. Constructing antiderivatives analytically. 
  4. Sec. 6.3-6.4: Differential equations and motions. The second fundamental theorem of Calculus.  
  5. Sec. 7.1: Integrations by substitutions.
  6. Sec. 7.2: Integrations by parts. 
  7. Sec. 7.3. Tables of integrals.
  8. Sec. 7.4: Algebraic identities and trigonometric substitutions.
  9. Sec. 7.6-7.7: Improper integrals. Comparison of improper integrals.  
  10. Sec. 8.1-8.2: Areas and volumes.  Applications to Geometry (skip arc length of a parametric curve).
  11. Sec. 9.2: Geometric series.
  12. Sec. 10.1: Taylor polynomials. 
  13. Sec. 11.1, 11.4, 11.5: What is a differential equation? Separation of variables. Growth and decay. 
  14. Sec.11.6: Applications and modeling.