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