MATH – 20B.
Calculus
Summer, July, 2015
MWF,
2:00pm-3:50pm, APM B402a.
NEWS
HOMEWORK HANDOUTS
Instructor: Professor Vladimir
Rotar; office: APM-7450, 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:
Rogawski, Calculus: Early
Transcendentals, 2nd
edition, and
The supplement to Rogawski’s book. (download
here).
Examinations: There
will be several quizzes, and a final exam. Homework will be assigned each
lecture and posted in 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.
5.2-5.4: Review of the Fundamental Theorem of Calculus. Sec. 5.5: Total change as the integral
of a rate.
- Sec.
5.6: The substitution algorithm for integrals. Sec. 6.1: Areas between curves.
- Sec.
6.2-6.3: Volumes; average value of a function; the mean value theorem. The
basic method is slicing a solid into pieces of known cross-sectional area;
solids of revolution are a special case.
- Sec. 11.3-11.4: Polar coordinates; areas in polar
coordinates. Supp. 1–2: Complex
numbers and complex exponentials: De Moivre’s
theorem, complex roots, and Euler’s formula.
- Sec. 7.1: Integration by parts. Sec. 7.2, 7.4, Supp
3. Trigonometric integrals, Sec. 7.3: Trigonometric substitution (may be
omitted).
- Supp. 4-5,
Sec. 7.5: The fundamental theorem of algebra; partial fractions and
integration of rational functions using partial fractions.
- MIDTERM (can be replaced by quizzes).
- Sec. 7.6: Improper integrals. Sec. 7.8. Numerical integration.
- Sec. 10.1: Sequences: limits, convergence, and
divergence.
- Sec. 10.2: Series. Sec. 10.3: Series with positive
terms: the integral and comparison tests.
- Sec. 10.4-10.5: Absolute convergence; the ratio and
root tests. Sec. 10.6: Power series.
- Sec.10.7: Taylor
series.
- Sec. 9.1-9.2: Solving differential equations;
exponential models.