Meeting Time  Mon., Wed., Fri., 12:00  12:50 
Location  PETERSON 108 
Instructor 
Dragos Oprea

Course Assistants 
Zhehua Li
 Section B01, 11:50PM, WLH 2115
 Section B02, 22:50PM, WLH 2115.
 Office: APM 5412
 Office
Hours: Thursday 1112, Calculus Lab Tuesday 12.
 Email:
zhl033 at ucsd
dot edu.
Brian Longo
 Section B03, 33:50PM, WLH 2115.
 Section B04, 44:50PM, WLH 2115.
 Office: APM 6414
 Office Hours: Thursday 12,
Calculus Lab Tuesday 23.
 Email: blongo at math dot ucsd dot
edu.
Daniel Schulheis
 Section B05, 55:50, WLH 2115.
 Section B06, 66:50, WLH 2115.
 Section B07, 77:50, WLH 2115.
 Section B08, 88:50, WLH 2115.
 Office: APM 6434
 Office Hours: Monday 12pm,
Calculus Lab Wednesday 35pm.
 Email: dschulth at math
dot
ucsd dot edu.

Textbook  Rogawski's Calculus,
Early Transcendentals Required and available at the bookstore and on reserve in the library.

Grade Breakdown  The grade is computed as the best of
the following weighed averages:
 Homework 15%, Midterm I 20%, Midterm II 20%, Final
Exam 45%.
 Homework 15%, Midterm I 15 %, Midterm II 15%, Final
Exam 55%.

Course Content  Vector geometry, vector functions and
their derivatives. Partial differentiation. Maxima and minima. Double
integration.

Prerequisites  AP Calculus BC score of 4 or 5 or Math 20B with a
grade of C
or better. 
Readings  Reading the sections of the textbook
corresponding to
the assigned homework exercises is considered part of the homework
assignment. You are responsible for material in the assigned reading
whether or not it is discussed in the lecture. It will be expected that
you read the assigned material in advance of each lecture. 
Calculators  Calculator use will not be
permitted
on exams. Graphing calculators are not required for the
course. 
Homework 
Homework problems will be assigned on the
course
homework
page. You may drop the homework in the drop box on the 6th floor of
AP&M by 4:30 PM on Friday. You may work together with your classmates
on your
homework
and/or ask the instructors, the TA's, or tutors in the calculus lab for
help on assigned homework problems. However, the work you turn in must be
your own. No late homework assignments will be accepted.
Please adhere to
the following neatness guidelines for homework that you turn in to be
graded.
 Write your name and section clearly on the front page of
your completed assignment.
 Clearly number each solution.
 Write clearly and legibly.


Midterm Exams  There will be two midterm exams given
in
class. The dates are Oct 21 and Nov 21. There will be no makeup exams. A
page of handwritten notes, front only, is allowed.

Final Exam  The final examination will be held on
Thursday, December 8, 11:302:30. There is no make up final
examination. It is your responsability
to ensure that you do not have a schedule conflict during the final
examination; you should not enroll in this class if you cannot
sit for the final examination at its scheduled time. 
Academic Dishonesty  Academic dishonesty is
considered a serious offense at UCSD. Students caught cheating will face
an administrative sanction which may include suspension or expulsion from
the university. 
Announcements and
Dates

 Friday, September 23: First lecture
 Friday, October 7: Add deadline
 Friday, October 21, Midterm I
 Friday, October 21: Drop deadline
 Friday, November 11: Veterans' Day
 Monday, November 21, Midterm II
 ThursdayFriday November 2425: Thanksgiving Recess  No Class
 Thursday, December 8: FINAL EXAM, 11:302:30 pm
Starting Monday, 10/10/11 we are moving to PETERSEN 108.

Exams 

Additional Help 
If you are having trouble with the homework or have questions about the
material, the best way to get help is to attend the office hours offered
by me and the teaching assistants. If you can't make the scheduled
times, then email us and we'll set up an appointment.
Additional help is given by

Lecture Summaries 
 Lecture 1: Course introduction and outline; policies.
 Lecture 2: Vectors and vector operations. Scalar
multiplication,
addition. Geometric applications: spheres, cylinders and lines.
 Lecture 3: Dot product. Algebraic definition. Angle between
two
vectors. Decomposing a vector into
components perpendicular and parallel to another fixed vector.
 Lecture 4: Cross product. Determinants.
Algebraic definition of cross products. Anticommutativity. Geometric
applications:
cross product is perpendicular to both vectors, length of the cross
product equal to area of parallelogram spanned by vectors, right hand
rule.
 Lecture 5: Applications of vectors: equations of planes. Plane
normal to a vector.
Plane through 3 points. Angle between planes.
 Lecture 6: Parametric curves in plane and space. Examples
including the cycloid and helix.
 Lecture 7: Vector valued functions. Limits. Continuity.
Derivatives. Rules: chain rule, product rules. Integration of vector
valued functions. Fundamental theorem of calculus.
 Lecture 8: Arclength. Examples: astroid, helix. Speed.
Parametrization by arclength. 4 step algorithm to find it. Examples.
 Lecture 9: Acceleration vector. Applications to mechanics.
 Lecture 10: Functions of several variables. Level curves and
graphs. Cones. Paraboloids.
 Lecture 11: Limits and continuity. Examples when the limit
does
not exist  approaching the origin from all possible slopes. The squeeze
theorem.
 Lecture 12: Midterm topics and review.
 Lecture 13: Partial derivatives. Definition and geometric
interpretation. Higher order derivatives. Order of differentiation.
 Lecture 14: Tangent plane to graphs. Linear approximation.
Examples.
 Lecture 15: Gradient. Tangent planes to level contours.
Directional derivative. Connection between directional derivatives and
gradient. Direction of steepest increas.
 Lecture 16: Multivariable chain rule and examples. Drawing
the tree diagram.
 Lecture 17: Critical points. Local min and local max. Saddle
points. Second derivative test. Examples.
 Lecture 18: Closed and bounded sets (compact sets). Continuous
functions on compact sets have at least one min and one max. Examples
(function defined on a rectangle, and function defined on a disk).
 Lecture 19: Lagrange multipliers: along constrained
optimization, gradients are parallel/proportional.
Several constraints. Examples.
 Lecture 20: Double integrals. Volume under graph. Iterated
integrals. Order of integration. Examples.
 Lecture 21: Double integrals over more complicated regions.
Simple regions. Changing the order of integration. Average value.
 Lecture 22: Triple integrals. Integrals over boxes and simple
regions. Examples. Applications: volume, density, average.
 Lecture 23: Midterm topics and review.
 Lecture 24: Polar, cylindrical and spherical coordinates.
Integration in polar coordinates.
 Lecture 25: Integration in cyldrical coordinates. Integration
in spherical
coordinates. Examples.
 Lecture 26: Final Exam Topics and Review.
