Math 20 C - Fall 2011

Meeting Time	Mon., Wed., Fri., 12:00 - 12:50
Location	PETERSON 108
Instructor	Dragos Oprea Office: APM 6-101 Office Hours: Wednesday 5-6, Friday 3-4 APM 6-101. Email: `doprea at math dot ucsd dot edu`
Course Assistants	Zhehua Li Section B01, 1-1:50PM, WLH 2115 Section B02, 2-2:50PM, WLH 2115. Office: APM 5412 Office Hours: Thursday 11-12, Calculus Lab Tuesday 1-2. Email: `zhl033 at ucsd dot edu.` Brian Longo Section B03, 3-3:50PM, WLH 2115. Section B04, 4-4:50PM, WLH 2115. Office: APM 6414 Office Hours: Thursday 1-2, Calculus Lab Tuesday 2-3. Email: `blongo at math dot ucsd dot edu.` Daniel Schulheis Section B05, 5-5:50, WLH 2115. Section B06, 6-6:50, WLH 2115. Section B07, 7-7:50, WLH 2115. Section B08, 8-8:50, WLH 2115. Office: APM 6434 Office Hours: Monday 1-2pm, Calculus Lab Wednesday 3-5pm. 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, 11:30-2:30. 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 Thursday-Friday November 24-25: Thanksgiving Recess -- No Class Thursday, December 8: FINAL EXAM, 11:30-2:30 pm Starting Monday, 10/10/11 we are moving to PETERSEN 108.
Exams	Practice Problems and solutions for Midterm I Midterm I and Solutions Practice Problems and solutions for Midterm II Midterm II and Solutions Practice Problems for the Final Exam and Solutions Final Exam and Solutions
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 Calculus Tutoring Calculus Online Community.
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.