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Mechanical Engineering and Mechanics
Subhrajit Bhattacharya

Teaching >>
Calculus II (Math 114-001, Spring 2016, UPenn)
Jan 02, 2016


Functions of several variables, vector-valued functions, partial derivatives and applications, double and triple integrals, conic sections, polar coordinates, vectors and vector calculus. Applications to physical sciences.

Hours and Location

Lectures: Tuesdays and Thursdays, 10:30am - noon (1.5 hours each).
Lecture Location: DRL room A1.
Recitations: Mondays & Wednesdays, 8am-9am & 9am-10am (please check your respective schedules for the exact hours and locations).

Important Dates

  • Lectures start on Jan 14. Last lecture on Apr 26. (Total number of lectures: approx. 28)
  • List of days without lectures: March 8, 10 (Spring Break).
  • Drop Period ends: Feb 19. Last day to withdraw from a course: March 25.
  • First mid-term: Feb 11 (in-class exam)
  • Second mid-term: TBA
  • Final exam: Thursday May 5, 12:00-2:00pm (See https://www.math.upenn.edu/ugrad/calc/m114/ for details.)

Instructor

Subhrajit Bhattacharya
E-mail: subhrabh@math.upenn.edu
Web-site: http://www.math.upenn.edu/~subhrabh
Office location: DRL 3C7
Office hours: Fridays 1-3pm (or by appointment)

Teaching Assistant

Phil Pham
E-mail: See canvas page
Office location: See canvas page
Office hours: See canvas page

Jason Liu
E-mail: See canvas page
Office location: See canvas page
Office hours: See canvas page

Textbooks

  • Thomas' Calculus: Early Transcendentals. (Custom Edition for the University of Pennsylvania), Pearson 2012. ISBN : 978-1-256-82329-2. [Note that this is a customized version specifically made for Penn. The Penn Bookstore should have copies. Homeworks will be assigned from the book, and a few homeworks will be assigned at the MyMathLab online system, the subscription for which comes with the book. So it's strongly recommended that you purchase the book.]

Attendance, Homeworks, Quizzes and Exams

  • Attendance and participation in class is expected. You are expected to attend every lecture and recitation. In case you miss a lecture, you will need to figure out what was covered in that class either by talking to your fellow students, or by stopping by my office hours. It is your responsibility that you do these to catch up with the class.
  • There will be weekly set of recommended homework problems assigned from the textbook, which you do not need to turn in.
  • There will be a few online homeworks assigned through the MyMathLab system, which you'll need to submit online.
  • There will be weekly quizzes at the recitations.
  • There will be three exams: two mid-terms and one final. The first mid-term will tentatively take place around mid-February, and the second mid-term around mid-March.
  • If you miss a weekly quiz due to medical or other emergencies, and need to take a makeup quiz, you'll need to send an official course absence report (CAR) from the university in advance, reporting your absence on the day of the missed quiz. For taking makeup exam, in addition to sending an official course absence report, you'll also need to have an email sent to me by your academic advisor confirming your valid/serious reason of absence on the day of exam. No other form of letter/certificate will be accepted. CAR sent more than a week from the day of missed quiz/exam cannot be accepted and no makeup quiz/exam will be allowed in that case.

Grading Scheme

Weekly quizzes and online homeworks: 15%
Midterm 1: 25%
Midterm 2: 25%
Finals: 35%


[ + ]   Detailed List of Topics Covered by Date.
Day Topics covered
Jan 14 Three-Dimensional Coordinate Systems (section 12.1), Vectors (section 12.2)
Jan 19 Dot product (12.3), Cross product (12.4)
Jan 21 Cross product (12.4), Lines in Space (12.5)
Jan 26 Lines and Planes in Space (12.5), Conic Sections (11.6), Quadric Surfaces (12.6)
Jan 28 Quadric Surfaces (12.6), Curves in Space and their Tangents (13.1)
Feb 2 Curves in Space and their Tangents (13.1), Integral of Vector Functions, Projectiles (13.2)
Feb 4 Integral of Vector Functions, Projectiles (13.2), Arc length in space (13.3), Curvature (13.4)
Feb 9 Curvature and Normal Vector (13.4), Tangent and Normal components of acceleration (13.5)
Feb 11 Midterm 1
Feb 16 Tangent and Normal components of acceleration (13.5), Velocity and Acceleration in Polar Coordinates (13.6)
Feb 18 (Lecture by Dr. Shilin Yu) Functions of Several Variables (14.1), Limits and Continuity in Higher Dimensions (14.2)
Feb 23 Limits and Continuity in Higher Dimensions (14.2), Partial derivatives (14.3), Chain rule (14.4)
Feb 25 Chain rule (14.4), Directional derivative and Gradient (14.5)
Mar 1 Directional derivative and Gradient (14.5)
Mar 3 Directional derivative and Gradient (14.5), Tangent plane and Differentials (14.6)
Mar 15 Tangent plane and Differentials (14.6), Extreme Values and Saddle points (14.7)
Mar 16 Midterm 2
Mar 22 (Lecture by Dr. Robert Ghrist) Constrained Optimization / Lagrange Multipliers (14.8)
Mar 24 (Lecture by Dr. Shilin Yu) Double and iterated integrals over Rectangles (15.1), Double integrals over general regions (15.2)
Mar 29 Double integrals over general regions (15.2), Area by double integration (15.3), Double Integrals in Polar form (15.4)
Mar 31 Double integrals in polar form (15.4), Triple integral in rectangular coordinates (15.5)
Apr 5 Triple integral in rectangular coordinates (15.5), Moments and Centers of Mass (15.6)
Apr 7 Moments and Centers of Mass (15.6), Triple Integrals in Cylindrical and Spherical Coordinates (15.7)
Apr 12 Line Integrals (16.1), Vector fields (16.2)
Apr 14 Vector Fields and Line Integrals (16.2), Path independence (16.3)
Apr 19 Path Independence, Conservative Fields, and Potential Functions (16.3), Green's Theorem in the Plane (16.4)
Apr 21 Green's Theorem in the Plane (16.4), Surfaces and Area (16.5), Surface Integrals (16.6), Stokes' Theorem (16.7)
Apr 26 Surface Integrals (16.6), Stokes' Theorem (16.7), Divergence Theorem (16.8)

Course Outline (Subject to Change)

See the Mathematics Department's Calculus Homepages for Math 114.

Additional Resources


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