Math 0200: Intermediate Calculus (Physics/Engineering)
S 01



This is the website for Section 1 of Math 0200: Intermediate Calculus (Physics/Engineering). You should also periodically check the main course website for homework information.

Announcements  · Course Information  ·  Homework Assignments  ·  Lecture Summary


Announcements


Course Information

A PDF copy of the syllabus can be downloaded here.

Instructor:

Samuel Walsh (Samuel_Walsh "at" brown.edu)

TA:

Dylan Cashman (Dylan_Cashman "at" brown.edu)

Text:

Edwards & Penney, Multivariable Calculus (6th edition)

Lectures:

12:00--12:50 MWF, 12:00--12:50 R (Recitation) in BH163

Office hours:

(Sam) M: 11:00--11:50, (Room 020, 182 George St.)
W: 4:30--5:30 (M level of Science Library.)

(Dylan) W: 2:00-4:00
(M level of Science Library)


Overview.   Multivariable calculus is one of the central tools of the physical sciences. For example, the motion of an incompressible (Newtonian) fluid is governed by the Navier-Stokes equation,


and the fundamental laws of electromagnetism are described by Maxwell's equations,


The goal of this course is fairly simple: by the end of the semester, you should be able to understand equations like those above. More than that, though, you should be comfortable enough with calculus in several variables to manipulate the quantities involved. The course will cover Chapters 12 through 15 of Edwards and Penney. The following is a rough list of topics.
  • Vectors, curves, surfaces. 2-d and 3-d vectors, dot product, cross product, lines and planes in space, curves.
  • Differential calculus in higher dimensions. Continuity, limits, partial differentiation, optimization, chain rule, gradients.
  • Multiple integrals. Double integrals, area, volume, triple integrals, integration in other coordinate systems, change of variables.
  • Vector calculus. Vector fields, line integrals, Green's theorem, surface integrals, divergence theorem, Stokes' theorem.
Recitations.   Beginning 9/17, there will be a recitation session held every Thursday from 12:00--12:50 in BH 163. Recitations are meant primarily to reinforce the material presented in the lecture, as well as giving you the opportunity to discuss the homework assignments. You should view these sessions as part of the course proper, i.e., you need to go to them.

Office hours.   I plan (tentatively) to hold office hours following class Mondays and Wednesdays, from 1:00-1:50 in Room 020, 182 George St. (the Applied Math building, adjacent Barus and Holley.) You can also email me to set up an appointment if that time is inconvenient.

Homework.   The majority of your learning for the course will come through completing the homework assignments. These will be posted weekly on the course website. Homework is to be turned in Fridays at the beginning of class. You are encouraged to work together, but each student must write his or her own; do not simply copy one another. Also, please remember that the grader has to be able to follow your thought process in order to award credit. It is incumbent on you to ensure that your assignments are readable, both in terms of legibility and comprehensibility. Given the size of the course, and the speed at which we're going to be moving, late homework will not be accepted.

Exams.   There will be two midterm exams as well as a cumulative final:

Midterm I:

7:00 PM, October 7th

Midterm II:

7:00 PM, November 11th

Final:

2:00 PM, December 15th

Room information will be given closer to the date; see the course website for details. The exams are common among all sections of the course.

Grading.   Your final grade will be determined according to the following formula:

Homework:

20%

Midterm I & II:

30% (15% each)

Final:

50%


Homework Assignments

Assignment 1 (Due: 9/17)
12.1: 34, 46, 47; 12.2: 26, 40, 56; 12.3: 2, 14.

Assignment 2 (Due: 9/24)
12.3: 18, 20, 36; 12.4: 2, 14, 48, 54; 12.5: 2, 40, 44.

Assignment 3 (Due: 10/01)
12.5: 50, 58, 64; 12.6: 2, 8, 54; 12.7: 4, 6, 34, 54.

Assignment 4 (Due: 10/09)
Chapter 12 (Misc. Problems): 6, 9, 12, 15, 20, 22, 43, 51; 13.2: 34, 40, 56.

Assignment 5 (Due: 10/16)
13.4: 14, 18, 24, 32, 38, 56, 58; 13.5: 14, 22, 40, 46; 13.6: 32.

Assignment 6 (Due: 10/23)
13.6: 34, 44; 13.7: 2, 20, 30, 34, 38, 48; 13.8: 12, 50, 56.

Assignment 7 (Due: 10/30)
13.9: 2, 14, 40, 44, 62; 13.10: 6, 10, 28, 30.
(In problems 6 and 10 sketch the level curves ("contour plot") of f.)

Assignment 8 (Due: 11/6)
14.1: 16, 32 14.2: 2, 8, 18, 22, 28, 32; 14.3: 4, 20, 28, 40, 44.

Assignment 9 (Due: 11/14)
14.4: 4, 32 14.5: 41; Chapter 13 (Misc. Problems): 36, 39; Chapter 14 (Misc. Problems): 2,4,8,16,26.

Assignment 10 (Due: 11/20)
14.6: 10, 44, 50, 51 14.8: 4, 6, 16;


Lecture Summary

I will maintain a list of the topics covered in each lecture, as well as a best estimate of what we'll talk about in the upcoming lectures. Most people find it very beneficial to read the section in advance.
  • Lecture   1: Section 12.1: 2-d vectors, algebra of vectors; magnitude.
  • Lecture   2: First half of section 12.2: Geometry of 3-d space, vectors in 3-d, algebraic rules for the dot product (scalar product), geometric interpretation of the dot product.
  • Lecture   3: Projections, work, power. Section 12.3: definition of cross product, matrix representation.
  • Lecture   4: Geometric interpretation of cross product, algebraic properties, scalar triple product.
  • Lecture   5: 12.4: Lines and beginning of planes.
  • Lecture   6: Finish description of planes in 3-d. 12.5: parametric curves in space; calculus with vector-valued functions.
  • Lecture   7: Velocity, acceleration; integration of vector-valued functions and applications.
  • Lecture   8: 12.6: arc length and curvature of plane curves.
  • Lecture   9: Finish discussion of curvature. 12.7: Quadric surfaces.
  • Lecture 10: A few more examples of quadric surfaces; 13.2: Level curves and contours; 13.3: Limits in multiple dimensions.
  • Lecture 11: Start 13.4: Partial derivatives and applications.
  • Lecture 12: Higher-order partial derivatives; 13.5: optimization for functions of several variables.
  • Lecture 13: Applied optimization problems. Start 13.6: linear approximations and increments.
  • Lecture 14: Continue with linear approximation, differentials, gradients. Start 13.7: Multivariable chain rule.
  • Lecture 15: More multivariable chain rule, Implicit Function Theorem.
  • Lecture 16: Change of variables; Start 13.8: Directional derivatives and the gradient.
  • Lecture 17: Applications of the directional derivative; the gradient revisited.
  • Lecture 18: Lagrange multipliers: the two- and three-dimensional case.
  • Lecture 19: Continuation of Lagrange multipliers: more examples, multiple constraints.
  • Lecture 20: 13.10: Classification of critical points. Start 14.1: Double integrals.
  • Lecture 21: Riemann sums for functions of two variables; analytic evaluation of double integrals via the Fubini-Tonelli theorem and iterated integrals; Start 14.2: Integration over more general domains.
  • Lecture 22: Continue discussion of integration over general domains; Start 14.3: Calculation of area and volume by integration.
  • Lecture 23: 14.4: Double integration in polar coordinates.
  • Lecture 24: Finish double integration in polar; 14.5: Applications of double integration, centroids.
  • Lecture 25: 14.6: Triple integration.
  • Lecture 26: A few more examples of triple integrals; Integration in cylindrical coordinates; A few words on surface parameterization.
  • Lecture 27: Calculation of surface area; Introduction to vector fields.
  • Lecture 28: More vector fields: divergence, and curl. 15.2: Line integrals.
  • Lecture 29: Line integrals with respect to arc length and coordinates.
  • Lecture 30: (Upcoming) Line integrals of vector fields; 15.3: Path independence.