MATH2010 Multivariable Calculus and Matrix Algebra

Course Outline

MTRF 1.30–3.35 (virtual). WebEx: 2.30-3.30, class days, mitchj Summer 2020

Instructor: John Mitchell, Amos Eaton 325, x6915, mitchj at rpi dot edu

Teaching Assistant: Rachel Wesley, wesler at rpi dot edu

Text:

Part A: Multivariable Calculus: | Calculus: Early Transcendentals, 3rd or 4th edition, by J. Rogawski and C. Adams (and R. Franzosa). Required. |

Part B: Matrix Algebra: | Introduction to Linear Algebra, 5th edition, by L. W. Johnson, R. D. Riess, and J. T. Arnold. Required. |

Approximate schedule: (some sections may be omitted, depending on time)

Multivariable calculus: Section numbers are from the 4th edition. The chapter numbers in the 3rd edition are larger by one, so the course covers material from Chapters 15–18 in the 3rd edition.

- Week 1:

Functions of several variables and level curves (14.1), Partial derivatives (14.3), Tangent plane and differentials (14.4), Chain rules (14.6), Directional derivative and gradient (14.5), General tangent plane (14.5), Max/Min problems for functions of two variables (14.7), Lagrange multipliers (14.8). - Week 2:

Integration in two variables (15.1), over more general regions (15.2), Triple integrals (15.3), Change of variables: polar coordinates (15.4), Applications of multiple integrals (15.5). - Week 3:

Vector fields: curl, divergence, conservative fields (16.1), Line integrals and work (16.2), Conservative vector fields and path independence (16.3), Fundamental Theorem of line integrals (16.3), Green’s Theorem (17.1).

Matrix algebra:

- Week 4:

Matrices and systems of equations (1.1), Echelon forms and Gauss-Jordan elimination (1.2), Consistent systems (1.3), Matrix operations (1.5), Identity matrix and transpose (1.6), Linear Independence and nonsingularity (1.7), Matrix inverse and properties (1.9). - Week 5:

Vector space ℝ^{n}and subspaces (3.2), Span, nullspace, range, rowspace (3.3) Basis and coordinates (3.4), Dimension; rank, nullity (3.5), Orthogonal bases: Gram-Schmidt procedure (3.6). - Week 6:

Eigenvalues for 2 × 2 matrices (4.1), Determinants and eigenvalues (4.2), Elementary operations and determinants (4.3), Characteristic polynomial (4.4), Eigenvectors and eigenspaces (4.5), Complex eigenvalues (4.6), Diagonalization (4.7).

Lectures: Lectures will be prerecorded. They will be posted on LMS and on box. Typed slides will be made available, as will the lectures themselves, which will consist of an audio track while the notes are presented on an ipad. The ipad notes will also be available. I will be available on webex for questions for the second hour of each lecture slot.

Homework: There will be approximately two weekly assignments, generally based on the text. The assigned
questions should be written up neatly and submitted on LMS.

Collaboration: You are encouraged to discuss the problems with your classmates, but the work you turn in must be
all your own. It is not acceptable to copy all or part of homework solutions from another person, whether or not
that person is currently enrolled in the course.

Late policy: All assignments will have a specific due date, usually on Mondays and Thursdays. Because of the accelerated summer schedule, late homeworks will not be accepted.

Exams: There will be two exams, both required:

Friday June 12, | covering multivariable calculus | |

Friday July 10, | covering matrix algebra. |

As you would expect, no collaboration is permitted on the exams. The exact structure of the exams is still to be determined. Currently, my plan is to allow you to choose a start time: either the class start time, or 10pm eastern. You’d then have 6 hours to complete the exam. Each exam should not require nearly this much time, but I am adding in some time to allow for download and upload.

Grades: 50% for homeworks, 25% for each exam. The percentages for grade cutoffs will be no stricter than:

A | A- | B+ | B | B- | C+ | C | C- | D+ | D |

93 | 90 | 87 | 83 | 80 | 77 | 73 | 70 | 67 | 60 |

The World Wide Web: This outline, the homeworks, and other information about the course will be available
via my homepage,

http://www.rpi.edu/~mitchj/math2010

There will also be an LMS page for the course.

Office hours:

John Mitchell | MTRF 2:30– 3:30 | webex: mitchj |

Rachel Wesley | webex and slack as needed
| |

Course learning outcomes: Upon successful completion of the course, students will be able to demonstrate the ability to:

- solve multivariable optimization problems
- evaluate differential form line integrals using path independence and the Fundamental Theorem of Line Integrals when appropriate
- use Green’s Theorem to evaluate circulation line integrals
- solve linear systems using Gauss-Jordan elimination
- compute the inverse of a non-singular matrix and use it to solve a linear system
- find a basis for and the dimension of subspaces relating to solving linear systems
- compute the eigenvalues and corresponding eigenvectors of a square matrix

Computer packages: Packages you may find useful include Matlab, Maple, and Mathematica. The course will not require the use of these packages. Some concepts will be illustrated using figures generated using Matlab.

Academic integrity: Student-teacher relationships are based on mutual trust. Acts which violate this trust undermine the educational process. The Rensselaer Handbook defines various forms of academic dishonesty and procedures for responding to them. The penalties for cheating can include failure in the course, as well as harsher punishments.

Appealing grades: As with any other administrative question regarding this course, see me in the first instance. If we are unable to reach agreement, you may appeal my decision to Professor Schwendeman.