Fall 2020 MAT 307: Multivariable mathematics
ScheduleMW 4:25-5:45pm Frey Hall 104
InstructorRobert Hough
Office hoursF 9-11am in Math Tower 4-118, W 6-7pm in Math Learning Center
TAJared Krandel
RecitationsM 6:05-7pm or Th 4:45-5:40pm in Earth and Space 69
Description Introduction to linear algebra: vectors, matrices, systems of linear equations, bases and dimension, dot product, determinants. Multivariate differential and integral calculus, divergence and curl, line and surface integrals, theorems of Green, Gauss, and Stokes. More theoretical and intensive than MAT 203, this course is primarily intended for math majors. Together with MAT 308, it forms a 2-semester sequence covering the same material as the 3-semester sequence of MAT 205, MAT 211 and MAT 305. May not be taken for credit in addition to MAT 203, MAT 205 or AMS 261.
Prerequisites MAT 127 or MAT 132
TextbookWilliamson and Trotter. Multivariable Mathematics. Pearson Education (2004).
Homework Weekly problem sets will be assigned, and collected in class on Monday. Late homework is not accepted, but under documented extenuating circumstances the grade may be dropped. Your lowest homework grade will be dropped at the end of the class.
GradingHomework: 20%, Midterm I: 20%, Midterm II: 20%, Final: 40%.

Face mask policy: If a student does not wear a face mask, please follow these steps: Students should be aware that a face mask is required while in the classroom. If a student does not comply, the student will be asked to leave the classroom. If the student does not comply or leave the classroom, we will end the class and the students will be reported to the Office of Student Conduct and Community Standards at communitystandards@stonybrook.edu.

Accommodations for students with hearing and communication impairments: Some students with hearing and communication impairments may need their instructor to wear a clear mask for lip and facial expression purposes. If the student has registered with the Student Accessibility Support Center (SASC) and has requested an accommodation for clear masks, SASC will reach out to the students instructors and provide a clear mask for them to wear while teaching and/or interacting with the student. If you have questions, please email sasc@stonybrook.edu or call (631) 632-6748.

Face mask accommodations, modifications or exemptions: The Student Accessibility Support Center (SASC) works with students who may require academic accommodations. If a student is unable to wear a mask for health reasons, the student should contact SASC at sasc@stonybrook.edu. SASC will work with the student to help identify arrangements to complete in-person courses in an alternate format. If, however, there is an in-person class that cannot be accommodated in an alternate format, a student may be approved by the Medical Director of Student Health Services to wear a modified face mask or no face covering. In this situation, SASC will communicate this information to the faculty member. Approved students will also be provided with a written exemption from the Medical Director of Student Health Services that indicates any modifications or exceptions, which they must carry with them to show faculty if requested. Please note that medical exemptions are rare and are based solely on medical necessity. If a student is exempt from the face mask policy, please consider how to seat students to ensure proper social distancing within a given instructional setting. If you have questions regarding accommodations, please email sasc@stonybrook.edu. For health related concerns in the classroom, please contact Dr. Rachel Bergeson, Medical Director, at rachel.bergeson@stonybrook.edu.

Syllabus/schedule (subject to change)
Mon 8/241. Vectors, Slides 1.1-1.4
Wed 8/262. Lines, planes, dot product, SlidesHW Due 8/31: p.7 #9, p.16 #9, p.23 #7, 15, 20, 25, p.31 #2, 7, 14, 17
Mon 8/313. Euclidean geometry, cross product, Slides 1.5-1.6, 2.1-2.2
Wed 9/24. Linear systems, matrix methods Slides HW Due 9/9: p.36 #5, 13, 20, p.42 #3, 11, 21, p.51 #8, 12, 16, p.58 # 7, p.69 #7, 16, 19, 23, p.73 #4, 11
Mon 9/7 No class - Labor day 2.3-2.4
Wed 9/95. Matrix algebra, inverse matrices Odd numbered slides, Even numbered slides HW Due 9/14: p.80 #3, 29, 33, 40, 50, p.86 #5, 8, 14, 34
Mon 9/146. Determinants, linear functions Odd numbered slides, Even numbered slides 2.5, 3.1-3.3
Wed 9/167. Vector spaces, linear functions Odd numbered slides, Even numbered slides HW Due 9/21: p.98 #2, 6, 11, 22, p.110 #4, 16, p.118 #12, 13, 21, 32, p.125 #17, 20
Mon 9/218. Image, null set, coordinates, dimension Odd numbered slides, Even numbered slides 3.4-3.7
Wed 9/239. Eigenvalues, eigenvectors, inner products Odd numbered slides, Even numbered slides HW Due 9/30: p.130 #13, 16, 21, p.137 #27, p.142 #7, 10, p.148 #6, p.154 #2, 4, 9, 15, p.158 #6, 11, p.167 #4, 12, p.170 #2, 6
Mon 9/28 Midterm 1 Practice Midterm, Solutions, Midterm 1 solutions4.1-4.2
Wed 9/3010. Functions of one variable, several independent variables Odd numbered slides, Even numbered slides HW Due 10/5: p.182 #12, 14, 17, 34, 35, p.185 #5, p.187 #13, 23, p.192 #16, p.195 #16, p.198 #5
Mon 10/511.Partial derivatives, parametric surfaces Odd numbered slides, Even numbered slides 4.3-4.4, 5.1-5.2
Wed 10/712. Limits, continuity, real functions Odd numbered slides, Even numbered slides HW Due 10/12: p.203 #4, 22, 34, 36, 38, 48, p.210 #23, 26, p.224 #32, 34, 35, 36, p.232 #6, 12, 21, 24
Mon 10/1213. Directional derivatives, vector valued functions Odd numbered slides, Even numbered slides 5.3-5.5, 6.1
Wed 10/1414. Newton's method, gradient fields Odd numbered slides, Even numbered slides HW Due 10/19: p.236 #9, 17, 22, p.243 #4, 9, 26, p.250 #3, p.257 #2, 10, 27, 39, p.261 #4
Mon 10/1915. Chain rule, implicit differentiation Odd numbered slides, Even numbered slides 6.2-6.5
Wed 10/2116. Extreme values, curvilinear coordinatesHW Due 10/28: p.269 #2, 8, 13, p.274 #9, p.281 #3, 14, 18, p.292 #4, 12, 23, 30, 31, p.298 #4, p.308 #8, 10, 11
Mon 10/26 Midterm 2 Practice Midterm 2, Solutions, Midterm 2 solutions 7.1-7.2
Wed 10/2817. Iterated integrals, multiple integrals Odd numbered slides, Even numbered slides HW Due 11/2: p.321 #3, 4, 8, 27, p.332 #8, 9, 12, 13, 18
Mon 11/218. Integral theorems, change of variable Odd numbered slides, Even numbered slides 7.3-7.6
Wed 11/419. Centroids, moments, improper integrals Odd numbered slides, Even numbered slides HW Due 11/9: p.336 #3, 8, p.346 #4, 11, 27, p.352 #7, 9, 23, p.358 #7, 15, 16
Mon 11/920. Numerical integration, line integrals Odd numbered slides, Even numbered slides 7.7, 8.1-8.3
Wed 11/1121. Weighted curves, surfaces of integration Odd numbered slides, Even numbered slides HW Due 11/16: p.363 #9, p.376 #1, 5, 23, 28, p.382 #7, 10, 11, p.385 #5, 8, 11
Mon 11/1622. Flow lines, divergence, curl, Green's theorem Odd numbered slides, Even numbered slides 8.4, 9.1-9.3
Wed 11/1823. Conservative vector fields, surface integrals Odd numbered slides, Even numbered slides HW Due 11/30: p.394 #5, 14, p.408 #11, 13, 17, 20, p.419 #5, 11, 14, 20, p.429 #4, 10, 27
Mon 11/23 No class - Thanksgiving
Wed 11/25 No class - Thanksgiving
Mon 11/3024. Gauss' Theorem, Stokes' Theorem9.4-9.6
Wed 12/225. Vector field operationsHW Due 12/7 (optional): p.437 #9, 17, 20, 22, 27, p.447 #3, 9, 14, 20, p.457 #12, 16
Mon 12/726. Review
Final Exam: Wednesday December 9, 8:30-11:00PM Practice final, practice final solutions.

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