|Fall 2020 MAT 307: Multivariable mathematics|
|Schedule||MW 4:25-5:45pm Frey Hall 104|
|Office hours||F 9-11am in Math Tower 4-118, W 6-7pm in Math Learning Center|
|Recitations||M 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|
|Textbook||Williamson 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.|
|Grading||Homework: 20%, Midterm I: 20%, Midterm II: 20%, Final: 40%.|
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Syllabus/schedule (subject to change)
|Mon 8/24||1.||Vectors, Slides||1.1-1.4|
|Wed 8/26||2.||Lines, planes, dot product, Slides||HW Due 8/31: p.7 #9, p.16 #9, p.23 #7, 15, 20, 25, p.31 #2, 7, 14, 17|
|Mon 8/31||3.||Euclidean geometry, cross product, Slides||1.5-1.6, 2.1-2.2|
|Wed 9/2||4.||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 9/9||5.||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 9/14||6.||Determinants, linear functions Odd numbered slides, Even numbered slides||2.5, 3.1-3.3|
|Wed 9/16||7.||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 9/21||8.||Image, null set, coordinates, dimension Odd numbered slides, Even numbered slides||3.4-3.7|
|Wed 9/23||9.||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 solutions||4.1-4.2|
|Wed 9/30||10.||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 10/5||11.||Partial derivatives, parametric surfaces Odd numbered slides, Even numbered slides||4.3-4.4, 5.1-5.2|
|Wed 10/7||12.||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 10/12||13.||Directional derivatives, vector valued functions Odd numbered slides, Even numbered slides||5.3-5.5, 6.1|
|Wed 10/14||14.||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 10/19||15.||Chain rule, implicit differentiation Odd numbered slides, Even numbered slides||6.2-6.5|
|Wed 10/21||16.||Extreme values, curvilinear coordinates||HW 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 10/28||17.||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 11/2||18.||Integral theorems, change of variable Odd numbered slides, Even numbered slides||7.3-7.6|
|Wed 11/4||19.||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 11/9||20.||Numerical integration, line integrals Odd numbered slides, Even numbered slides||7.7, 8.1-8.3|
|Wed 11/11||21.||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 11/16||22.||Flow lines, divergence, curl, Green's theorem Odd numbered slides, Even numbered slides||8.4, 9.1-9.3|
|Wed 11/18||23.||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 11/30||24.||Gauss' Theorem, Stokes' Theorem||9.4-9.6|
|Wed 12/2||25.||Vector field operations||HW Due 12/7 (optional): p.437 #9, 17, 20, 22, 27, p.447 #3, 9, 14, 20, p.457 #12, 16|
Disability Support Services: If you have a physical, psychological, medical, or learning disability that may affect your course work, please contact Disability Support Services (DSS) office: ECC (Educational Communications Center) Building, room 128, telephone (631) 632-6748/TDD. DSS will determine with you what accommodations are necessary and appropriate. Arrangements should be made early in the semester (before the first exam) so that your needs can be accommodated. All information and documentation of disability is confidential. Students requiring emergency evacuation are encouraged to discuss their needs with their professors and DSS. For procedures and information, go to the following web site http://www.ehs.stonybrook.edu and search Fire safety and Evacuation and Disabilities.
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