# Math 321: Applied Mathematical Analysis I (Fall 2019) (Vector and Complex Calculus for the Physical Sciences)

 Lecture Room: B239 Van Vleck Lecture Time: 9:30–10:45 TuTh Lecturer: Jean-Luc Thiffeault Office: 503 Van Vleck Email: Office Hours: see syllabus

## Syllabus

See the syllabus for information about the class, including textbook, homeworks, discussions, grading, midterm and exam dates.

## Course website

The main course website is hosted on Canvas.

## Schedule of Topics

 lecture date pages topic 1 09/05 9–14 Review of vectors in 2D and 3D 2 09/10 14–22 Addition and scaling of vectors; General vector spaces; Bases and components 3 09/12 23–29 Lines and planes; Medians of a triangle; Dot product 4 09/17 30–39 Orthonormal bases; Dot products and norms in Rn; Cross product; Orientation of bases 5 09/19 37–47 Triple vector product; Levi-Civita symbol; Index notation; Einstein convention 6 09/24 48–63 Mixed product and determinant; Lines and planes again (and spheres!); Orthogonal transformations and matrices 7 09/26 61–67 Matrices; Euler angles; Gram–Schmidt 8 10/01 73–75 Vector functions 9 10/03 75–77 Vector functions (cont'd) 10 10/08 79–80 Homework problems; Newtonian mechanics 11 10/10 80–91 Newtonian mechanics; Curves 12 10/15 91–94 Curvature and torsion; Integrals on curves 13 10/17 94–99 Integrals on curves; Surfaces 14 10/22 – Review for midterm – 10/24 – Midterm 1 15 10/29 99–106 Surface integrals 16 10/31 106–109 Volumes 17 11/05 109–111 Curvilinear coordinates 18 11/07 111–120 Grad 19 11/12 121–124 Div, curl 20 11/14 125–135 Div, curl in polars; Green's theorem 21 11/19 135–155 Stokes' theorem; Divergence theorem; Complex numbers – 11/21 – Midterm 2 22 11/26 158–166 Polar form; Complex roots; Cauchy–Riemann relations 23 12/03 166–168, 179–181 Cauchy's theorem; Contour integration 24 12/05 181–189 Poles; Residue theorem; Cauchy's formula 25 12/10 190–195 Using complex integration