Complex and Vector Analysis for Engineers

Schaum’s Outline of Advanced Mathematics for Engineers and Scientists
- Murray Spiegel
- McGraw-Hill
- # ISBN-10: 0070602166
- # ISBN-13: 978-0070602168

To get the latest version of Maple: Go to Drexel Software Server

Lecture Notes

Final exam: Tuesday 9/4/2012, 10:30-12:30, Curtis 231

Topics

Linear Algebra, Vector Calculus
- Basic operations with vectors
- Exterior algebra and determinants
  - Exterior products
  - Wikipedia page for exterior algebra
- Animations to demonstrate the osculating circle (also called the circle of curvature)
- Cross products
- Matrix eigenvalue problems
  - Eigenvalues and eigenvectors, characteristic polynomial
    Notes on eigenvalues
  - Diagonalizing a matrix
  - Applications of diagonal forms
  - normal forms of a matrix
    Jordan canonical form
Vector differential calculus: div, grad, curl
- vector and scalar fields, physical significance
- Geometric significance of divergence
- Notes on vector calculus
- Maxwell’s equations
- Vector integral calculus: Integral theorems
  - Double and triple integrals
  - Line integrals
    - Green’s theorem in the plane
  - Surface integrals
    - The divergence theorem
    - Stokes theorem
Fourier analysis and partial differential equations
- Partial differential equations
  - First-order linear equations: the method of characteristics
  - Separable second-order equations: Laplace’s equation, the heat equation, and the wave equation.
  - Fourier series and integrals
  - Applications to partial differential equations
  - Maple worksheet solving the Heat Equation (save this link!)
  - Maple worksheet solving the Wave Equation (save this link!)
Complex numbers and functions.
- Complex differentiability: the Cauchy-Riemann equations
- Cauchy’s Integral Theorem
- Power series and taylor series.
- Calculus of Residues and definite integrals
- Liouville’s theorem

Goals of this course

Students will acquire an understanding of vector-calculus, complex analysis and their relation to problems in engineering and physics.
Students will learn general problem-solving techniques.

Grading Policy

Grades will be based on graded homework, three one-hour exams (weeks three, six, and nine), and a final exam.

Quizzes will be given during the Recitation classes.

The final counts twice, giving a total of four exam-based grades. The lowest of these five grades ill be dropped. This means that the lowest exam grade will not count. If the final is the lowest grade, it will count half as much as otherise.

Homeworks and quizzes will count as one tenth of an exam.

Academic Policies

Justin R. Smith