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\def\classTime{{"R  from 05:30 pm to 08:10 pm in Center for Engr. Educ. \& Res. 208.","R from 05:30 pm to 08:10 pm in Online SYN.",""}}
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\def\classInstructor{{"Ahmad Hoorfar","Ahmad Hoorfar",""}}
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\def\classInstrOffHrs{{"Thursday 4:00 pm to 5:15pm (or by appointment) at Villanova. Also: questions can be asked via email or via phone.","Thursday 4:00 pm to 5:15pm (or by appointment) at Villanova. Also: questions may be asked via email or via phone.",""}}
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\newcommand\semester{Fall 2023}
\newcommand\rsemester{202420}
\newcommand\courseNum{ECE 8001}
\newcommand\courseName{Engineering Math I}
\newcommand\courseCoordinator{Ahmad Hoorfar}
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\newcommand\meetingDesc{One 150 min lecture per week}
\newcommand\meetingMisc{Special notes on meeting info go here, if specified}
\newcommand\instructorMisc{Special notes on instructor(s), TA(s) go here, if specified}
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\newcommand\textBookTitle{Advanced Engineering Mathematics, 10th edition}
\newcommand\textBookAuth{Erwin Kreyszig}
\newcommand\textBookPub{John Wiley \& Sons}
\newcommand\textBookYr{2011}
\newcommand\textBookISBN{978-0-470-45836-5}
\newcommand\supplMaterials{Extensive "Hand-Out" Class Notes}
\newcommand\refPapers{\\1. Francis B. Hildebrand, “Advanced Calculus for Applications, Prentice Hall, 2nd edition, 1976.
\\2. Peter V. O'Neil, "Advanced Engineering Mathematics", PWS-Kent Publishing Company, 4th edition, 1995.}
\newcommand\textBookMisc{Special notes on textbook(s) go here, if specified}
\newcommand\catalogDesc{Applied mathematics course tailored to the needs of EE graduate students. Topics: i) Complex variable theory, ii) Sturm-Liouville problem, eigen-function expansion and special functions, iii) Matrix theory, eigen value and diagonalization, iv) Fourier analysis, multi-dimensional Fourier series and transforms, and v) Partial differential equations. Various examples from engineering and physics will be incorporated as appropriate.}
\newcommand\preReqs{None}
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\newcommand\courseExpectation{This course is an applied mathematics course tailored to the needs of engineering graduate students.  As a result of instruction in this course, the students should be able to skillfully apply the following areas of advanced calculus to various areas of engineering and physical sciences. The course begins with a detailed treatment of complex variable theory, which includes Cauchy’s theorem, classification of isolated singularities, multi-valuedness and branch-cut singularities, Taylor and Laurent series and contour integration methods for evaluation of integrals. Next, we introduce vector spaces and linear operators which then leads to an in-depth treatment of the following three topics: i) Series solution of differential equations and special functions (e.g.: Bessel, Hankel, Legendre, Gamma functions etc.), ii) Sturm-Liouville and boundary value problems, and iii) Generalized Fourier series, eigen-values and eigen-function expansion. These topics then lead to Fourier analysis, and multi-dimensional Fourier series and transforms. A study of partial differential equations, selected topics in higher dimensional calculus, variational calculus and Green’s function theory (if time permitted) will conclude the course. Various examples from engineering and physics will be incorporated in the above topics as appropriate.}
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\newcommand\covTopics{\item Complex Variable Analysis and Residue Calculus 
\item Linear Spaces and Linear Operators 
\item Series solution of diff. equations 
\item Bessel and Legendre Equations; Special functions 
\item Boundary Value/Sturm-Liouville Problem and Eigenfunction Expansion 
\item Matrix Theory
\item Multi-Dim. Fourier Analysis: Fourier Series and Transform
\item Partial Differential Equations 
\item Green’s function Theory, Potential Theory 
\item Topics in Higher Dimensional Calculus, Calculus of Variations}
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\caption*{Tentative Schedule for \textbf{All Sections}} \vspace{0.05in}
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\begin{tabularx}{\linewidth}{l|l}
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\large \textbf{Number of weeks (Tentative)} & \large \textbf{Topics}\\
\midrule \midrule
2.5 & Complex Variable Analysis and Residue Calculus\\
1.5 & Linear Spaces and Linear Operators\\
1 & Series solution of diff. equations\\
1.5 & Bessel and Legendre Equations; Special functions\\
1.5 & Boundary Value/Sturm-Liouville Problem and Eigenfunction Expansion\\
0.5 & Matrix Theory\\
1.5 & Multi-Dim. Fourier Analysis: Fourier Series and Transform\\
2 & Partial Differential Equations\\
1 & Green’s function Theory, Potential Theory\\
0.5 & Topics in Higher Dimensional Calculus, Calculus of Variations\\
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\\Homework Problems 25\%
\\Mid-term Exam 35\%
\\Final Exam 40\%
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There will be one mid-term and one final exam. Final exam will be 'take-home'.}
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