Problem Solving in Undergraduate Physics
| 1. | Overview of Materials |
| 2. | Introduction to IDL |
| 3. | Introduction to MATLAB |
| 4. | Introduction to MACSYMA |
| 5. | Introduction to MAPLE |
| 6. | Introduction to Mathematica |
| 7. | Introduction to Programming in FORTRAN and/or C |
| 8. | Introduction to Numerical Recipes |
| 9. | Solving ODEs |
| 10. | Introduction to LSODE |
| 11. | Evaluating Integrals |
| 12. | Finding Roots |
| A. | Introduction to \LaTeX |
| B. | Introduction to TGIF |
Chapter 3: Introduction to MATLAB
| 3.1 | Beginning a MATLAB Session |
| 3.2 | Basic Entities in MATLAB |
| 3.3 | A Sampling of MATLAB Capabilities |
| 3.4 | Properties, Objects, and Handles |
| 3.5 | Saving/Retrieving a MATLAB Session |
| 3.6 | Loops/Logical Expressions/Conditionals |
| 3.7 | Reading Data from a File |
| 3.8 | On-line Help |
| 3.9 | M-Files |
| 3.10 | Eigenvalues and Eigenvectors |
| 3.11 | Graphing Functions of One Variable |
| 3.12 | Making Hard Copy |
| 3.13 | Graphing Functions of Two Variables |
| 3.14 | Graphing Functions of Three Variables |
| 3.15 | Graphing Vector Fields |
| 3.16 | Animation |
| 3.17 | Advanced Graphing Features |
| 3.18 | Miscellaneous Occasionally Useful Tidbits |
| 3.19 | References |
| 3.20 | Exercises |
Chapter 11: Evaluating Integrals
| 11.1 | Sample Problems |
| 11.2 | Evaluating Integrals Symbolically with MACSYMA |
| 11.3 | Evaluating Integrals Symbolically with MAPLE |
| 11.4 | Evaluating Integrals Symbolically with MATHEMATICA |
| 11.5 | Algorithms for Numerical Integration |
| 11.6 | Evaluating Integrals Numerically with IDL |
| 11.7 | Evaluating Integrals Numerically with MATLAB |
| 11.8 | Evaluating Integrals Numerically with MACSYMA |
| 11.9 | Evaluating Integrals Numerically with MAPLE |
| 11.10 | Evaluating Integrals Numerically with MATHEMATICA |
| 11.11 | Evaluating Integrals Numerically with FORTRAN |
| 11.12 | Evaluating Integrals Numerically with C |
| 11.13 | Exercises |
| 11.A | Listing of trapezoidal.f |
| 11.B | Listing of trapezoidal.c |
| 11.1.1. | One-Dimensional Trajectories |
| 11.1.2. | Center of Mass |
| 11.1.3. | Moment of Inertia |
| 11.1.4. | Large-Amplitude Pendulum |
| 11.1.5. | Statistical Data Analysis |
| 11.1.6. | The Cornu Spiral |
| 11.1.7. | Electric/Magnetic Fields and Potentials |
| 11.1.8. | Quantum Probabilities |
| 11.1.9. | Expansion in Orthogonal Functions |
Note: This guide must be locally written following a supplied template.
| Su Eve | Orientation to UNIX, LaTeX, |
| Compile C/FORTRAN | |
| Programs, Print Files, ... | |
| Mo AM | Continue Sunday Eve |
| Mo PM | Orientation to IDL or MATLAB |
| Tu AM | Orientation to MAPLE or MATHEMICA |
| Tu PM | Catch-up |
| We AM | ODEs with MAPLE |
| We PM | ODEs with IDL or MATLAB |
| Th AM | Integration with MAPLE or MATHEMATICA |
| Th PM | Integration with IDL or MATLAB |
| Fr AM | Root Finding |
| Fr PM | Use of Numerical Recipes |
| Sa AM | General Discussion |
\begin{slide} \begin{center} {\bf UNDERLYING CONVICTIONS} (1) \end{center} \begin{itemize} \item Students must learn to use: \begin{itemize}\itemsep=0pt\parskip=0pt\parsep=0pt \item an operating system \item a good text editor \item a spreadsheet \item an array/number processor \item a computer algebra system \item a visualization tool \item a standard computational language \item a technical publishing system \end{itemize} \item Students must learn to use these tools for \begin{itemize}\itemsep=0pt\parskip=0pt\parsep=0pt \item solving algebraic equations \item solving ODEs and PDEs \item evaluating integrals \item finding roots \item analyzing data \item fitting curves to data \item manipulating images \item preparing reports \end{itemize} \end{itemize} \end{slide} \begin{slide} \begin{center} {\bf UNDERLYING CONVICTIONS} (2) \end{center} Students must \begin{itemize} \item be introduced to computational resources {\em early}. \item use computational resources {\em throughout the curriculum}. \item focus {\em initially\/} on the tools themselves. \end{itemize} \end{slide} \begin{slide} \begin{center} \bf COMPUTATIONAL COMPONENTS \end{center} {\bf Intro Physics} (fresh): LoggerPro, Kaleidagraph, Excel for data acquisition and analysis, curve fitting, visualization \\[6pt] {\bf Electronics} (soph): Electronics Workbench for circuit simulation \\[6pt] {\bf Computational Mechanics} (soph): IDL, MAPLE, \LaTeX{} for ODEs, integrals, visualization, documentation \\[6pt] {\bf Electromagnetic Theory} (soph): IDL, MAPLE for visualization, integrals, Laplace's equation \\[6pt] {\bf Quantum Mechanics, Plasma Physics, Advanced Mechanics, Computational Physics, Mathematical Methods} (jr,sr): IDL, MAPLE, \LaTeX{}, LSODE, MUDPACK, $\dots$, in many contexts \\[6pt] {\bf Other courses and projects} (jr,sr): Majors use computation {\em on their own initiative} \end{slide} \end{document}