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Calculus Lab, 15 MATH 256-257
Calculus 256, 257 are one hour lab course to be taken in conjunction with Calculus 252 and 253. The software package Mathematica is used in the lab to enhance the learning of the concepts of calculus.
Course Information
Calculus Lab 256 Course Materials: CalcLabs with Mathematica, Single Variable, by Selwyn Hollis. Syllabus: The following sections from Hollis text should be covered at the beginning of the course: 1.1, 1.2, 1.3, 1.4 thru NestList, and 1.8. The instructor must cover required topics ‘Integration Using Tables and Computer Algebras Systems’ (Stewart 5.8) and ‘Approximate Integration’ (Stewart 5.9). For the remainder of the quarter the instructor can choose his favorite topics from the Calculus 2 syllabus to cover in lab. Most of these are found in Chapters 4 and 5 of Hollis text.
Mathematica competencies to be stressed by the instructor together with the section number from Hollis text.
1. The use of the Help Browser, 1.1, the question mark, 1.8, and the double question mark for attributes.
2. When to use Parentheses, Brackets, and Braces, 1.1.
3. Using Mathematica as a computer algebra system, 1.1.
4. Defining functions, 1.2, Set (=) versus SetDelayed (:=), 1.2, Applying functions with //, 1.2.
5. Equations and using the solver: Solve, Nsolve, FindRoot – how and when to use each of these, 1.3.
6. How Mathematica handles lists including the Range, Table, TableForm, and NestList commands, 1.4.
7. Symbolic vs. Numerical, 1.1 & 1.8, Exact vs. Approximate.
8. Loading packages, 1.7: how to load packages and how to get yourself out of trouble if you have forgotten to load a package, 1.8, quitting and restarting the kernel, 1.8.
9. Knowledge of how to use the following packages: FillPlot, 1.7, RealOnly, 1.10, ImplicitPlot, 1,7, Graphics, 8.2
10. Two dimensional plotting with Plot, 1.1, FillPlot, 1.7, ImplicitPlot, 1.7, PolarPlot, 8.2
11. The difference between input and text cells, 1.1 & 1.9.
12. Avoiding and getting out of trouble, 1.8. (Included here should be how a student can recognize from the output that he/she has made a mistake, i.e., like forgetting to put the space between x and y and having xy appear in a numerical output, or Log[e] with the wrong e, also how to dissect something like Integrate[F[r[t]].r’[t], 0,5] when it fails to compute to locate the problem)
13. Clearing variables and avoiding multiple definitions of variables, 1.8.
14. Trouble Shooting -- help students with trouble shooting so they can look at their output to get an idea of what error they are making,
Calculus Lab 257 Course Materials: CalcLabs with Mathematica, Single Variable, by Selwyn Hollis and CalcLabs with Mathematica, Multivariable, by Selwyn Hollis. Syllabus: The instructor can choose from various topics where the graphical/computational power of Mathematica can be used to help the student with the learning/understanding of the concepts from Calculus III. Possible topics are cylindrical coordinates, infinite series, power series, Taylor series, vector equations of lines and planes in space, space curves, vector-valued functions, parametric surfaces, functions of two variables, partial derivatives and tangent planes.