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| Lessons | ||
| logID | Lesson Name | Topics Covered |
| calitbx | calculus 2 TOOLBOX* | notes and hints on all course topics |
| FUNDAMENTAL CONCEPTS | ||
| cali1 | antiderivatives | antidifferentiating and differential equations. |
| cali1.1 | areas with Riemann sums | basic priciples of integration: summing rectangles |
| alg12 | summations | summation theorems and formulae |
| TECHNIQUES OF INTEGRATION | ||
| cali2 | integration by parts | includes "boomerang" integral |
| cali2.1 | the "boomerang" integral | integrals that come back to you |
| cali3 | integration by substitution | change of variable |
| cali3.1 | trig integrals | techniques for integrating trig functions |
| cali3.2 | partial fraction decomposition | techniques for integrating rational functions |
| cali3.3 | quadratic expression integrands | integrating irreducible quadratics |
| cali4 | trig substitutions | x = a sin h, x = a tan h, and x = a sec h |
| APPLICATIONS OF THE DEFINITE INTEGRAL | ||
| cali1.0 | area | finding area between curves |
| cali1.2 | volumes by disk method | solids of revolution, volume, cylindrical disks |
| cali1.3 | volumes by shell method | solids of revolution, volume, cylindrical shells |
| cali1.4 | arc length | finding length of an arc segment along a curve |
| cali1.5 | volumes by slicing | volumes of solids by summing area of slices |
| INDETERMINATE FORMS, IMPROPER INTEGRALS | ||
| cali5 | l'Hopital's rule | limits of indeterminate forms with derivatives |
| cali6 | improper integrals | infinite limits of integration, discontinuities on integrand |
| INFINITE SERIES | ||
| cali7 | testing infinite series-1 | geometric series, p-series, integral & nth term test |
| cali7.1 | testing infinite series-2 | basic & limit comparison, ratio & root tests. |
| cali7.2 | alternating series test | testing series with alternating signs -- simple test |
| cali7.3 | absolute & conditional convergence | series that can be convergent and/or divergent |
| srststs | guide to tests on infinite series | table of info on the infinite series tests |
| Practice Exercises & Assignments | ||
| logID | Exercise or Assignment | Topics Covered |
| asgn1 | assignment # 1 | Mean Value Theorem, integration by substitution |
| asgn2 | assignment # 2 | area, volumes by revolving and slicing, arc length |
| asgn3 | assignment # 3 | all techniques of integration |
| asgn4 | assignment # 4 | l'Hopital's rule, improper integrals |
| asgn5 | assignment # 5 | testing infinite series for convergence |
| intprac | integral practice exercise | all techniques of integration with solutions |
| Tests and Exams | ||
| calitst1 | Calculus II test #1 | integrals, area, volumes, Mean Value Theorem, |
| calitst1sl | Solutions: Calculus II test #1 | solutions for test #1 |
| cal2infosh | information & formulas for test #2 | trig integrals, inverse trig integrals, identities |
| calitst2 | Calculus II test #2 | integration techniques, volume, arc length |
| calitst2sl | Solutions: Calculus II test #2 | solutions for test #2 |
| cal2tst3 | Calculus II test #3 | integration techniques, l'Hopital, convergence |
| cal2tst3sl | Solutions: Calculus II test #3 | solutions for test #3 |
| califnl | Final exam | all topics on cal II course (science) |
| califnlsl | Solutions for Final exam | skimpy solutions -- by now you don't need more! |
| prctexams | practice-exams | 3 recent finals from Dawson |
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