This is not a new content week. Per the course schedule (see the calendar), Week 17 carries no assigned reading and no MyLab homework. Use it to consolidate: revisit weak spots flagged by the self-check quizzes, redo any MyLab problem you got wrong, and work back through the worked examples in each week's lecture notes rather than re-reading passively.
Scope note. The syllabus's catalog description mentions vector analysis, but no week in the actual schedule — including this one — assigns it. This review therefore covers only the material that was actually taught: §1.1 through §9.10.
17.1 Post-Midterm Map: Weeks 9–16
The midterm (Week 8) covered up through the definite integral. Everything since builds a single continuous line: evaluate integrals exactly (FTC, substitution), use them to measure geometric quantities (volume, arc length, surface area, work), extend differentiation and integration to inverse and transcendental functions, resolve indeterminate forms and stubborn integrals, then step from finite sums to infinite ones (sequences → series → convergence tests → power and Taylor series).
| Week | Topic | Thomas' § | Quick link |
|---|---|---|---|
| 9 | Fundamental Theorem & Substitution | 5.4–5.6 | Notes · Quiz |
| 10 | Volumes, Arc Length & Surface Area | 6.1–6.4 | Notes · Quiz |
| 11 | Work, Inverse & Exponential Functions | 6.5, 7.1–7.3 | Notes · Quiz |
| 12 | L'Hôpital's Rule & Integration Techniques I | 7.5, 8.1–8.3 | Notes · Quiz |
| 13 | Integration Techniques II & Improper Integrals | 8.4, 8.5, 8.8 | Notes · Quiz |
| 14 | Sequences & Infinite Series | 9.1–9.2 | Notes · Quiz |
| 15 | Convergence Tests for Series | 9.3–9.6 | Notes · Quiz |
| 16 | Power Series & Taylor Series | 9.7–9.10 | Notes · Quiz |
17.2 Full-Course Review Checklist
A self-diagnostic pass, not new material. If any item feels shaky, follow its link back to the original worked examples rather than re-deriving from scratch under exam pressure.
- Foundations (Weeks 1–3). Can you shift/scale/combine functions, evaluate limits by algebraic manipulation, and classify discontinuities? → W1, W2, W3
- Differentiation (Weeks 4–6). Can you apply the product/quotient/chain rules, differentiate implicitly, set up related-rates problems, and use derivatives to find extrema, concavity, and optimize? → W4, W5, W6
- Integration basics (Weeks 7, 9). Can you build a Riemann sum, apply the FTC in both directions, and integrate by substitution? → W7, W9
- Geometric applications (Week 10). Can you set up disk/washer/shell volume integrals, an arc-length integral, and a surface-area-of-revolution integral? → W10
- Transcendental functions (Week 11). Can you differentiate and integrate inverse functions, ln, and e^x, and set up a work integral? → W11
- Indeterminate forms and integration techniques (Weeks 12–13). Can you apply L'Hôpital's Rule correctly (checking the indeterminate form first), integrate by parts, use trigonometric substitution, and evaluate an improper integral? → W12, W13
- Sequences and series (Weeks 14–16). Can you determine whether a sequence converges, recognize a geometric or telescoping series, choose the right convergence test (Integral, Comparison, Ratio, Root, Alternating Series), and build/apply a Taylor series? → W14, W15, W16
17.3 How the Weeks Connect
The course was never a list of eighteen independent topics. A few threads run through nearly all of it, and reviewing along these threads is often faster than reviewing week by week:
- The dominant-term shortcut (first stated Week 3, §3.9) resurfaces to evaluate limits at infinity, to justify the Limit Comparison Test (Week 15, §15.4), and to choose comparison series throughout Week 15.
- The Riemann sum (Week 7) is the same picture behind the Integral Test's area comparison (Week 15, §15.1) and behind every volume/arc-length/surface-area setup in Week 10.
- Substitution (Week 9) reappears inside trigonometric substitution (Week 12) and inside every term-by-term integration of a power series (Week 16, §16.3, §16.7).
- The limit (1+1/n)^n → e (built in Week 12, §12.4) reappears unchanged inside the Ratio Test computation in Week 15's Example 15.3.
- Geometric series (Week 14, §14.6) is the same object as the power series 1/(1−x) (Week 16, Eq. 16.3d) — one is a special case of the other, not two unrelated formulas to memorize separately.
Looking ahead. Week 18 is the Final Examination. It has not been built as a content page on this site (per this term's scope), since it is an assessment, not new material. Consult the syllabus and calendar for the exact date, time, room, and coverage announced by the instructor.
17.4 References
- Thomas, G. B., Weir, M. D. and Hass, J. Thomas' Calculus, SI Units, 15th ed. Pearson, 2024. — full review scope: §1.1–1.3, §2.1–2.6, §3.1–3.9, §4.1–4.5, §5.1–5.6, §6.1–6.5, §7.1–7.5, §8.1–8.5, §8.8, §9.1–9.10
- Pearson MyLab Math — no new assignment this week; use the review mode on past assignments to re-attempt missed problems.