Johns Hopkins AS.110.109 Calculus II: Topics and Practice
A study guide for Johns Hopkins AS.110.109 Calculus II: integration, polar and parametric curves, Taylor's theorem and series, with free practice.
Johns Hopkins University Updated 3 min read
At a glance
- Course code
- AS.110.109
- Credits
- 4
- Offered
- Not stated in the catalogue entry
- Prerequisites
- Recommended background: a C- or better in AS.110.106 or AS.110.108, or a 5 on the AP Calculus AB exam
- Covers
- Differential and integral calculus continued, including polar coordinates, parametric equations, Taylor's theorem and applications, and infinite sequences and series
- Next course
- AS.110.202 (Calculus III)
- Practice here
- Calculus 2
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On this page
Johns Hopkins AS.110.109, Calculus II (For Physical Sciences and Engineering), is the second semester of the single-variable calculus sequence for Hopkins students in physics, chemistry, engineering and nearby fields. It continues AS.110.108 and leads to Calculus III. This guide explains what the catalogue says and links each Calculus II topic to free practice with instant feedback.
What AS.110.109 covers
The Johns Hopkins e-catalogue gives AS.110.109 the same description as AS.110.108: differential and integral calculus, including analytic geometry, functions, limits, integrals and derivatives, polar coordinates, parametric equations, Taylor's theorem and applications, and infinite sequences and series, with applications to the physical sciences and engineering.
Because the description covers the whole sequence, the topics that most clearly belong to the second semester are the ones at the end of the list: polar coordinates, parametric equations, Taylor's theorem with its applications, and infinite sequences and series. Calculus II courses also usually continue integration with further techniques and applications, but the catalogue does not list individual techniques, so use your syllabus to confirm the details.
The catalogue recommends a C- or better in AS.110.106 or AS.110.108, or a 5 on the AP Calculus AB exam, before taking AS.110.109.
AS.110.109 topic map
| Calculus II topic | Practice | Read |
|---|---|---|
| Integration by parts | Integration by parts | Integration by parts guide |
| Other integration techniques | Choosing a strategy | Partial fractions |
| Improper integrals | Integrating to infinity | Improper integrals |
| Infinite sequences | Sequences | Limits at infinity |
| Infinite series | Series and partial sums | Geometric series |
| Convergence tests | Choosing a test | Convergence tests |
| Power series | Power series and radius | Power series |
| Taylor's theorem and applications | Estimating with Taylor | Taylor's theorem, Taylor series |
| Parametric equations | Parametric curves | Parametric motion |
| Polar coordinates | Polar coordinates | Parametric and polar practice |
| Areas in polar form | Polar area | Polar slopes |
Choosing a Calculus II at Hopkins
| Course | Who it is for |
|---|---|
| AS.110.107 Calculus II (For Biological and Social Science) | Continues 110.106, with applications to the biological and social sciences |
| AS.110.109 Calculus II (For Physical Sciences and Engineering) | Continues 110.108 for the physical sciences and engineering |
| AS.110.113 Honors Single Variable Calculus | A theoretical alternative covering both Calculus I and II, with credit counting as one course |
Example problems at the AS.110.109 level
1. A Maclaurin series.
2. A parametric slope. For x = t^2, y = t^3, \frac{dy}{dx} = \frac{3t^2}{2t} = \frac{3t}{2}, so at t = 2 the slope is 3.
3. A polar area. The area inside r = 2\cos\theta is
How to do well in AS.110.109
- Make series your daily habit. Series questions reward pattern recognition, which comes from many short practice sets like the series practice.
- Use Taylor polynomials as tools. The catalogue stresses Taylor's theorem and applications, so practice estimating values and bounding errors.
- Draw polar graphs. Sketching first prevents wrong limits of integration in polar area problems.
- Keep Calculus I fresh. Revisit u-substitution and derivative rules, which appear in every unit.
After Calculus II, see the AS.110.202 guide for multivariable calculus.
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Sequences and their limits
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