# 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.

Source: https://practicecalculus.com/courses/johns-hopkins-as-110-109
Updated: 2026-11-08

## 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](/learn/calculus-2)

## Key takeaways

- AS.110.109 is the Calculus II course at Johns Hopkins for the physical sciences and engineering.
- It is a 4-credit course, and the recommended background is a C- or better in 110.106 or 110.108, or a 5 on AP Calculus AB.
- The catalogue highlights polar coordinates, parametric equations, Taylor's theorem and infinite sequences and series.
- A C- or better in AS.110.109 is one of the ways to meet the prerequisite for AS.110.202 Calculus III.

**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](/courses/johns-hopkins-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](/learn/calculus-2/integration-techniques/integration-by-parts) | [Integration by parts guide](/blog/integration-by-parts) |
| Other integration techniques | [Choosing a strategy](/learn/calculus-2/integration-techniques/choosing-a-strategy) | [Partial fractions](/blog/partial-fractions) |
| Improper integrals | [Integrating to infinity](/learn/calculus-2/improper-integrals-and-applications/infinite-limits-of-integration) | [Improper integrals](/blog/improper-integrals) |
| Infinite sequences | [Sequences](/learn/calculus-2/sequences-and-series/sequences) | [Limits at infinity](/blog/limits-at-infinity) |
| Infinite series | [Series and partial sums](/learn/calculus-2/sequences-and-series/series-and-partial-sums) | [Geometric series](/blog/geometric-series) |
| Convergence tests | [Choosing a test](/learn/calculus-2/sequences-and-series/choosing-a-test) | [Convergence tests](/blog/convergence-tests) |
| Power series | [Power series and radius](/learn/calculus-2/power-series-parametric-polar/power-series-and-radius) | [Power series](/blog/power-series) |
| Taylor's theorem and applications | [Estimating with Taylor](/learn/calculus-2/power-series-parametric-polar/estimating-with-taylor) | [Taylor's theorem](/theorems/taylors-theorem), [Taylor series](/blog/taylor-series) |
| Parametric equations | [Parametric curves](/learn/calculus-2/power-series-parametric-polar/parametric-curves) | [Parametric motion](/learn/calculus-2/power-series-parametric-polar/parametric-motion) |
| Polar coordinates | [Polar coordinates](/learn/calculus-2/power-series-parametric-polar/polar-coordinates) | [Parametric and polar practice](/practice-problems/parametric-and-polar) |
| Areas in polar form | [Polar area](/learn/calculus-2/power-series-parametric-polar/polar-area) | [Polar slopes](/learn/calculus-2/power-series-parametric-polar/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.**

$$\frac{1}{1 - x} = 1 + x + x^2 + x^3 + \cdots \quad \text{for } |x| < 1$$

**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

$$\frac{1}{2}\int_{-\pi/2}^{\pi/2} 4\cos^2\theta\,d\theta = \pi$$

## 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](/learn/calculus-2/sequences-and-series/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](/learn/calculus-1/integrals/u-substitution) and derivative rules, which appear in every unit.

After Calculus II, see the [AS.110.202 guide](/courses/johns-hopkins-as-110-202) for multivariable calculus.

## Frequently asked questions

### What is Johns Hopkins AS.110.109?

AS.110.109 is Calculus II (For Physical Sciences and Engineering), a 4-credit course continuing differential and integral calculus with polar coordinates, parametric equations, Taylor's theorem and infinite sequences and series.

### What background do I need for AS.110.109?

The catalogue recommends a C- or better in AS.110.106 or AS.110.108, or a 5 on the AP Calculus AB exam.

### Does AS.110.109 cover integration techniques?

The catalogue lists integrals as part of the sequence but does not list individual techniques. Most Calculus II courses cover substitution, integration by parts and partial fractions, so check your syllabus.

### Can I take AS.110.113 instead?

AS.110.113 Honors Single Variable Calculus is an honors alternative to the 106-107 or 108-109 sequences. It meets the requirement for both Calculus I and II, although its credit counts for only one course.

### What comes after AS.110.109?

AS.110.202 Calculus III, which requires a C- or better in 110.109 (or one of several other courses) or a 5 on the AP BC exam.