# Johns Hopkins AS.110.108 Calculus I: Topics and Practice

> A study guide for Johns Hopkins AS.110.108 Calculus I (Physical Sciences and Engineering): limits, derivatives, integrals and more, with free practice.

Source: https://practicecalculus.com/courses/johns-hopkins-as-110-108
Updated: 2026-11-08

## At a glance

- **Course code:** AS.110.108
- **Credits:** 4
- **Offered:** Not stated in the catalogue entry
- **Prerequisites:** None listed in the catalogue entry
- **Covers:** Differential and integral calculus: analytic geometry, functions, limits, integrals and derivatives, with applications to the physical sciences and engineering
- **Next course:** AS.110.109 (Calculus II for Physical Sciences and Engineering)
- **Practice here:** [Calculus 1](/learn/calculus-1)

## Key takeaways

- AS.110.108 is the Calculus I course at Johns Hopkins designed for students in the physical sciences and engineering.
- It is a 4-credit course in the Quantitative and Mathematical Sciences distribution area.
- The catalogue gives one shared description for 110.108 and 110.109, listing analytic geometry, functions, limits, integrals and derivatives, polar coordinates, parametric equations, Taylor's theorem and series.
- AS.110.106 is the parallel Calculus I for biology and social sciences, and AS.110.113 is an honors alternative.

**Johns Hopkins AS.110.108**, Calculus I (Physical Sciences & Engineering), is the first calculus course for Hopkins students heading into physics, chemistry, engineering and related fields. It is a 4-credit course in the Krieger School's mathematics department. This guide explains what the catalogue says and maps each Calculus I topic to free practice with instant feedback.

## What AS.110.108 covers

The Johns Hopkins e-catalogue describes AS.110.108 as differential and integral calculus. It lists analytic geometry, functions, limits, integrals and derivatives, polar coordinates, parametric equations, Taylor's theorem and applications, and infinite sequences and series. It adds that some applications to the physical sciences and engineering are discussed, and that "the courses" are designed to meet the needs of students in these disciplines.

That wording matters: the catalogue uses the same description for AS.110.108 and AS.110.109, so it describes the whole two-semester sequence. In a typical split, Calculus I covers functions, limits, derivatives and the beginning of integration, while polar coordinates, parametric equations, Taylor's theorem and series belong to [AS.110.109](/courses/johns-hopkins-as-110-109). The catalogue does not give a week-by-week split, so check your course syllabus.

The catalogue lists no prerequisite for AS.110.108. The course counts toward the Quantitative and Mathematical Sciences distribution area and the Science and Data foundational ability.

## AS.110.108 topic map

| Calculus I topic | Practice | Read |
| --- | --- | --- |
| Functions and analytic geometry | [Function notation](/learn/calculus-1/functions-warmup/function-notation) | [Polynomial functions](/functions/polynomial-functions) |
| Slopes and lines | [Slope and rate of change](/learn/calculus-1/functions-warmup/slope-and-rate-of-change) | [Linear function](/functions/linear-function) |
| Limits | [What is a limit?](/learn/calculus-1/limits/what-is-a-limit) | [How to evaluate limits](/blog/how-to-evaluate-limits) |
| Limits at infinity | [Limits at infinity](/learn/calculus-1/limits/limits-at-infinity) | [Limits at infinity guide](/blog/limits-at-infinity) |
| Continuity | [Continuity](/learn/calculus-1/limits/continuity) | [Continuity guide](/blog/continuity) |
| The derivative | [The limit definition](/learn/calculus-1/the-derivative/limit-definition) | [Limit definition of the derivative](/blog/limit-definition-of-the-derivative) |
| Derivative rules | [Product rule](/learn/calculus-1/derivative-rules/product-rule) | [Product and quotient rules](/blog/product-and-quotient-rules) |
| Chain rule | [Chain rule in general](/learn/calculus-1/derivative-rules/chain-rule-general) | [Chain rule](/rules/chain-rule) |
| Related rates | [Related rates](/learn/calculus-1/applications-of-derivatives/related-rates) | [Related rates guide](/blog/related-rates) |
| Optimization | [Optimization](/learn/calculus-1/applications-of-derivatives/optimization) | [Optimization problems](/blog/optimization-problems) |
| Integrals | [Riemann sums](/learn/calculus-1/integrals/riemann-sums) | [Fundamental Theorem of Calculus](/blog/fundamental-theorem-of-calculus) |
| Substitution | [U-substitution](/learn/calculus-1/integrals/u-substitution) | [U-substitution guide](/blog/u-substitution) |
| Applications of integrals | [Area between curves](/learn/calculus-1/applications-of-integrals/area-between-curves) | [Volumes of revolution](/blog/volumes-of-revolution) |

## Choosing a Calculus I at Hopkins

Johns Hopkins runs two parallel Calculus I courses and an honors option:

| Course | Who it is for |
| --- | --- |
| AS.110.106 Calculus I (Biology and Social Sciences) | Students in the biological and social sciences, with topics such as functions of several variables and probability distributions |
| AS.110.108 Calculus I (Physical Sciences & Engineering) | Students in the physical sciences and engineering |
| AS.110.113 Honors Single Variable Calculus | A more theoretical alternative that meets the requirement for both Calculus I and II |

All three are 4-credit courses, according to the catalogue.

## Example problems at the AS.110.108 level

**1. A limit at infinity.**

$$\lim_{x \to \infty} \frac{3x^2 + 1}{x^2 - 4} = 3$$

**2. A related rate.** A circle's radius grows at 2 cm/s. When $r = 5$, $\frac{dA}{dt} = 2\pi r \frac{dr}{dt} = 20\pi$ cm²/s.

**3. A definite integral.**

$$\int_0^{\pi} \sin x\,dx = [-\cos x]_0^{\pi} = 2$$

## How to do well in AS.110.108

- **Strengthen functions first.** Analytic geometry and functions open the catalogue description, so revise [exponent rules](/learn/calculus-1/functions-warmup/exponent-rules) and [key trig values](/learn/calculus-1/functions-warmup/key-trig-values).
- **Practice a little every day.** Derivative rules become automatic only through repetition.
- **Focus on physical meaning.** The course emphasizes science and engineering applications, so practice reading derivatives as velocities and integrals as accumulated change.
- **Prepare for exams** with timed [practice exams](/practice) and the [formula sheet](/formulas).

## Frequently asked questions

### What is Johns Hopkins AS.110.108?

AS.110.108 is Calculus I (Physical Sciences & Engineering), a 4-credit course in differential and integral calculus with applications to the physical sciences and engineering.

### What are the prerequisites for AS.110.108?

The Johns Hopkins e-catalogue entry does not list a prerequisite for AS.110.108.

### What is the difference between 110.106 and 110.108?

Both are Calculus I. AS.110.106 is for biology and social sciences and adds topics such as functions of several variables and probability distributions. AS.110.108 is designed for the physical sciences and engineering.

### Which topics are in 110.108 and which in 110.109?

The catalogue uses one description for the two-course sequence. Limits, derivatives and the start of integration are usually Calculus I material, while polar coordinates, parametric equations, Taylor's theorem and series usually come in Calculus II. Check your syllabus for the exact split.

### What comes after AS.110.108?

AS.110.109, Calculus II for Physical Sciences and Engineering, which recommends a C- or better in 110.106 or 110.108, or a 5 on the AP AB exam.