# Dalhousie MATH 1000 Calculus I: Syllabus, Topics and Practice

> A study guide for Dalhousie MATH 1000 (Differential and Integral Calculus I): limits, derivative rules, applications and integrals, with practice.

Source: https://practicecalculus.com/courses/dalhousie-math-1000
Updated: 2026-11-08

## At a glance

- **Course code:** MATH 1000.03
- **Credit hours:** 3 (lecture)
- **Prerequisites:** Nova Scotia Mathematics advanced 11 and 12 or pre-calculus (pre-calculus highly recommended)
- **Exclusions:** MATH 1215.03 (MATH 1000 is equivalent to MATH 1280.03)
- **Covers:** Functions, limits, derivatives of polynomial, trig, exponential and log functions, product, quotient and chain rules, applications of differentiation, antiderivatives, definite integrals, substitution
- **Next course:** MATH 1010 (Differential and Integral Calculus II) or MATH 1290
- **Practice here:** [Calculus 1](/learn/calculus-1)

## Key takeaways

- MATH 1000 is a 3 credit hour, self-contained introduction to differential and integral calculus at Dalhousie.
- It covers functions, limits and the main derivative rules for polynomial, trig, exponential and log functions.
- It finishes with antiderivatives, definite integrals and integration by substitution.
- MATH 1010 is the usual next course, and MATH 1000 is equivalent to MATH 1280.

**MATH 1000** is Differential and Integral Calculus I at Dalhousie University in Halifax. The calendar calls it a self-contained introduction to calculus, so it starts from functions and limits and does not assume you have seen calculus before. It covers the derivative rules and their applications and ends with a first look at integration. This guide maps each MATH 1000 topic to free practice so you can learn every idea by solving problems.

## What Dalhousie MATH 1000 covers

The Dalhousie academic calendar lists the topics as functions, limits, differentiation of polynomial, trigonometric, exponential and logarithmic functions, the product, quotient and chain rules, applications of differentiation, antiderivatives and definite integrals, and integration by substitution. It is a 3 credit hour lecture course. The prerequisite is Nova Scotia Mathematics advanced 11 and 12 or pre-calculus, and the calendar says pre-calculus is highly recommended.

This lines up closely with a standard **Calculus 1** course. Integration techniques beyond substitution, such as integration by parts, wait for MATH 1010.

## MATH 1000 topic map

| MATH 1000 topic | Practice | Read |
| --- | --- | --- |
| Functions | [Function notation](/learn/calculus-1/functions-warmup/function-notation) | [Polynomial functions](/functions/polynomial-functions), [exponential functions](/functions/exponential-functions) |
| Limits | [What is a limit?](/learn/calculus-1/limits/what-is-a-limit) | [How to evaluate limits](/blog/how-to-evaluate-limits), [limit laws](/rules/limit-laws) |
| 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) |
| Polynomial derivatives | [Power rule](/learn/calculus-1/derivative-rules/power-rule) | [Power rule](/rules/power-rule) |
| Trig, exponential and log derivatives | [Trig derivatives](/learn/calculus-1/derivative-rules/trig-derivatives), [exp and log](/learn/calculus-1/derivative-rules/exponential-and-log-derivatives) | [Trig derivatives guide](/blog/derivatives-of-trig-functions) |
| Product and quotient rules | [Product rule](/learn/calculus-1/derivative-rules/product-rule), [quotient rule](/learn/calculus-1/derivative-rules/quotient-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) |
| Applications of differentiation | [Optimization](/learn/calculus-1/applications-of-derivatives/optimization), [related rates](/learn/calculus-1/applications-of-derivatives/related-rates) | [Curve sketching](/blog/curve-sketching-with-derivatives) |
| Antiderivatives | [Undoing derivatives](/learn/calculus-1/integrals/undoing-derivatives) | [Antiderivatives guide](/blog/antiderivatives) |
| Definite integrals | [FTC part 2](/learn/calculus-1/integrals/fundamental-theorem-part-2) | [FTC guide](/blog/fundamental-theorem-of-calculus) |
| Integration by substitution | [u-substitution](/learn/calculus-1/integrals/u-substitution) | [u-substitution guide](/blog/u-substitution) |

## MATH 1000 in the Dalhousie sequence

| Course | Title | Main focus |
| --- | --- | --- |
| MATH 1000 | Differential and Integral Calculus I | Limits, derivatives, first integrals |
| [MATH 1010](/courses/dalhousie-math-1010) | Differential and Integral Calculus II | Integration techniques, ODEs, polar, series |
| [MATH 2001](/courses/dalhousie-math-2001) | Intermediate Calculus I | Vectors and several variables |

MATH 1000 is equivalent to MATH 1280, and MATH 1215 is an exclusion.

## Example problems at the MATH 1000 level

**1. A limit by factoring.**

$$\lim_{x\to 3}\frac{x^2 - 9}{x - 3} = \lim_{x\to 3}(x + 3) = 6$$

**2. The quotient rule.** For $f(x) = \frac{\ln x}{x}$, $f'(x) = \frac{1 - \ln x}{x^2}$, which is zero at $x = e$.

**3. Substitution.** With $u = x^2 + 1$:

$$\int 2x\,(x^2 + 1)^4\,dx = \frac{(x^2 + 1)^5}{5} + C$$

## How to do well in MATH 1000

- **Take the pre-calculus advice seriously.** Logs, exponents and trig identities appear in almost every derivative. Our [warm-up unit](/learn/calculus-1/functions-warmup/warmup-practice) is a quick check.
- **Practise rules in mixed sets.** Real problems mix the product, quotient and chain rules, so practise them together in [mixed rules practice](/learn/calculus-1/derivative-rules/derivative-rules-practice).
- **Set up word problems carefully.** For optimization and related rates, draw a picture and name each variable before you differentiate.
- **Check antiderivatives by differentiating.** It is the fastest way to catch a sign or constant error.

## Common mistakes in a first calculus course

- **Dropping the inner derivative.** With the chain rule, the derivative of $\sin(3x)$ is $3\cos(3x)$, not $\cos(3x)$. Always ask what is inside.
- **Forgetting the constant.** Every indefinite integral needs $+ C$. On a definite integral, it cancels, so it does not appear.
- **Mixing up the quotient rule order.** It is the bottom times the derivative of the top, minus the top times the derivative of the bottom, all over the bottom squared.
- **Changing variables halfway.** With substitution, rewrite everything in terms of $u$, including $dx$, before you integrate.

Our list of [common calculus mistakes](/blog/common-calculus-mistakes) covers more of these, with examples.

> **Tip:** most limit questions that give $\frac{0}{0}$ can be solved by factoring and cancelling, or by multiplying by a conjugate.

## Frequently asked questions

### What is MATH 1000 at Dalhousie?

MATH 1000 is Differential and Integral Calculus I. The Dalhousie calendar describes it as a self-contained introduction to calculus covering functions, limits, differentiation of polynomial, trigonometric, exponential and logarithmic functions, the product, quotient and chain rules, applications of differentiation, antiderivatives and definite integrals, and integration by substitution.

### Do I need calculus before MATH 1000?

No. The calendar lists Nova Scotia Mathematics advanced 11 and 12 or pre-calculus as the prerequisite, and says pre-calculus is highly recommended. Previous calculus is not required.

### What comes after MATH 1000?

The calendar names MATH 1010 (Differential and Integral Calculus II) or MATH 1290 as sequels. MATH 1010 covers Riemann sums, integration techniques, differential equations, polar coordinates and series.

### Can I take MATH 1000 and MATH 1215?

No. MATH 1215 is listed as an exclusion, so you can only get credit for one of them.