# UH MATH 2413 Calculus I: Syllabus, Topics and Practice

> A study guide for University of Houston MATH 2413 Calculus I (formerly MATH 1431): limits, derivatives, curve sketching, optimization and integrals.

Source: https://practicecalculus.com/courses/university-of-houston-math-2413
Updated: 2026-11-08

## At a glance

- **Course code:** MATH 2413 (previously MATH 1431)
- **Credits:** Not printed on the course page; the Texas course number 2413 indicates 4 semester credit hours
- **Prerequisites:** Credit for MATH 2312 with a grade of C- or higher, or a satisfactory score on a placement examination
- **Covers:** Limits, continuity, derivatives, the Mean Value Theorem, applications of the derivative, motion problems, optimization, antiderivatives, the definite integral, the Fundamental Theorem of Calculus, numerical integration
- **Next course:** MATH 2414 Calculus II
- **Practice here:** [Calculus 1](/learn/calculus-1)

## Key takeaways

- MATH 2413 is Calculus I at the University of Houston; it was previously numbered MATH 1431.
- It covers limits, continuity, derivatives, the Mean Value Theorem, curve sketching, optimization, antiderivatives, the definite integral and the Fundamental Theorem of Calculus.
- You need MATH 2312 with a C- or higher, or a satisfactory placement score.
- The department topic list also includes exponential, log, inverse trig and hyperbolic functions, differentials and L'Hospital's rule.

**UH MATH 2413** (Calculus I) is the first course in the University of Houston calculus sequence, followed by MATH 2414 and MATH 2415. It was previously numbered MATH 1431, so older advice and syllabi may use that number. This guide maps the official UH topic list to lessons you can practice with instant feedback.

## What UH MATH 2413 covers

The UH Department of Mathematics publishes a course guideline for MATH 2413. Its description reads: calculus of single variable functions, limits, continuity, derivatives, mean value theorem, applications of the derivative, motion problems, optimization, antiderivatives, the definite integral, fundamental theorem of calculus, and numerical integration. The department notes that this is a guideline and that your instructor has the current syllabus.

The published topic list is organized in six chapters:

1. **Limits and continuity:** review of functions, limits and limit rules, continuity, the Intermediate Value Theorem, trig limits and the Pinching Theorem.
2. **Differentiation:** the definition of the derivative, polynomial and trig derivatives, differentiation rules, implicit differentiation.
3. **Applications of the derivative:** related rates, the Mean Value Theorem, increase and decrease, extreme values, concavity and inflection points, curve sketching.
4. **Transcendental functions:** inverse functions, the exponential and natural log functions, inverse trig and hyperbolic functions.
5. **Further applications:** optimization, differentials, L'Hospital's rule.
6. **Integration:** the definite integral, the Fundamental Theorem of Calculus, basic integration rules and substitution.

## MATH 2413 topic map

| MATH 2413 topic | Practice | Read |
| --- | --- | --- |
| Limits and limit rules | [What is a limit?](/learn/calculus-1/limits/what-is-a-limit) | [Limit laws](/rules/limit-laws) |
| Continuity and the IVT | [Intermediate Value Theorem](/learn/calculus-1/limits/intermediate-value-theorem) | [Intermediate Value Theorem](/theorems/intermediate-value-theorem) |
| Pinching (squeeze) theorem | [Squeeze theorem](/learn/calculus-1/limits/squeeze-theorem) | [Squeeze theorem](/theorems/squeeze-theorem) |
| Definition of the derivative | [Limit definition](/learn/calculus-1/the-derivative/limit-definition) | [Limit definition of the derivative](/blog/limit-definition-of-the-derivative) |
| Differentiation rules | [Product rule](/learn/calculus-1/derivative-rules/product-rule) | [Product and quotient rules](/blog/product-and-quotient-rules) |
| Implicit differentiation | [Implicit differentiation](/learn/calculus-1/derivative-rules/implicit-differentiation) | [Implicit differentiation](/blog/implicit-differentiation) |
| Related rates | [Related rates](/learn/calculus-1/applications-of-derivatives/related-rates) | [Related rates](/blog/related-rates) |
| Mean Value Theorem | [Linear approximation and the MVT](/learn/calculus-1/applications-of-derivatives/linear-approximation-and-mvt) | [Mean Value Theorem](/theorems/mean-value-theorem) |
| Curve sketching | [Second derivative](/learn/calculus-1/applications-of-derivatives/second-derivative) | [Curve sketching](/blog/curve-sketching-with-derivatives) |
| Exponential, log, inverse trig | [Inverse trig derivatives](/learn/calculus-1/derivative-rules/inverse-trig-derivatives) | [Natural logarithm](/functions/natural-logarithm) |
| Hyperbolic functions | [Exponential and log derivatives](/learn/calculus-1/derivative-rules/exponential-and-log-derivatives) | [Hyperbolic functions](/functions/hyperbolic-functions) |
| Optimization and differentials | [Optimization](/learn/calculus-1/applications-of-derivatives/optimization) | [Linear approximation](/blog/linear-approximation) |
| L'Hospital's rule | [L'Hopital's rule](/learn/calculus-1/applications-of-derivatives/lhopitals-rule) | [L'Hopital's rule](/rules/lhopitals-rule) |
| Definite integral and FTC | [Fundamental Theorem, part 2](/learn/calculus-1/integrals/fundamental-theorem-part-2) | [Fundamental Theorem](/blog/fundamental-theorem-of-calculus) |
| Substitution | [u-substitution](/learn/calculus-1/integrals/u-substitution) | [u-substitution](/blog/u-substitution) |

## MATH 2413 in the UH sequence

| Course | Old number | Prerequisite |
| --- | --- | --- |
| MATH 2413 Calculus I | MATH 1431 | MATH 2312 with C- or placement |
| [MATH 2414 Calculus II](/courses/university-of-houston-math-2414) | MATH 1432 | MATH 2413 with C- |
| [MATH 2415 Calculus III](/courses/university-of-houston-math-2415) | MATH 2433 | MATH 2414 |

## Example problems at the MATH 2413 level

**1. Implicit differentiation.** For $x^2 + y^2 = 25$, differentiating gives $2x + 2y\,y' = 0$, so $y' = -\frac{x}{y}$.

**2. A motion problem.** If $s(t) = 16t^2$, the velocity is $v(t) = 32t$ and the acceleration is $32$.

**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 2413

- **Do the online quizzes on time.** UH delivers quizzes and homework through CASA, and they track the topic list closely.
- **Do not skip the transcendental functions chapter.** Exponentials, logs and inverse trig come back in every later course.
- **Use a checklist for curve sketching:** domain, intercepts, asymptotes, $f'$ sign chart, $f''$ sign chart.
- **Earn the C- with room to spare,** since MATH 2414 requires it.
- **Practice with timed [practice exams](/practice)** and [evaluating limits problems](/practice-problems/evaluating-limits).

> **Tip:** the Mean Value Theorem needs a function that is continuous on $[a, b]$ and differentiable on $(a, b)$. Check both conditions before you use it.

## Frequently asked questions

### What is MATH 2413 at the University of Houston?

MATH 2413 Calculus I covers the calculus of single variable functions: limits, continuity, derivatives, the mean value theorem, applications of the derivative, motion problems, optimization, antiderivatives, the definite integral, the fundamental theorem of calculus, and numerical integration.

### Is MATH 2413 the same as MATH 1431?

Yes. The UH math department says MATH 2413 was previously MATH 1431.

### What is the prerequisite for MATH 2413?

Credit for MATH 2312 (Pre-Calculus) with a grade of C- or higher, or a satisfactory score on a placement examination.

### Where do I get the MATH 2413 textbook?

The department says the textbook, online quizzes and extra help materials are available by logging into CASA Campus Services (CCS), with digital textbook details in Canvas.

### What comes after MATH 2413?

MATH 2414 Calculus II, which requires credit for MATH 2413 with a grade of C- or higher.