UH MATH 2413 Calculus I: Syllabus, Topics and Practice

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 in the UH sequence

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:

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 and evaluating limits problems.

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.