UH MATH 2414 Calculus II: Syllabus, Topics and Practice

UH MATH 2414 (Calculus II) is the second course in the University of Houston calculus sequence and was previously numbered MATH 1432. It requires MATH 2413 with a C- or higher. This guide maps the department's published topic list to lessons you can practice with instant feedback.

What UH MATH 2414 covers

The UH Department of Mathematics course guideline describes MATH 2414 as the calculus of transcendental functions: additional techniques and applications of integration, indeterminate forms, improper integrals, Taylor's formula, and infinite series. Its curriculum details add parametric equations and polar coordinates. The learning outcomes include using definite integrals for area, volume and work, evaluating integrals by substitution, parts, trig substitution, partial fractions and tables, defining improper integrals, testing sequences and series, and representing functions with Taylor and Maclaurin series.

The topic list is organized in four chapters:

1. Applications of integration: integration review, the Mean Value Theorem for integrals, area, volume, arc length, centroids and surface area, differential equations and exponential growth and decay.
2. Techniques of integration: integration by parts, powers of trig functions, trig substitutions, rational functions, improper integrals, numerical integration.
3. Sequences and series: bounded sets and sequences, convergence, the integral and comparison tests, ratio and root tests, alternating series and absolute convergence, power series, Taylor series.
4. Polar coordinates and parametric equations: polar graphs and area, parametric curves, tangents, arc length and surface area.

MATH 2414 topic map

MATH 2414 in the UH sequence

Example problems at the MATH 2414 level

1. A power of sine. Using \sin^2 x = \frac{1 - \cos 2x}{2}:

2. The ratio test. For \sum \frac{2^n}{n!}, the ratio \frac{2}{n+1} \to 0 < 1, so the series converges.

3. A tangent to a parametric curve. For x = t^2, y = t^3 at t = 1:

How to do well in MATH 2414

• Keep up with poppers and online quizzes. They are small, frequent checks that show you where you are slipping.
• Practice choosing an integration method with choosing a strategy.
• Start the series chapter strong. Learn when each test works using choosing a test.
• Review polar graphs by plotting points before computing polar areas.
• Prepare with timed practice exams and power series problems.

Tip: for polar area, the formula is \frac{1}{2}\int r^2\,d\theta. Forgetting the \frac{1}{2} or the square is the most common mistake.