# UH MATH 2414 Calculus II: Syllabus, Topics and Practice > A study guide for University of Houston MATH 2414 Calculus II (formerly MATH 1432): integration techniques, series, polar and parametric curves. Source: https://practicecalculus.com/courses/university-of-houston-math-2414 Updated: 2026-11-08 ## At a glance - **Course code:** MATH 2414 (previously MATH 1432) - **Credits:** Not printed on the course page; the Texas course number 2414 indicates 4 semester credit hours - **Prerequisites:** Credit for MATH 2413 with a grade of C- or higher - **Covers:** Applications and techniques of integration, indeterminate forms, improper integrals, Taylor's formula, infinite series, parametric equations and polar coordinates - **Next course:** MATH 2415 Calculus III - **Practice here:** [Calculus 2](/learn/calculus-2) ## Key takeaways - MATH 2414 is Calculus II at the University of Houston; it was previously numbered MATH 1432. - It covers applications of integration, integration techniques, improper integrals, numerical integration, sequences and series, power and Taylor series, and polar and parametric curves. - The prerequisite is credit for MATH 2413 with a C- or higher. - It leads to MATH 2415 Calculus III. **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 topic | Practice | Read | | --- | --- | --- | | Mean Value Theorem for integrals | [Average value](/learn/calculus-1/applications-of-integrals/average-value) | [MVT for integrals](/theorems/mean-value-theorem-for-integrals) | | Area and volume | [Area between curves](/learn/calculus-1/applications-of-integrals/area-between-curves) | [Volumes of revolution](/blog/volumes-of-revolution) | | Arc length, centroids, surface area | [Arc length and surface area](/learn/calculus-2/improper-integrals-and-applications/arc-length-and-surface-area) | [Center of mass](/learn/calculus-2/improper-integrals-and-applications/center-of-mass) | | Growth and decay | [Growth and decay](/learn/calculus-2/improper-integrals-and-applications/growth-and-decay) | [Separable equations](/learn/calculus-2/improper-integrals-and-applications/separable-equations) | | Integration by parts | [Integration by parts](/learn/calculus-2/integration-techniques/integration-by-parts) | [Integration by parts](/blog/integration-by-parts) | | Powers of trig functions | [Trig integrals](/learn/calculus-2/integration-techniques/trig-integrals) | [Trig integrals problems](/practice-problems/trig-integrals) | | Trig substitutions | [Trig substitution](/learn/calculus-2/integration-techniques/trig-substitution) | [Trig substitution](/blog/trig-substitution) | | Rational functions | [Partial fractions](/learn/calculus-2/integration-techniques/partial-fractions) | [Partial fractions](/blog/partial-fractions) | | Improper integrals | [Infinite discontinuities](/learn/calculus-2/improper-integrals-and-applications/infinite-discontinuities) | [Improper integrals](/blog/improper-integrals) | | Sequences and series | [Integral test and p-series](/learn/calculus-2/sequences-and-series/integral-test-and-p-series) | [Convergence tests](/blog/convergence-tests) | | Ratio, root and alternating tests | [Alternating series](/learn/calculus-2/sequences-and-series/alternating-series) | [Ratio test](/rules/ratio-test) | | Power and Taylor series | [Maclaurin series](/learn/calculus-2/power-series-parametric-polar/maclaurin-series) | [Taylor series](/blog/taylor-series) | | Polar coordinates and area | [Polar area](/learn/calculus-2/power-series-parametric-polar/polar-area) | [Polar slopes](/learn/calculus-2/power-series-parametric-polar/polar-slopes) | | Parametric curves | [Parametric arc length](/learn/calculus-2/power-series-parametric-polar/parametric-arc-length) | [Parametric and polar problems](/practice-problems/parametric-and-polar) | ## MATH 2414 in the UH sequence | Course | Old number | Prerequisite | | --- | --- | --- | | [MATH 2413 Calculus I](/courses/university-of-houston-math-2413) | MATH 1431 | MATH 2312 with C- or placement | | MATH 2414 Calculus II | 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 2414 level **1. A power of sine.** Using $\sin^2 x = \frac{1 - \cos 2x}{2}$: $$\int \sin^2 x\,dx = \frac{x}{2} - \frac{\sin 2x}{4} + C$$ **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 $t = 1$: $$\frac{dy}{dx} = \frac{3t^2}{2t} = \frac{3}{2}$$ ## 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](/learn/calculus-2/integration-techniques/choosing-a-strategy). - **Start the series chapter strong.** Learn when each test works using [choosing a test](/learn/calculus-2/sequences-and-series/choosing-a-test). - **Review polar graphs by plotting points** before computing polar areas. - **Prepare with timed [practice exams](/practice)** and [power series problems](/practice-problems/power-series). > **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. ## Frequently asked questions ### What is MATH 2414 at the University of Houston? MATH 2414 Calculus II covers the calculus of transcendental functions: additional techniques and applications of integration, indeterminate forms, improper integrals, Taylor's formula, and infinite series. The department's curriculum details also list parametric equations and polar coordinates. ### Is MATH 2414 the same as MATH 1432? Yes. The UH math department says MATH 2414 was previously MATH 1432. ### What is the prerequisite for MATH 2414? Credit for MATH 2413 with a grade of C- or higher. ### How is MATH 2414 graded? The department lists regular exams, a final exam, online and written quizzes, homework and in-class quizzes called poppers, but says to consult your instructor's syllabus for the grading breakdown. ### What comes after MATH 2414? MATH 2415 Calculus III, which lists MATH 2414 as its prerequisite.