# Arizona MATH 129 Calculus II: Syllabus, Topics and Practice

> A study guide for University of Arizona MATH 129 Calculus II: integration techniques, applications, differential equations and Taylor series.

Source: https://practicecalculus.com/courses/university-of-arizona-math-129
Updated: 2026-11-08

## At a glance

- **Course code:** MATH 129
- **Units:** 3
- **Prerequisites:** Continuation of MATH 122B or MATH 125 (see the department's Math Course Placement Chart for eligibility)
- **Covers:** Symbolic and numerical integration, applications of the definite integral to geometry, physics, economics and probability, differential equations, modeling, Taylor series
- **Textbook:** Calculus: Single Variable, 6th edition (Hughes-Hallett et al.), Chapters 7 to 11.6
- **Calculator:** Graphing calculator required (TI-83 or TI-84 recommended); CAS models not allowed
- **Next course:** MATH 223 Vector Calculus
- **Practice here:** [Calculus 2](/learn/calculus-2)

## Key takeaways

- MATH 129 Calculus II is a 3-unit course at the University of Arizona and a continuation of MATH 122B or MATH 125.
- It covers symbolic and numerical integration, applications of the definite integral, differential equations and Taylor series.
- The department course page lists Hughes-Hallett's Calculus: Single Variable, Chapters 7 to 11.6.
- A graphing calculator is required, symbolic (CAS) calculators are not allowed, and exams are proctored.

**Arizona MATH 129** (Calculus II) is the University of Arizona's second-semester calculus course and a continuation of MATH 122B or MATH 125. The catalog lists it at 3 units. This guide maps the official description and the department's course objectives to lessons you can practice right now.

## What Arizona MATH 129 covers

The University of Arizona catalog describes MATH 129 as a continuation of MATH 122B or MATH 125 covering techniques of symbolic and numerical integration, applications of the definite integral to geometry, physics, economics and probability, differential equations from a numerical, graphical and algebraic point of view, modeling using differential equations, and approximations by Taylor series. It also says a graphing calculator is required, symbolic calculators cannot be used, and examinations are proctored.

The Department of Mathematics course page lists four objectives: use techniques of analytical and numerical integration, apply the definite integral to problems in geometry and in physics or probability, work with infinite series and calculate and use Taylor series, and analyze first order differential equations graphically and algebraically. It names *Calculus: Single Variable* (6th edition, Hughes-Hallett et al.), Chapters 7 to 11.6, with WebAssign homework and a common final exam.

## MATH 129 topic map

| MATH 129 topic | Practice | Read |
| --- | --- | --- |
| Substitution | [u-substitution refresher](/learn/calculus-2/integration-techniques/u-substitution-refresher) | [u-substitution](/blog/u-substitution) |
| Integration by parts | [Integration by parts](/learn/calculus-2/integration-techniques/integration-by-parts) | [Integration by parts](/blog/integration-by-parts) |
| Partial fractions and trig substitution | [Partial fractions](/learn/calculus-2/integration-techniques/partial-fractions) | [Trig substitution](/blog/trig-substitution) |
| Numerical integration | [Trapezoid sums](/learn/calculus-1/integrals/trapezoid-sums) | [Riemann sums](/blog/riemann-sums) |
| Improper integrals | [Infinite limits of integration](/learn/calculus-2/improper-integrals-and-applications/infinite-limits-of-integration) | [Improper integrals](/blog/improper-integrals) |
| Geometry: area and volume | [Volumes by washers](/learn/calculus-1/applications-of-integrals/volumes-washers) | [Volumes of revolution](/blog/volumes-of-revolution) |
| Physics: work and center of mass | [Work](/learn/calculus-2/improper-integrals-and-applications/work) | [Center of mass](/learn/calculus-2/improper-integrals-and-applications/center-of-mass) |
| Differential equations, graphically | [Slope fields](/learn/calculus-2/improper-integrals-and-applications/slope-fields) | [Euler's method](/learn/calculus-2/improper-integrals-and-applications/eulers-method) |
| Differential equations, algebraically | [Separable equations](/learn/calculus-2/improper-integrals-and-applications/separable-equations) | [Differential equations problems](/practice-problems/differential-equations) |
| Modeling with differential equations | [Logistic growth](/learn/calculus-2/improper-integrals-and-applications/logistic-growth) | [Growth and decay](/learn/calculus-2/improper-integrals-and-applications/growth-and-decay) |
| Infinite series | [Geometric series](/learn/calculus-2/sequences-and-series/geometric-series) | [Convergence tests](/blog/convergence-tests) |
| Taylor series | [Taylor polynomials](/learn/calculus-2/power-series-parametric-polar/taylor-polynomials) | [Taylor series](/blog/taylor-series) |

## MATH 129 in the Arizona sequence

| Course | Units | Notes |
| --- | --- | --- |
| [MATH 122B First-Semester Calculus](/courses/university-of-arizona-math-122b) | 4 | Calculus 1, with MATH 122A at the start of the term |
| MATH 129 Calculus II | 3 | Continuation of MATH 122B or MATH 125 |
| [MATH 223 Vector Calculus](/courses/university-of-arizona-math-223) | See department page | Calculus 3 |

## Example problems at the MATH 129 level

**1. A trapezoid estimate.** With $\Delta x = 1$ and values $f(0) = 1$, $f(1) = 2$, $f(2) = 5$:

$$\int_0^2 f(x)\,dx \approx \frac{1}{2}\left(1 + 2\cdot 2 + 5\right) = 5$$

**2. Exponential growth.** If $\frac{dP}{dt} = 0.03P$ and $P(0) = 200$, then $P(t) = 200e^{0.03t}$.

**3. A Taylor approximation.** Using the series for $\sin x$:

$$\sin(0.1) \approx 0.1 - \frac{0.1^3}{6} \approx 0.09983$$

## How to do well in MATH 129

- **Learn to read slope fields and graphs,** not just to solve equations. The course treats differential equations numerically and graphically too.
- **Practice integration without a CAS calculator,** since symbolic calculators are not allowed. [Choosing a strategy](/learn/calculus-2/integration-techniques/choosing-a-strategy) helps you pick the right technique.
- **Set up application integrals from a slice:** write the area, volume or work for one thin piece, then add them up.
- **Use the department's final exam review packets** and our timed [practice exams](/practice).
- **Use the free Think Tank tutoring** when a topic does not click.

> **Tip:** for a Taylor approximation, the more terms you keep, the better the estimate near the center. Far from the center, even many terms can be poor.

## Frequently asked questions

### What is MATH 129 at the University of Arizona?

MATH 129 Calculus II continues MATH 122B or MATH 125. The University of Arizona catalog lists techniques of symbolic and numerical integration, applications of the definite integral to geometry, physics, economics and probability, differential equations from a numerical, graphical and algebraic point of view, modeling with differential equations, and approximations by Taylor series.

### How many units is MATH 129?

The University of Arizona catalog lists MATH 129 at 3 units.

### Does MATH 129 cover infinite series?

Yes. The department's course objectives include working with infinite series and calculating and using Taylor series, and the catalog lists approximations by Taylor series.

### What calculator can I use in MATH 129?

A graphing calculator is required, and the TI-83 or TI-84 is recommended. Calculators that do symbolic manipulation, such as the TI-89, Nspire CAS or HP50g, cannot be used.

### What comes after MATH 129?

MATH 223 Vector Calculus, the University of Arizona's Calculus 3 course.