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.
University of Arizona Updated 3 min read
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
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On this page
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 | u-substitution |
| Integration by parts | Integration by parts | Integration by parts |
| Partial fractions and trig substitution | Partial fractions | Trig substitution |
| Numerical integration | Trapezoid sums | Riemann sums |
| Improper integrals | Infinite limits of integration | Improper integrals |
| Geometry: area and volume | Volumes by washers | Volumes of revolution |
| Physics: work and center of mass | Work | Center of mass |
| Differential equations, graphically | Slope fields | Euler's method |
| Differential equations, algebraically | Separable equations | Differential equations problems |
| Modeling with differential equations | Logistic growth | Growth and decay |
| Infinite series | Geometric series | Convergence tests |
| Taylor series | Taylor polynomials | Taylor series |
MATH 129 in the Arizona sequence
| Course | Units | Notes |
|---|---|---|
| MATH 122B First-Semester Calculus | 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 | 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:
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:
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 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.
- 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.
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Integration by parts
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