**Students for Whom the Placement Test is Recommended or Appropriate**

Students who completed AP Calculus BC prior to their senior year of high school and whose high school offered a multivariable calculus course which the student took after AP Calculus BC, whether the multivariable calculus course was offered as a dual credit course or not, are eligible to attempt Credit by Examination for M 408D. Students who have a failing grade in M 403L, M 408D, M 408M, or M 308M are ineligible for attempting Credit by Examination for M 408D. Credit for M 408D may not be earned after a student has received credit for M 403L, M 408D, M 408M, or M 308M with a grade of C- or better.

**Where and When to Take the Test**

The UT Exam for M 408D is administered in August and January only, just before classes start for the fall and spring semesters respectively. Students interested in taking the UT Exam for M 408D must first contact MPA Advising at mpaadv@austin.utexas.edu to express interest and evaluate prior Calculus experience. If approved, you will be contacted by Student Testing Services regarding registration.

This exam is administered on the UT Austin campus. Please review the ID Requirements, as students arriving without proper ID may not test.

**Exam Content and Format: **

This exam tests your knowledge of integration techniques, first-order differential equations, and introductory multivariable calculus including parametric equations, partial derivatives, and multiple integrals. Exam questions will be chosen from the topics that are covered in M 408D. In particular, the student should review the following sections and topics from the textbook *Calculus, Early Transcendentals, 8th Edition* by Stewart.

- 7 Techniques of Integration
- Substitution Review
- 7.1 Integration by Parts
- 7.2 Trigonometric Integrals
- 7.3 Trigonometric Substitution
- 7.4 Integration of Rational Functions by Partial Fractions
- 7.5 Strategy for Integration
- 7.8 Improper Integrals

- 9 Differential Equations
- 9.1 Modeling with Differential Equations
- 9.2 Direction Fields and Eulerâ€™s Method
- 9.3 Separable Equations
- 9.4 Models for Population Growth
- 9.5 Linear Equations

- 10 Parametric Equations and Polar Coordinates
- 10.1 Curves Defined by Parametric Equations
- 10.2 Calculus with Parametric Curves
- 10.3 Polar Coordinates
- 10.4 Areas and Lengths in Polar Coordinates

- 11 Infinite Sequences and Series
- 11.1 Sequences
- 11.2 Series
- 11.3 The Integral Test and Estimates of Sums
- 11.4 The Comparison Tests
- 11.5 Alternating Series
- 11.6 Absolute Convergence and the Ratio and Root Tests
- 11.7 Strategy for Testing Series
- 11.8 Power Series
- 11.9 Representations of Functions as Power Series
- 11.10 Taylor and Maclaurin Series
- 11.11 Applications of Taylor Polynomials

- 14 Partial Derivatives
- 14.1 Functions of Several Variables
- 14.2 Limits and Continuity
- 14.3 Partial Derivatives
- 14.5 The Chain Rule

- 15 Multiple Integrals
- 15.1 Double Integrals over Rectangles
- 15.2 Double Integrals over General Regions
- 15.3 Double Integrals in Polar Coordinates
- 15.9 Change of Variables in Multiple Integrals

The exam contains approximately 11 multiple-choice questions and 3 free-response questions.

**Exam Resources:**

Calculators are not allowed to be used during this exam. Students may use blank scratch paper.

**Study Resources:**

Most college-level multivariable calculus textbooks cover the above topics and are appropriate to use in preparing for this exam. UT uses the textbook *Calculus, Early Transcendentals, 8th Edition* by Stewart.

**Registration Fee: **

The total of the fees for this test is $85. When you register for a test, you will immediately be billed for the non-refundable test registration fee of $25. After you take the test, you will be billed for the test fee of $60. Payments are due within 14 days of the billing date. All fees are subject to change.

**Test Results and Retakes: **

You may take the UT Exam for M 408D (Sequences, Series, and Multivariable Calculus) Credit only once.

Results are available within a few days after the test date, in time to register for classes.

UT Austin Courses | Score Range | Notes | ||
---|---|---|---|---|

M 408D | No cut scores are publicized for this test. | |||