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Mathematics & Statistics

**Prerequisites:** C (2.0) or better in MAC 2282, or C (2.0) or better in MAC 2312.

**Course Description:** The course meets for approximately 55 hours during a 15-week semester. Successful completion of the course merits 4 semester hours of credit. The schedule outlined below allows time for four midterm exams plus a cumulative final exam, which are the norms for this course. (* Note:* A “lecture” is defined as a 50-minute time period.)

**Text:** *Essential Calculus: Early Transcendentals*, USF Custom Edition, by Stewart

**Alt. Text:** *Essential Calculus: Early Transcendentals*, 2nd Edition, by Stewart

**Course Content**

**9. Parametric Equations and Polar Coordinates** (2 weeks)

9.1 Parametric Curves

9.2 Calculus with Parametric Curves

9.3 Polar Coordinates

9.4 Areas and Lengths in Polar Coordinates

9.5 Conic Sections in Polar Coordinates (omit)

Review

**10. Vectors and the Geometry of Space** (3-4 weeks)

10.1 Three-Dimensional Coordinate Systems

10.2 Vectors

10.3 The Dot Product

10.4 The Cross Product

10.5 Equations of Lines and Planes

10.6 Cylinders and Quadric Surfaces

10.7 Vector Functions and Space Curves

10.8 Arc Length and Curvature

10.9 Motion in Space: Velocity and Acceleration (optional)

Review

**11. Partial Derivatives** (3-4 weeks)

11.1 Functions of Several Variables

11.2 Limits and Continuity

11.3 Partial Derivatives

11.4 Tangent Planes and Linear Approximations

11.5 The Chain Rule

11.6 Directional Derivatives and the Gradient Vector

11.7 Maximum and Minimum Values

11.8 Lagrange Multipliers

Review

**12. Multiple Integrals** (3-4 weeks)

12.1 Double Integrals over Rectangles

12.2 Double Integrals over General Regions

12.3 Double Integrals in Polar Coordinates

12.4 Applications of Double Integrals

12.5 Triple Integrals

12.6 Triple Integrals in Cylindrical Coordinates (optional)

12.7 Triple Integrals in Spherical Coordinates (optional)

12.8 Change of Variables in Multiple Integrals (optional)

Review

**13. Vector Calculus** (2-3 weeks)

13.1 Vector Fields

13.2 Line Integrals

13.3 The Fundamental Theorem for Line Integrals

13.4 Green's Theorem (optional)

13.5 Curl and Divergence (optional)

13.6 Parametric Surfaces and Their Areas (optional)

13.7 Surface Integrals (optional)

13.8 Stokes' Theorem (optional)

13.9 The Divergence Theorem (optional)

Review

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