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# MAC 2313 — Calculus III — Syllabus

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

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
10.7 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