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: Calculus: Early Transcendental Functions, 4th Edition, by Larson, Hostetler, and Edwards

Course Content

Chapter 10: Conics, Parametric Equations, and Polar Coordinates (1-3 lectures, with some material covered as needed in later chapters)

10.1 Conics and Calculus (optional)
10.2 Plane Curves and Parametric Equations (optional)
10.3 Parametric Equations and Calculus (optional)
10.4 Polar Coordinates and Polar Graphs
10.5 Area and Arc Length in Polar Coordinates (optional)
10.6 Polar Equations of Conics and Kepler's Laws (omit)

Chapter 11: Vectors and the Geometry of Space (6-8 lectures)

11.1 Vectors in the Plane
11.2 Space Coordinates and Vectors in Space
11.3 The Dot Product of Two Vectors
11.4 The Cross Product of Two Vectors in Space
11.5 Lines and Planes in Space
11.6 Surfaces in Space (optional)
11.7 Cylindrical and Spherical Coordinates (optional)

Chapter 12: Vector-Valued Functions (3-8 lectures)

12.1 Vector-Valued Functions
12.2 Differentiation and Integration of Vector-Valued Functions
12.3 Velocity and Acceleration
12.4 Tangent Vectors and Normal Vectors (optional)
12.5 Arc Length and Curvature (optional)

Chapter 13: Functions of Several Variables (8-10 lectures)

13.1 Introduction to Functions of Several Variables
13.2 Limits and Continuity
13.3 Partial Derivatives
13.4 Differentials
13.5 Chain Rules for Functions of Several Variables
13.6 Directional Derivatives and Gradients
13.7 Tangent Planes and Normal Lines
13.8 Extrema of Functions of Two Variables
13.9 Applications of Extrema of Functions of Two Variables
13.10 Lagrange Multipliers

Chapter 14: Multiple Integration (5-9 lectures)

14.1 Iterated Integrals and Area in the Plane
14.2 Double Integrals and Volume
14.3 Change of Variables: Polar Coordinates
14.4 Center of Mass and Moments of Inertia
14.5 Surface Area (optional)
14.6 Triple Integrals and Applications
14.7 Triple Integrals in Cylindrical and Spherical Coordinates (optional)
14.8 Change of Variables: Jacobians (optional)

Chapter 15: Vector Analysis (3-9 lectures)

15.1 Vector Fields
15.2 Line Integrals
15.3 Conservative Vector Fields and Independence of Path
15.4 Green's Theorem (optional)
15.5 Parametric Surfaces (optional)
15.6 Surface Integrals (optional)
15.7 Divergence Theorem (optional)
15.8 Stokes's Theorem (optional)

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