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King Fahd University of Petroleum & Minerals

College of Computing and Mathematics

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MATH201: Calculus III

Core chapter notes, learning outcomes, grading guidance, and textbook information for Calculus III. Use the chapter cards below to go directly to the main content.

Department Department of Mathematics
College College of Computing and Mathematics
Prerequisite MATH102
Credit Hours 3-0-3

Chapter Notes

The chapter links are the primary navigation for the published course notes.

Chapter 10 Parametric and Polar Curves Plane curves, parametric representations, polar coordinates, and the calculus of parametric and polar graphs. Chapter 11 Vectors and Geometry of Space Vectors, lines, planes, surfaces, cylindrical coordinates, and spherical coordinates in three-dimensional space. Chapter 13 Functions of Several Variables Limits, continuity, partial derivatives, gradients, tangent planes, and extrema for multivariable functions. Chapter 14 Multiple Integrals Double and triple integrals in rectangular, polar, cylindrical, and spherical coordinate systems.

Textbook

Calculus: Early Transcendental Functions textbook cover

The course follows the adopted syllabus text and the chapter progression used in the published notes.

Larson, R. & Edwards, B., Calculus: Early Transcendental Functions, Metric Version, 7th edition, Cengage Learning, Inc., 2019.

Learning Outcomes

Based on the course syllabus.

  1. Describe and analyze parametric and polar curves, and identify surfaces in space.
  2. Compute areas, arc lengths, and surface areas in plane curves.
  3. Perform vector operations and determine equations of lines and planes in three-dimensional space.
  4. Analyze limits and continuity of multivariable functions.
  5. Compute directional derivatives, gradients, and tangent planes.
  6. Find local and global extrema of multivariable functions, including constrained extrema via Lagrange multipliers.
  7. Evaluate multiple integrals in rectangular, polar, cylindrical, and spherical coordinates.

Grading Policy

Summary of the syllabus grading weights and the class work normalization rule.

  • Exam I75/300 (25%)
  • Exam II75/300 (25%)
  • Final Exam105/300 (35%)
  • Class Work45/300 (15%)

Class Work Formula

y = 9 * (median(Exam I %) + median(Exam II %)) / 40

Expected class work average interval: [y - 1.5, y + 1.5]

If the Exam I median is 72% and the Exam II median is 68%, then y = 9 * (72 + 68) / 40 = 31.5. That means the section class work average is expected to lie in [30.0, 33.0].

Course Description

This course provides a comprehensive introduction to multivariable calculus, covering parametric and polar curves, vectors, lines, planes, and surfaces in space, cylindrical and spherical coordinates, functions of several variables, partial and directional derivatives, gradients, tangent planes, extrema with and without constraints, and double and triple integrals in various coordinate systems.