Calculus 3-4 CHS (College in the High School - Bellevue College) - MT608A/B

Calculus 3-4 CHS (College in the High School - Bellevue College) - MT608A/B

Prerequisites: Must have completed AP Calculus BC or AP Calculus AB with a score of 5 on the AP Exam  prior to taking this class.

Learning Recommendations: Designed for students who earn a 5 on the AP Calculus AB exam or a 3 or above on the AP Calculus BC exam. A strong foundation in limits, derivatives, integration, polynomial approximations, and series is required.

General Description: This one-year advanced mathematics course extends the calculus sequence for students who have completed AP Calculus BC. Following the college syllabi for Calculus 3 and 4, the course explores topics such as infinite sequences and series, vector calculus, functions of several variables, and multiple integrals. It is ideal for students aiming to deepen their understanding of calculus concepts and maintain continuity in their mathematics education, particularly those planning to pursue STEM degrees.

College Credit: Students earning an A or B in this course qualify at no cost for 10 Math credits for Math& 153 and Math& 254 at Bellevue College.

Content:

• Vectors and Geometry of Space:
  • 3D coordinate systems, vector operations, equations of lines and planes, cylinders, and quadric surfaces.
• Vector Functions:
  • Derivatives, integrals, arc length, curvature, and motion in space (velocity and acceleration).
• Partial Derivatives:
  • Functions of several variables, tangent planes, chain rule, optimization, and Lagrange multipliers.
• Multiple Integrals:
  • Double and triple integrals, including polar, cylindrical, and spherical coordinates; change of variables and surface area calculations.
• Infinite Sequences and Series:
  • Taylor polynomials, error bounds, and series manipulations.
• Vector Calculus:
  • Vector fields, line integrals, Green's Theorem, Stokes' Theorem, and the Divergence Theorem.

Homework: Nightly practice problems (30–45 minutes per night) designed to reinforce daily lessons and enhance mastery through incremental learning. Homework quizzes assess the application of concepts from these practice problems.