Course Overview

Calculus B continues the study of calculus by focusing on integration, differential equations, and the broad applications of integral calculus. Building upon the foundations of limits and differentiation from Calculus A, this course equips students with advanced problem-solving tools for mathematics, science, and engineering.

Key Learning Focus

Students will learn to:

• Compute antiderivatives using a variety of techniques, including substitution.
• Evaluate definite and indefinite integrals, applying both analytical and numerical methods.
• Apply Riemann sums and the Fundamental Theorem of Calculus to solve real-world problems.
• Differentiate and integrate logarithmic, exponential, and inverse trigonometric functions.
• Solve simple differential equations using separation of variables.
• Apply integration to find area between curves, volumes, and surface areas.
• Use integration in applied contexts such as work, center of mass, and fluid force.

Instructional Approach

The course integrates multiple representations of calculus concepts—graphical, numerical, and analytical—to ensure deep understanding. A graphing calculator is considered essential and is used throughout to support visualization, confirm results, and enhance problem-solving.

Applications and Connections

Students will apply integration techniques across diverse real-world and cross-disciplinary scenarios. From physics and engineering to economics and natural sciences, instruction emphasizes the relevance of integral calculus in modeling, analysis, and problem-solving.

Outcome

By the end of Calculus B, students will have mastered the fundamentals of integration and its applications, preparing them for advanced study in multivariable calculus, differential equations, and higher-level STEM coursework. Students will leave with both the analytical and practical skills necessary for academic and professional success.