Calculus B is the second part of a two-course sequence designed for non-STEM majors at the University of Notre Dame. This course builds on foundational calculus concepts, focusing on applications and methods that are essential for understanding the mathematical world around us.

Key Topics Include:

• Integration and Applications: Techniques and applications of integration, including finding areas, volumes, and solving problems in physics like density, work, and energy.
• Advanced Integration Methods: U-substitution, integration by parts, trigonometric substitution, partial fractions, improper integrals, and numerical integration techniques.
• Two-Variable Calculus: Partial derivatives, double integrals, and applications in both Cartesian and polar coordinates.
• Introduction to Differential Equations and Numerical Methods: Basic differential equations, along with numerical solutions, and Lagrange multipliers.
• Sequences and Series: Convergence tests (including ratio test), geometric and infinite series, power series, and Taylor polynomials.

The course emphasizes real-world applications of mathematics, helping students develop strong problem-solving skills, attention to detail, and the ability to synthesize solutions across different contexts.

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