Calculus II builds on the techniques of integration and introduces infinite processes like sequences and series.

Key Topics

• Techniques of Integration — Integration by parts, trigonometric substitution, partial fractions, and improper integrals.
• Sequences — Convergence and divergence of infinite sequences.
• Series — Infinite sums, geometric series, and the telescoping series.
• Convergence Tests — Ratio test, comparison test, integral test, root test, and alternating series test.
• Power Series — Representing functions as infinite polynomials: \(\sum_{n=0}^{\infty} c_n (x-a)^n\).
• Taylor and Maclaurin Series — Approximating functions around a point using derivatives.
• Parametric Equations and Polar Coordinates — Calculus with curves defined by parameters or polar equations.

Why It Matters

The integration techniques from Calculus II appear constantly in physics and engineering. Series representations are the foundation of how computers evaluate functions, and how signals are analyzed in telecommunications.