Course Overview

This syllabus outlines the key topics and learning outcomes for MATH 2242 Calculus II at Georgia Southern University. The course covers advanced integration techniques, transcendental functions, parametric and polar coordinates, sequences, and series, providing a comprehensive foundation for further study in mathematics and related fields.

Major Topics in Calculus II

Techniques and Applications of Integration

Integration is a fundamental concept in calculus, used to find areas, volumes, and solve various applied problems. Calculus II expands on basic integration methods and introduces advanced techniques.

• Integration by Parts: A method based on the product rule for differentiation, useful for integrating products of functions. Formula:

• Trigonometric Integrals: Techniques for integrating powers and products of trigonometric functions, often using identities.

• Trigonometric Substitution: Substituting trigonometric expressions to simplify integrals involving square roots. Example: For , use .

• Partial Fractions: Decomposing rational functions into simpler fractions for easier integration. Example:

• Improper Integrals: Integrals with infinite limits or integrands with infinite discontinuities, evaluated using limits. Formula:

Applications of Integration

Integration is applied to solve real-world problems involving accumulation and area.

• Area and Volume: Calculating the area under curves and the volume of solids of revolution. Formula for volume (disk method):

• Work and Physics Applications: Using integration to compute work done by a variable force, center of mass, and other physical quantities.

Transcendental Functions

Transcendental functions include exponential, logarithmic, and hyperbolic functions, which extend the range of calculus applications.

• Exponential and Logarithmic Functions: Functions of the form and , with unique properties and applications in growth and decay models.

• Hyperbolic Functions: Analogous to trigonometric functions but based on hyperbolas. Definitions: ,

Parametric Equations and Polar Coordinates

Parametric and polar representations allow for the description of curves and regions not easily handled by standard Cartesian equations.

• Parametric Equations: Expressing curves using a parameter , such as , .

• Polar Coordinates: Describing points in the plane using radius and angle . Conversion: ,

• Calculus with Parametric and Polar Curves: Finding derivatives, areas, and arc lengths for curves in these forms. Arc length (parametric):

Sequences and Series

Sequences and series are foundational for understanding convergence, infinite sums, and power series representations of functions.

• Sequences: Ordered lists of numbers, often defined recursively or by a formula.

• Series: Sums of sequences, with convergence determined by various tests. Example: Geometric series converges if .

• Taylor Series: Representing functions as infinite sums of derivatives at a point. Formula:

Course Learning Outcomes

• Use integration by parts to compute integrals

• Compute trigonometric integrals

• Use trigonometric substitution in compute integrals

• Understand integration of rational functions using partial fractions

• Understand improper integrals

• Apply integrals to solve volume problems

• Understand the convergence of series and the convergence of infinite series

• Understand polar series and Taylor series

• Apply calculus of parametric and polar curves

Grading Policy Table

Final Letter Grade Ranges

Additional info:

• This syllabus provides a comprehensive overview of Calculus II topics, including all major chapters relevant to a college-level calculus course.

• Students are expected to use a scientific calculator and online homework platform (MyLab Math).

• Attendance, academic honesty, and accessibility policies are included to support student success.