Calculus II

Program Overview

This program provides a comprehensive foundation in calculus, differential equations, infinite series, and functions of several variables. It covers essential techniques and applications, equipping students with the mathematical skills necessary for careers in science, engineering, and other fields. The program emphasizes problem-solving and critical thinking, preparing students to tackle real-world challenges.

Program Outline

Outline:

Module 1: Techniques and Applications of Integration

• Indefinite integrals and the Fundamental Theorem of Calculus
• Techniques of integration, including integration by substitution, by parts, and by trigonometric substitution
• Applications of integration to the calculation of areas, volumes, and other quantities

Module 2: Differential Equations

• First-order differential equations, including separable and linear equations
• Second-order differential equations, including homogeneous and nonhomogeneous equations
• Applications of differential equations to modeling real-world phenomena

Module 3: Infinite Series

• Sequences and series, including convergence and divergence tests
• Power series, including Taylor and Maclaurin series
• Applications of power series to representing functions and solving differential equations

Module 4: Functions of Several Variables

• Functions of several variables and their graphs
• Limits and continuity of functions of several variables