Calculus II Course Outline

Course Description

Calculus II is the second course in the calculus sequence and builds upon the foundations established in Calculus I. This course continues the study of calculus with a focus on integration techniques, applications of integration, sequences and series, parametric equations, polar coordinates, and differential equations. Students will develop deeper mathematical reasoning skills and the ability to apply calculus concepts to real-world problems.

Course Objectives

Upon successful completion of this course, students will be able to:

Demonstrate proficiency with various integration techniques including substitution, integration by parts, trigonometric substitution, and partial fractions
Apply integration to solve problems involving areas, volumes, work, and other physical applications
Analyze sequences and series for convergence using appropriate tests
Represent functions as power series and determine intervals of convergence
Parametrize curves and calculate arc length and surface area of revolution
Work with polar coordinates and sketch polar curves
Solve basic differential equations

Prerequisites

Students should have successfully completed Calculus I (or equivalent) with a grade of C or better. A solid understanding of limits, derivatives, basic integration, and functions is essential.

Course Schedule

Unit 1: Advanced Integration Techniques

Review of basic integration from Calculus I
Integration by parts
Trigonometric integrals
Trigonometric substitution
Integration of rational functions using partial fractions
Integration strategies and practice
Improper integrals

Duration: 3 weeks

Unit 2: Applications of Integration

Areas between curves
Volumes by slicing (disk and washer methods)
Volumes by cylindrical shells
Arc length
Surface area of revolution
Physical applications (work, center of mass, fluid pressure)

Duration: 2 weeks

Unit 3: Sequences and Series

Sequences and their limits
Series and convergence tests
The Integral Test and p-series
Comparison tests
Alternating series and absolute convergence
Ratio and Root tests

Duration: 2 weeks

Unit 4: Power Series

Power series and radius of convergence
Representing functions as power series
Taylor and Maclaurin series
Applications of Taylor series
Binomial series

Duration: 2 weeks

Unit 5: Parametric Equations and Polar Coordinates

Parametric equations and curves
Calculus with parametric curves
Polar coordinates
Areas and lengths in polar coordinates
Conic sections in polar coordinates

Duration: 2 weeks

Unit 6: Introduction to Differential Equations

Modeling with differential equations
Direction fields and Euler's method
Separable differential equations
Linear equations
Second-order linear equations (introduction)

Duration: 2 weeks

Assessment Methods

Assessment	Weight	Description
Homework Assignments	15%	Weekly problem sets to reinforce concepts
Quizzes	20%	Short assessments on specific topics
Midterm Examination 1	15%	Units 1-2
Midterm Examination 2	15%	Units 3-4
Final Project	10%	Application of calculus concepts to real-world problems
Final Examination	25%	Comprehensive assessment covering all course material

Recommended Resources

Required Textbook: Stewart, J. (2021). "Calculus: Early Transcendentals" (9th ed). Cengage Learning.
Online Resources: Khan Academy, Paul's Online Math Notes, MIT OpenCourseWare
Graphing Calculator: TI-84 or equivalent (or approved graphing app)
Mathematical Software: Desmos, GeoGebra, or Wolfram Alpha

Academic Policies

Academic Integrity: All work submitted must be your own. Plagiarism and cheating will result in disciplinary action according to university policy.
Late Work: Late assignments will be penalized 10% per day unless prior arrangement has been made with the instructor.
Attendance: Regular attendance is expected. Excessive absences may impact your final grade.
Make-up Exams: Make-up exams will only be given for documented emergencies or university-sanctioned events.