Math 252: Calculus II
Department of Mathematics | Spring Semester 2023
Course Overview
Math 252: Calculus II continues the study of differential and integral calculus begun in Calculus I. This course focuses on advanced techniques of integration, applications of integration, sequences and series, and parametric equations. Students will learn to solve complex problems that require multiple mathematical concepts and develop the analytical skills necessary for further study in mathematics, sciences, and engineering.
The course consists of three 50-minute lectures and one 110-minute recitation section per week. Recitations provide opportunities for collaborative problem-solving and individual assistance with challenging concepts. Through homework, exams, and participation, students will demonstrate their understanding of calculus concepts and their ability to apply them to various problems.
Prerequisites
Math 251: Calculus I (or equivalent) with a grade of C- or better is required. Students should be comfortable with the following topics from Calculus I:
- Limits and continuity
- Derivatives and differentiation rules
- Applications of derivatives (optimization, related rates)
- Basic integration techniques
- Fundamental Theorem of Calculus
- Basic applications of integration (area, volume)
Note: Students who need to review these topics are encouraged to consult the Mathematics Department's online resources and seek help from the Math Help Center during the first week of classes.
Topics Covered
1. Techniques of Integration
- Integration by parts
- Trigonometric integrals
- Trigonometric substitution
- Integration of rational functions via partial fractions
- Strategy for integration
- Integration using tables and computer algebra systems
- Improper integrals
2. Applications of Integration
- Areas between curves
- Volumes using cross-sections (disks, washers)
- Volumes by cylindrical shells
- Arc length
- Area of a surface of revolution
- Applications to physics and engineering (work, hydrostatic force, moments and centers of mass)
3. Sequences and Series
- Sequences and their limits
- Series (convergence, divergence)
- Integral test and p-series
- Comparison tests
- Alternating series test
- Ratio and root tests
- Absolute and conditional convergence
- Strategy for testing series
- Power series
- Representations of functions as power series
- Taylor and Maclaurin series
- Applications of Taylor polynomials
4. Parametric Equations and Polar Coordinates
- Curves defined by parametric equations
- Calculus with parametric curves
- Polar coordinates
- Areas and lengths in polar coordinates
- Conic sections in polar coordinates
Textbook and Resources
Required Textbook: Calculus: Early Transcendentals, 9th Edition by James Stewart, Cengage Learning.
Online Resources:
- WebAssign online homework system (access code included with new textbook purchase)
- Course website with additional notes, practice problems, and exam information
- Video tutorials covering key concepts
- Math Help Center (Math Building, Room 102) provides free tutoring
Calculators: A TI-83, TI-84, or equivalent graphing calculator is recommended for visualizing concepts. While calculators may be used during lectures and for homework, their use on exams may be restricted. Instructions regarding calculator policy for each exam will be announced in class.
Learning Outcomes
Upon successful completion of Math 252, students should be able to:
- Apply various integration techniques to solve definite and indefinite integrals
- Use integration to solve applied problems involving area, volume, work, and other physical quantities
- Understand the concept of sequences and determine their convergence
- Apply appropriate tests to determine convergence or divergence of infinite series
- Represent functions as power series and use Taylor series for approximation of functions
- Analyze and work with parametric equations and polar coordinates
- Apply calculus concepts to curves represented in parametric and polar forms
- Communicate mathematical ideas clearly in written and oral form
- Solve multi-step problems that integrate different concepts from the course
Assessment Methods
Student mastery of the course material will be evaluated through the following components:
| Component | Weight | Description |
|---|---|---|
| Online Homework | 15% | Weekly assignments via WebAssign |
| Recitation Activities | 10% | In-class problem-solving and quizzes |
| Midterm Exams | 50% | Three in-class exams during the semester |
| Final Examination | 25% | Comprehensive exam during finals week |
Grading Scale
- A: 93-100%
- A-: 90-92%
- B+: 87-89%
- B: 83-86%
- B-: 80-82%
- C+: 77-79%
- C: 73-76%
- C-: 70-72%
- D+: 67-69%
- D: 60-66%
- F: Below 60%
Exam Policies: All exams are cumulative, with emphasis on material since the previous exam. Make-up exams are only given for documented emergencies with prior notification when possible. During exams, students may use calculators as specified by the instructor but no other electronic devices. Academic dishonesty will result in a zero for the exam and may lead to further disciplinary action.
Course Schedule
Week 1-2: Techniques of Integration
- Review of integration concepts
- Integration by parts
- Trigonometric integrals and substitution
- Partial fractions
Week 3-4: Applications of Integration
- Areas between curves
- Volumes by various methods
- Arc length and surface area
- Physical applications
Week 5: Midterm Exam I
Week 6-8: Sequences and Series
- Sequences and limits
- Series and convergence tests
- Alternating series and absolute convergence
- Power series
Week 9: Midterm Exam II
Week 10-12: Power Series
- Representing functions as power series
- Taylor and Maclaurin series
- Applications of Taylor polynomials
Week 13: Midterm Exam III
Week 14-15: Parametric Equations and Polar Coordinates
- Parametric curves and calculus
- Polar coordinates
- Areas and lengths in polar form
- Conic sections
Week 16: Review and Final Exam
Instructor Information
Instructor: Dr. Sarah Johnson
Office: Mathematics Building, Room 412
Office Hours: Mondays and Wednesdays, 2:00-4:00 PM, or by appointment
Email: s.johnson@university.edu
Teaching Assistants:
- David Chen - Recitation Sections 001 and 002 (david.chen@university.edu)
- Amanda Rivera - Recitation Sections 003 and 004 (amanda.rivera@university.edu)
Lecture Times: Mondays, Wednesdays, Fridays, 10:00-10:50 AM, Science Hall 101
Recitation Times: Tuesdays, 2:00-3:50 PM, various locations
Important Announcements: All course announcements including exam locations and schedule changes will be posted on the course website. Students should check the website at least twice per week for updates.
