Math 114 Calculus II (Spring 2018)

Course Overview

Math 114, also known as Calculus II, is the second semester in the standard calculus sequence for engineering, natural sciences, and mathematics majors. The Spring 2018 offering was structured as a 15week semester with three 50minute lectures per week. The primary goal of the course is to deepen the conceptual understanding of integration and its applications, introduce techniques for handling infinite series, and explore multivariable concepts such as polar, cylindrical, and spherical coordinates.

The class met Mondays, Wednesdays, and Fridays in Room 212 of the Mathematics Building. The instructor, Dr. Laura M. Spencer, emphasized rigorous proof techniques alongside computational fluency. A typical week combined a lecture, a short inclass activity, and a problemsolving session. All homework was submitted online through the universitys Canvas portal.

Key Topics

• Techniques of Integration
  • Integration by parts, trigonometric integrals, and trigonometric substitution.
  • Partial fractions and rational functions.
  • Improper integrals and convergence tests.
• Infinite Series
  • Power series representations and radius of convergence.
  • Taylor and Maclaurin series derivation, error analysis, and applications.
  • Series tests: Comparison, Ratio, Root, Alternating, and Integral tests.
• Parametric Equations & Polar Coordinates
  • Parametric differentiation and arc length.
  • Area and volume using polar coordinates.
  • Conversions between Cartesian, polar, and parametric forms.
• Vectors & the Plane
  • Twodimensional vectors, dot product, and projection.
  • Equations of lines and planes in vector form.
• Applications of Integration
  • Work, fluid pressure, and center of mass.
  • Volumes of solids of revolution (washer, shell, and cylindrical methods).

Weekly Schedule (Selected Weeks)

All dates were subject to change based on lecture progress. The instructor posted any adjustments on Canvas at least 24 hours in advance.

Resources and Materials

The following resources were recommended for the Spring 2018 term:

• Textbook: James Stewart, Calculus: Early Transcendentals, 8th Edition. ISBN 978-1285231859.
• Online Platform: Canvas for lecture notes, homework uploads, and announcements.
• Supplemental Videos: Khan Academy playlists covering integration techniques and series.
• Study Guides: Weekly PDF outlines posted each Friday, summarizing the next weeks objectives.
• Office Hours: Dr. Spencer MWF 2:004:00pm, room 315 Math Bldg. Graduate TAs also held dropin sessions on Tuesdays.

Assessment Structure

Grading was based on the following components:

1. Homework (7 assignments) 25%
2. Quizzes (2) 10%
3. Midterm Exam 30%
4. Final Exam 35%

Homework was graded for completeness and correctness, with partial credit given for methodical work. Quizzes were short (1520minutes) and conducted in class; they focused on recent material to encourage consistent study habits. Both the midterm and final exams consisted of a mix of computational problems, prooftype questions, and conceptual multiplechoice items.

Study Tips for Success

• Practice Daily: Integration techniques become automatic only after regular practice.
• Master Series Tests: Knowing when a series converges saves time on exam problems.
• Use the Why? Approach: For each formula, ask how it was derived; this deepens understanding.
• Form Study Groups: Discussing problems with peers uncovers alternative methods.
• Utilize Office Hours: Bring specific questions; the instructor can point out subtle mistakes.
• Work the EndofChapter Problems: The textbooks Challenge problems reflect the difficulty of actual exams.
• Review Past Exams: Previous years tests (available in the department archive) illustrate the style of questions and expected rigor.

Contact Information

For any lingering questions about the course content, grading, or future semesters, you may reach out to: