Math 2B: Calculus - Lecture Notes

Professor Natalia Komarova

Course Introduction

• Instructor: Professor Natalia Komarova
• Course Website: Contains all relevant information
• Textbook:
  • "Calculus: Early Transcendentals" by Stewart (7th Edition)
  • Ensure it says "Early Transcendentals"
  • Secondhand copies are acceptable
  • Only need chapter material and homework problems

Exams

• Midterms: October 18th and November 8th
• Final Exam:
  • Common final on Saturday, December 7th, 1-3 PM
  • No books, notes, or calculators allowed
  • Valid UCI ID required
  • Inform math department secretaries early if you can't attend
• Quizzes:
  • Held weekly during discussion sessions
  • Based on homework assignments

Assignments

• Homework:
  • Optional but essential for understanding
  • List of problems provided on the class website
  • Not graded directly but helps with quizzes
• Webwork:
  • Online homework assignments
  • 8 assignments during the quarter
  • Released weekly on Thursdays, due the following Friday
  • Instructions and technical support details on the class website

Grading

• Breakdown:
  • Final: 40%
  • Midterms: 20% each
  • Webwork: 10%
  • Quizzes: 10%
• Policy:
  • Lowest quiz and webwork scores are dropped
  • No makeup opportunities for quizzes or webwork
  • No curve or extra credit

Calculus Review

• Antiderivatives
  • Definition: If F' is f, then F is an antiderivative of f
  • General form: F + C (C is a constant)
  • Examples:
    • f(x) = x^2, F(x) = (x^3/3) + C
    • f(x) = cos(x), F(x) = sin(x) + C
  • Power Rule: F(x) = (x^(n+1))/(n+1) + C for n ≠ -1
  • Special Case: f(x) = 1/x, F(x) = ln|x| + C

Practice Problems

• Finding Antiderivatives
  • Given f(x) = x^6, find F(x): F(x) = (x^7)/7 + C
  • Given f'(x) = 5 + cos(x) + 3x^2, find f(x): f(x) = 5x + sin(x) + (3x^3)/3 + x^(-1/2)/(-1/2) + C

Graphical Interpretation

• Velocity and Position
  • Velocity (rate of change) and position relation
  • Positive velocity -> Increasing position
  • Negative velocity -> Decreasing position
  • Zero velocity -> Maximum or minimum point

Differential Equations

• Problem: Given acceleration a(t) = t + 1, initial conditions s(0) = 2, v(0) = -1
  • Find velocity v(t): v(t) = (t^2)/2 + t - 1
  • Find position s(t): s(t) = (t^3)/6 + (t^2)/2 - t + 2

Summary

• Importance of understanding core concepts and practicing homework problems
• Utilize office hours and resources provided on the course website for additional help