Lecture Materials

Links to lectures and supplemental materials for each lecture will be posted here throughout the semester

Unit I: A Toolbox for Integration

Lecture I, Integration by Parts (Handwritten Notes)
Lecture 2, Trig Integrals (Handwritten Notes)
Lecture 3, Trig Substitution (Handwritten Notes)
Lecture 4, Integrating Rational Functions, Part I (Handwritten Notes) (Lecture notes revised to reflect what we actually covered in class!)
Lecture 5, Integrating Rational Functions, Part II (Handwritten Notes)
Lecture 6, Numerical Integration, Part I and Excel spreadsheet with examples for Midpoint and Trapezoid rules
Lecture 7, Numerical Integration, Part II and Excel spreadsheet with examples for Midpoint and Simpson's rule plus error analysis ( Handwritten Notes). You can find a nice explanation of error bounds in these notes from a math class at Carnegie-Mellon University
Lecture 8, Improper Integrals (Handwritten Notes) Note we didn't discuss the comparison test from these notes until Wednesday
Lecture 9, (Preview) Sequences (Handwritten Notes) I didn't get to the end of these in either lecture, so we'll continue Friday
Lecture 10, (Preview) Sequences by Recursion and Excel spreadsheet for the Fibonacci and Newton sequences
Lecture 11, Exam I Review

Unit II: Sequences and Series

Lecture 12, Introduction to Series (Handwritten Notes)
Lecture 13, The Integral Test (now with corrections and answers to in-class exercises)
Lecture 14, The Comparison Test and the Limit Comparison Test (Handwritten notes)
Lecture 15, The Alternating Series Test
Lecture 16, Absolute and Conditional Convergence
Lecture 17, The Ratio and Root Tests for Absolute Convergence