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
Lecture 18, Strategies for Testing Convergence
Lecture 19, Power Series (Handwritten notes - morning)
Lecture 20, Representing Functions by Power Series
Lecture 21, Taylor Series (Handwritten Notes)
Lecture 22, Exam II Review, Part I (Handwritten Notes - 10 AM) (Handwritten Notes - 2 PM)
Lecture 23, Exam II Review, Part II (Handwritten Notes)

Unit III: Applications of Integration, Motion in the Plane

Lecture 24, Average Value of a Function, Volumes
Lecture 25, Volumes with Known Cross-Section
Lecture 26, Volumes - Disc and Washer Method (Handwritten notes)
Lecture 27, Volumes - Cylindrical Shell Method
Lecture 28, Arc Length (Handwritten notes)
Lecture 29 , Surface Area (Handwritten notes)
Lecture 30, Center of Mass and Moments
Lecture 31, Parametric Curves
Lecture 32, Calculus on Parametric Curves (handwritten notes)
Lecture 33, Polar Coordinates (handwritten notes)
Lecture 34, Review - Applications of Integration (handwritten notes)
Lecture 35, Review - Parametric Curves

Unit IV: Conic Sections, Differential Equations

Lecture 36, Calculus for Polar Curves (Arc length and Area)
Lecture 37, Conic Sections (Part I of II) (with corrections) (handwritten notes)
Lecture 38, Conic Sections (Part II of II) (handwritten notes)
Lecture 39, Modeling with Differential Equations (handwritten notes)
Lecture 40, Direction Fields and Euler's Method (Spreadsheet: Euler's Method Ex. 1, Euler's Method Ex. 2,3; Euler vs. Predictor-Corrector)
Lecture 41, Separable Equations