Wolfram Alpha Integral Calculator
Mathematica Tutorial (Mathematica Notebook)
St. Andrews History of Mathematics Archive
Overleaf (free web-based version of LaTeX)
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Chapter 6: Applications of Integration
6.1: Areas Between Curves
Example 5 (Mathematica Notebook)
Read 6.1 in Stewart, Clegg, and Watson's Calculus Early Transcendentals (9th ed) (SCW)
6.2: Volumes
Read 6.2 in SCW
6.3: Volumes by Cylindrical Shells
Read 6.3 in SCW
6.4: Work
Read 6.4 in SCW
Chapter 7: Techniques of Integration
7.1: Integration by Parts
Read 7.1 in SCW
7.2: Trigonometric Integrals
Read 7.2 in SCW
7.3: Trigonometric Substitutions
Read 7.3 in SCW
7.4: Integration of Rational Functions by Partial Fractions
Partial Fraction Decomposition Examples (Mathematica Notebook)
Read 7.4 in SCW
Exam 1 will be given in-class on Friday, 9/19/25, at 3:00 - 3:50 pm. It will cover the material from Sections 6.1 - 6.4 and 7.1 - 7.4 (Lectures 1 - 8, relevant textbook readings, and WebAssign homework). Electronic devices, including calculators, are not to be used during this exam.
Two Useful Ideas for Integration
7.7: Numerical Integration
Example 1 (Mathematica Notebook)
Example 5 (Mathematica Notebook)
Example 6 (Mathematica Notebook)
Example 7 (Mathematica Notebook)
Answers (Mathematica Notebook)
Read 7.7 in SCW
7.8 Improper Integrals
Example 9 (Mathematica Notebook)
Read 7.8 in SCW
Chapter 8: Further Applications of the Integral
8.1 and 8.2: Arc Length and Area of a Surface of Revolution
Read 8.1 and 8.2 in SCW
8.3: Applications to Physics and Engineering
Example 2 (Mathematica Notebook)
Read 8.3 in SCW
Chapter 9: Differential Equations (A Brief Introduction)
9.1: Modeling with Differential Equations; 9.3: Separation of Variables
Read 9.1 and 9.3 in SCW
Chapter 10: Parametric Curves and Polar Coordinates
10.1: Curves Defined by Parametric Equations; 10.2: Calculus with Parametric Curves
Examples of Parametric Curves (Mathematica Notebook)
Read 10.1 in SCW
Read 10.2 in SCW
10.3: Polar Coordinates
Some Polar Plots (Mathematica Notebook)
Read 10.3 in SCW
Exam 2 will be given in-class on Friday, 10/24/25, at 3:00 - 3:50 pm. It will cover the material from Sections 7.7, 7.8, 8.1 - 8.3, , 9.1, 9.3, and 10.1 - 10.3 (Lectures 9 - 15, relevant textbook readings, and WebAssign homework). Electronic devices, including calculators, are not to be used during this exam.
10.4: Calculus in Polar Coordinates
Read 10.4 in SCW
Chapter 11: Sequences, Series, and Power Series
11.1: Sequences
Examples of Sequences (Mathematica Notebook)
Read 11.1 in SCW
11.2: Series
Read 11.2 in SCW
11.3: The Integral Test and Estimates of Sums
Work for Examples 3, 4, and 5 (Mathematica Notebook)
Read 11.3 in SCW
11.4: The Comparison Tests
Work for Example 4 (Mathematica Notebook)
Read 11.4 in SCW
11.5: Alternating Series and Absolute Convergence
Examples of Alternating Series (Mathematica Notebook)
Read 11.5 in SCW
11.6: The Ratio and Root Tests; 11.7: Strategy for Testing Series
Example 3 (Some Series Examples) (Mathematica Notebook)
Read 11.6 in SCW
Read 11.7 in SCW
11.8: Power Series
Read 11.8 in SCW
Exam 3 will be given in-class on Monday, 11/24/25, at 3:00 - 3:50 pm. It will cover the material from Sections 10.4 and 11.1 - 11.8 (Lectures 16 - 23, relevant textbook readings, and WebAssign homework). Electronic devices, including calculators, are not to be used during this exam.
11.9: Representation of Functions as Power Series
Read 11.9 in SCW
11.10: Taylor and Maclaurin Series
Read 11.10 in SCW