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Lecture Notes

  1. Sigma Notation, Riemman Sum, and Definite Integral (Ch 5.1 & 5.2)
  2. Fundamental Theorem of Calculus, Integrals of Even and Odd Functions (Ch 5.3 & 5.4)
  3. Mean Value Theorem for Integrals, Substitution Rule for Integrals (Ch 5.4 & 5.5)
  4. Substitution Rule using Properties of Trig Functions, Area between Two Curves (Ch 5.5 & 6.2)
  5. Area of the Region between Two Curves, Volume of Solid by Slicing (Ch 6.2 & 6.3)
  6. Volume by Shell Method, Arc Length of Curves, Area of Surface of Revolution (Ch 6.4, 6.5, 6.6)
  7. Area of Surface of Revolution, Physical Applications (Ch 6.6 & 6.7)
  8. Review for Midterm Exam 1: Integration and Its Applications (Ch 5.1 - 5.5, Ch 6.2 - 6.7). Review Slides
  9. Integration Techniques: Integration by Parts (Ch 7.1 & 7.2).
  10. Integration Techniques: Trigonometric Integrals and Substitution (Ch 7.3 & 7.4).
  11. Integration Techniques: Partial Fractions (Ch 7.5).
  12. Integration Techniques: Numerical Integration (Ch 7.7). Computer Algebra Demo.
  13. Integration Techniques: Improper Integrals (Ch 7.8).
  14. Introduction to Differential Equations (Ch 7.9).
  15. Recurrence Relation, Explicit Formula, Limit of a Sequence (Ch 8.1).
  16. Limit Laws for Sequences, Infinite Series, Geometric Series (Ch 8.2 - 8.3).
  17. Review for Midterm Exam 2: Integration Technique, Sequences and Series (Ch 7.1 - 8.3). Review Slides
  18. Telescoping Series, Divergence Test, and Integral Test (Ch 8.3 - 8.4).
  19. $p$-Series, Ratio Test, and Root Test (Ch 8.4 - 8.5).
  20. Comparison Test, Limit Comparison Test, and Alternating Test (Ch 8.5 - 8.6).
  21. Convergent Series, Power Series, Interval/Radius of Convergence (Ch 8.6 & 9.2).
  22. Convergence of Power Series, Combining/Differentiating/Integrating Power Series (Ch 9.2).
  23. Taylor Polynomial, Taylor Series, and MacLaurin Series (Ch 9.3).
  24. MacLaurin Series, and Remainder of Series/Alternating Series (Ch 8.6 & 9.3).
  25. Review for Final Exam: Sequences, Infinite Series, and Power Series (Ch 8 & 9). Review Slides