MAT 137: Calculus!
Slides from Joel's lectures (L0301)

• Intro to logic, quantifers, definitions, and proofs
  
  

  Date	Topics	Videos to watch before lecture	Slides used in lecture
  Fri, 8 Sep	Introduction	---	Sept 8 slides
  Mon, 11 Sep	Sets	1.1, 1.2, 1.3	Sept 11 slides
  Wed, 13 Sep	Quantifiers	1.4, 1.5, 1.6	Sept 13 slides
  Fri, 15 Sep	Conditionals	1.7, 1.8, 1.9	Sept 15 slides
  Mon, 18 Sep	Definitions and proofs	1.10, 1.11, 1.12, 1.13	Sept 18 slides
  Wed, 20 Sep	Induction	1.14, 1.15	Sept 20 slides

  
  
  
• Limits and continuity
  
  

  Date	Topics	Videos to watch before lecture	Slides used in lecture
  Fri, 22 Sep	Inequalities and absolute values	2.4	Sept 22 slides
  Mon, 25 Sep	The intuitive idea of limit	2.1, 2.2, 2.3	Sept 25 slides
  Wed, 27 Sep	Formal definition of limit	2.5, 2.6	Sept 27 slides
  Fri, 29 Sep	Formal definition of limit	2.7, 2.8	Sept 29 slides
  Mon, 2 Oct	Limit laws	2.9, 2.10	Oct 2 slides
  Wed, 4 Oct	More proofs with limits	2.11, 2.12, 2.13	Oct 4 slides
  Fri, 6 Oct	Continuity	2.14, 2.15, 2.16	Oct 6 slides
  Wed, 11 Oct	Trigonometric limits	2.17, 2.18	Oct 11 slides
  Fri, 13 Oct	EVT and IVT	2.19, 2.20	Oct 13 slides

  
  
  
• Derivatives
  
  

  Date	Topics	Videos to watch before lecture	Slides used in lecture
  Mon, 16 Oct	Definition of Derivative	3.1, 3.2, 3.3	Oct 16 slides
  Wed, 18 Oct	Differentiation rules	3.4, 3.5, 3.8	Oct 18 slides
  Fri, 20 Oct	Differentiation rules	3.6, 3.7, 3.9	Oct 20 slides
  Mon, 23 Oct	Chain rule	3.10	Oct 23 slides
  Wed, 25 Oct	Trig derivative and implicit differentiation	3.11, 3.12	Oct 25 slides
  Fri, 27 Oct	Exponentials and Logarithms	3.13, 3.14, 3.15, 3.16, 3.17, 3.18	Oct 27 slides

  
  
  
• Inverse functions
  
  

  Date	Topics	Videos to watch before lecture	Slides used in lecture
  Mon, 30 Oct	Functions	4.1, 4.2	Oct 30 slides
  Wed, 1 Nov	Inverse functions and their derivatives	4.3, 4.4, 4.5	Nov 1 slides
  Fri, 20 Oct	Inverse trigonometric functions	4.6, 4.7, 4.8	Nov 3 slides

  
  
  
• Mean value theorem and applications
  
  

  Date	Topics	Videos to watch before lecture	Slides used in lecture
  Mon, 13 Nov	Related rates	5.1	Nov 13 slides
  Wed, 15 Nov	Local extrema	5.2, 5.3, 5.4	Nov 15 slides
  Fri, 17 Nov	Rolle's Theorem	5.5, 5.6	Nov 17 slides
  Mon, 20 Nov	Mean Value Theorem	5.7,5.8,5.9	Nov 20 slides
  Wed, 22 Nov	Increasing functions	5.10, 5.11, 5.12	Nov 22 slides
  Fri, 24 Nov	Applied Optimization	none	Nov 24 slides

  
  
  
• Limits at infinity, l'Hopital's rule, curve sketching
  
  

  Date	Topics	Textbook sections to read before lecture	Slides used in lecture
  Mon, 27 Nov	Limits at infinity		Nov 27 slides
  Wed, 29 Nov	L'Hopital's rule	11.5	Nov 29 slides
  Fri, 1 Dec	L'Hopital's rule	11.6	Dec 1 slides
  Mon, 4 Dec	Concavity	4.6	Dec 4 slides
  Wed, 6 Dec	Asymptotes	4.7	Dec 6 slides
  Thu, 7 Dec	Curve sketching	4.8	Dec 7 slides

  
  
  
• Definition of the integral
  
  

  Date	Topics	Videos to watch before lecture	Slides used in lecture
  Fri Jan 5	Introduction and summation notation	7.1, 7.2	Jan 5 slides
  Mon Jan 8	Suprema and Infima	7.3, 7.4	Jan 8 slides
  Wed Jan 10	Integrable functions	7.5-7.9	Jan 10 slides
  Fri Jan 12	Integrable functions	7.5-7.9	Jan 12 slides
  Mon Jan 15	Riemann sums	7.10-7.12	Jan 15 slides

  
  
  
• Fundamental Theorem of calculus
  
  

  Date	Topics	Videos to watch before lecture	Slides used in lecture
  Wed Jan 17	More integration and indefinite integrals	8.1, 8.2	Jan 17 slides
  Fri Jan 19	Fundamental Theorem of Calculus	8.3, 8.4	Jan 19 slides
  Mon Jan 22	Fundamental Theorem of Calculus	8.5, 8.6, 8.7	Jan 22 slides

  
  
  
• Integration Methods
  
  

  Date	Topics	Videos to watch before lecture	Slides used in lecture
  Wed Jan 24	Integration by substitution	9.1-9.4	Jan 24 slides
  Fri Jan 26	Integration by parts	9.5-9.9	Jan 26 slides
  Mon Jan 29	Integration of trig functions	9.10-9.12	Jan 29 slides
  Wed Jan 31	Trig substitution	9.13, 9.14	Jan 31 slides
  Fri Feb 2	Integration of rational functions	9.15 - 9.17	Feb 2 slides

  
  
  
• Volumes
  
  

  Date	Topics	Textbook sections	Slides used in lecture
  Mon Feb 5	Volume by cross-sections	6.2	Feb 5 slides
  Wed Feb 7	Volume by shells	6.3	Feb 7 slides

  
  
  
• Sequences
  
  

  Date	Topics	Videos to watch before lecture	Slides used in lecture
  Fri Feb 9	Convergence of sequences	11.1-11.3	Feb 9 slides
  Mon Feb 12	Bounded and monotonic sequences	11.4-11.5	Feb 12 slides
  Wed Feb 14	The big theorem for sequences	11.6-11.8	Feb 14 slides

  
  
  
• Improper integrals
  
  

  Date	Topics	Videos to watch before lecture	Slides used in lecture
  Fri Feb 16	Improper integrals	12.1 - 12.6	Feb 16 slides
  Mon Feb 26	The basic comparison test	12.7, 12.8	Feb 26 slides
  Wed Feb 26	The limit comparison test	12.9, 12.10	Feb 28 slides

  
  
  
• Series
  
  

  Date	Topics	Videos to watch before lecture	Slides used in lecture
  Fri Mar 2	Introduction to Series	13.1 - 13.4	Mar 2 slides
  Mon Mar 5	Properties of series	13.5 - 13.7	Mar 5 slides
  Wed Mar 7	More properties of series	13.8, 13.9	Mar 7 slides
  Fri Mar 9	Integral and comparison tests	13.10 - 13.12	Mar 9 slides
  Mon Mar 12	Alernating series	13.13, 13.14	Mar 12 slides
  Wed Mar 14	Absolute and conditional convergence	13.15 - 13.17	Mar 14 slides
  Fri Mar 16	Ratio test	13.18, 13.19	Mar 16 slides

  
  
  
• Power series and Taylor series
  
  

  Date	Topics	Videos to watch before lecture	Slides used in lecture
  Mon Mar 19	Power series	14.1, 14.2	Mar 19 slides
  Wed Mar 21	Taylor polynomials	14.3, 14.4	Mar 21 slides
  Fri Mar 23	Taylor series	14.5, 14.6	Mar 23 slides
  Mon Mar 26	Analytic functions	14.7, 14.8	Mar 26 slides
  Wed Mar 28	More Taylor series	14.9, 14.10	Mar 28 slides
  Mon Apr 2	Estimating with Taylor series	14.11, 14.12	Apr 2 slides
  Wed Apr 4	Taylor series applications	14.13	Apr 4 slides
  Thu Apr 5	More Taylor series applications	14.14, 14.15	Apr 5 slides