# MAT137 Calculus! L0501

Lecturer: Qin Deng

E-mail: qin.deng@mail.utoronto.ca

Class Time: MWR4-5 @ MP202

Office Hours: W5-7 @ PG003

Unit 14: Power Series and Taylor Series

Date Topic Videos Slides Textbook section
M 19/03/18 Power Series 14.1, 14.2 Lec 14.1 slides 12.8, 12.9
W 21/03/18 Taylor Polynomials 14.3, 14.4 Lec 14.2 slides 12.6, 12.7
R 22/03/18 Taylor Series 14.5, 14.6 Lec 14.3 slides 12.6, 12.7
M 26/03/18 Analytic functions 14.7, 14.8 Lec 14.4 slides 12.6, 12.7
W 28/03/18 New Power Series 14.9, 14.10 Lec 14.5 slides 12.6 - 12.9
R 29/03/18 Applications 14.12, 14.14 Lec 14.6 slides 12.8, 12.9
M 02/04/18 Applications 14.11, 14.13 Lec 14.7 slides 12.6, 12.7
W 04/04/18 Applications 14.15 Lec 14.8 slides -

Unit 13: Series
Date Topic Videos Slides Textbook section
R 01/03/18 Definition of series 13.1, 13.2, 13.3, 13.4 Lec 13.1 slides 12.2
M 05/03/18 Properties of series 13.5, 13.6, 13.7 Lec 13.2 slides 12.2
W 07/03/18 More properties of series 13.8, 13.9 Lec 13.3 slides 12.2
R 08/03/18 Integral test and comparison test 13.10, 13.11, 13.12 Lec 13.4 slides 12.3
M 12/03/18 Alternating Series 13.13, 13.14 Lec 13.5 slides 12.5
W 14/03/18 Absolute and conditional convergence 13.15, 13.16, 13.17 Lec 13.6 slides 12.5
R 15/03/18 Ratio Test 13.18, 13.19 Lec 13.7 slides 12.4

Unit 12: Improper Integrals
Date Topic Videos Slides Textbook section
R 16/02/18 Definition of improper integral 12.1, 12.4 (12.1-12.6) Lec 12.1 slides 11.7
M 26/02/18 The Basic Comparison Test 12.7, 12.8 Lec 12.2 slides 11.7
W 28/02/18 The big theorem for improper integrals 12.9, 12.10 Lec 12.3 slides 11.7

Unit 11: Sequences
Date Topic Videos Slides Textbook section
R 08/02/18 Convergence of sequences 11.1, 11.2, 11.3 Lec 11.1 slides 11.2, 11.3
M 12/02/18 Bounded and monotone sequences 11.4, 11.5 Lec 11.2 slides 11.2, 11.3
W 14/02/18 The big theorem for sequences 11.6, 11.7, 11.8 Lec 11.3 slides 11.3, 11.4

Unit 10: Volume
Date Topic Videos Slides Textbook section
M 05/02/18 Volume by slices - Lec 10.1 slides 6.2
W 07/02/18 Volume by cylindrical shells - Lec 10.2 slides 6.3

Unit 9: Integration Methods
Date Topic Videos Slides Textbook section
W 24/01/18 Integration by substitution 9.1, (9.2, 9.3, 9.4) Lec 9.1 slides 5.7
R 25/01/18 Integration by parts 9.5, 9.6, (9.7, 9.8, 9.9) Lec 9.2 slides 8.2
M 29/01/18 Integration of trig functions 9.10, 9.11, (9.12) Lec 9.3 slides 8.3
W 31/01/18 Trig substitution 9.13, (9.14) Lec 9.4 slides 8.4
R 01/02/18 Integration of rational functions 9.15, (9.16, 9.17) Lec 9.5 slides 8.5

Unit 8: The Fundamental Theorem of Calculus
Date Topic Videos Slides Textbook section
W 17/01/18 Antiderivatives, indefinite integrals 8.1, 8.2 Lec 8.1 slides 5.3, 5.4
R 18/01/18 FTC I 8.3, 8.4 Lec 8.2 slides 5.3, 5.6, 5.8
M 22/01/18 FTC II 8.5, 8.6, 8.7 Lec 8.3 slides 5.4, 5.5

Unit 7: Definition of integral
Date Topic Videos Slides Textbook section
R 04/01/18 Sums and sigmas 7.1, 7.2 Lec 7.1 slides 12.1
M 08/01/18 Suprema and infima 7.3, 7.4 Lec 7.2 slides 11.1
W 10/01/18 Formal definition of integrals 7.5, 7.6, 7.7 Lec 7.3 slides -
R 11/01/18 Integrable functions 7.8, 7.9 Lec 7.4 slides -
M 15/01/18 Riemann sums 7.10, 7.11, 7.12 Lec 7.5 slides 5.2

Unit 6: Applications of derivatives
Date Topic Videos Slides Textbook section
M 27/11/17 Limits at infinity - Lec 6.1 slides -
W 29/11/17 L’Hopital’s Rule - Lec 6.2 slides 11.5
R 30/11/17 L’Hopital’s Rule - Lec 6.3 slides 11.6
M 04/12/17 Concavity - Lec 6.4 slides 4.1
W 06/12/17 Asymptotes - Lec 6.5 slides 4.2, 4.4
R 07/12/17 Graphing - Lec 6.6 slides 4.5

Unit 5: Mean Value Theorem and applications
Date Topic Videos Slides Textbook section
M 13/11/17 Related rates 5.1 Lec 5.1 slides 4.10
W 15/11/17 Local extrema 5.2, 5.3, 5.4 Lec 5.2 slides 4.3, 4.4
R 16/11/17 Rolle’s Theorem 5.5, 5.6 Lec 5.3 slides 4.1
M 20/11/17 MVT 5.7, 5.8, 5.9 Lec 5.4 slides 4.1
W 22/11/17 Increasing and decreasing 5.10, 5.11, 5.12 Lec 5.5 slides 4.2, 4.4
R 23/11/17 Applications to optimization - Lec 5.6 slides 4.5

Unit 4: Inverse functions

Date Topic Videos Slides Textbook section
M 30/10/17 Functions and inverses 4.1, 4.2 Lec 4.1 slides 7.1 (partially)
W 1/11/17 When do inverses exist? Properties of inverses 4.3, 4.4, 4.5 Lec 4.2 slides 7.1 (partially)
R 2/11/17 Inverse trig functions 4.6, 4.7, 4.8 Lec 4.3 slides 7.7

Unit 3: Derivatives

Date Topic Videos Slides Textbook section
M 16/10/17 Definition of derivatives 3.1, 3.2, 3.3 Lec 3.1 slides 3.1, 3.3, 3.4
W 18/10/17 Differentiation rules 3.4, 3.5 Lec 3.2 slides 3.2
R 19/10/17 Proof of differentiation rules 3.8, 3.6, 3.7 Lec 3.3 slides 3.2, 3.3
M 23/10/17 Chain rule 3.9, 3.10 Lec 3.4 slides 3.5
W 25/10/17 Trigonometric derivatives, Implicit differentiation 3.11, 3.12 Lec 3.5 slides 3.6, 3.7
R 26/10/17 Exponentials and logarithms 3.13 - 3.18 Lec 3.6 slides -

Unit 2: Limit and Continuity

Date Topic Videos Slides Textbook section
R 21/09/17 Inequalties, Absolute values 2.4 Lec 7 slides 1.3
M 25/09/17 Intuitive idea of a limit 2.1, 2.2, 2.3 Lec 8 slides 2.1
W 27/09/17 Definition and proof of limits 2.5, 2.6, 2.7 Lec 9 slides 2.2
R 28/09/17 Definition and proof of limits 2.8 Lec 10 slides, Proof from class 2.2
M 2/10/17 Limits not existing, Limit laws 2.9, 2.10 Lec 11 slides 2.3
W 4/10/17 Squeeze theorem, Continuity 2.11, 2.12, 2.13 Lec 12 slides 2.5, 2.4
R 5/10/17 Continuity theorems, Behaviour of limits under composition 2.14, 2.15 Lec 13 slides, Theorem from class, Sample student solution w/ comments 2.4
W 11/10/17 Discontinuity, Computations 2.16, 2.17, 2.18 Lec 14 slides 2.5
R 12/10/17 IVT, EVT 2.19, 2.20 Lec 15 slides 2.6

Unit 1: Set Theory and Logic

Date Topic Videos Slides Textbook section
R 07/09/17 Introduction - Lec 1 slides -
M 11/09/17 Sets, Quantifiers 1.1, 1.2, 1.3 Lec 2 slides -
W 13/09/17 Quantifiers, Negation 1.4, 1.5, 1.6 Lec 3 slides -
R 14/09/17 Conditionals, Negation 1.7, 1.8, 1.9 Lec 4 slides -
M 18/09/17 Definitions, Proofs 1.10, 1.11, 1.12, 1.13 Lec 5 slides -
W 20/09/17 Induction 1.14, 1.15 Lec 6 slides -