Slides from Francisco's lectures (L0401)

**Intro to logic, quantifers, definitions, and proofs**

Date Topics Required videos Textbook sections Lecture slides Mon, 10 Sep Introduction --- --- slides Wed, 12 Sep Sets and quantifiers 1.1, 1.2, 1.3, 1.4, 1.5, 1.6 1.1, 1.2, 1.3 slides Mon, 17 Sep Conditionals 1.7, 1.8, 1.9 1.3 slides Wed, 19 Sep Definitions, proofs and induction 1.10, 1.11, 1.12, 1.13, 1.14, 1.15 1.4 slides

**Limits and continuity**

Date Topics Required videos Supplementary videos Textbook sections Lecture slides Mon, 24 Sep Absolute value, distance and inequalities 2.4 --- 1.2, 1.8 slides Wed, 26 Sep Limits 2.1, 2.2, 2.3, 2.5, 2.6 --- 2.1, 2.2 slides Mon, 1 Oct Proofs from the definition of limit 2.7, 2.8 2.9 2.2 slides Wed, 3 Oct Limit laws and squeeze theorem 2.10, 2.11, 2.12, 2.13 --- 2.3 slides Wed, 10 Oct Continuity 2.14, 2.15, 2.16, 2.17 2.18 2.4 slides Mon, 15 Oct Computations 2.19,2.20 --- 2.1, 2.3,2.4 slides Wed, 17 Oct (1st part) IVT and EVT 2.21, 2.22 --- 2.5 slides

**Derivatives**Date Topics Required videos Supplementary videos Textbook sections Lecture slides Wed, Oct 17 (2nd part) Definition of a derivative 3.1, 3.2, 3.3 --- 3.1 slides Mon, Oct 22 Differentiation rules 3.4, 3.5, 3.8 --- 3.2, 3.3 slides Wed, Oct 24 Proof of the differentiation rules and the chain rule 3.6, 3.7, 3.9, 3.10 --- 3.1, 3.3, 3.5 slides Mon, Oct 29 Trigonometric derivatives and implicit differentiation 3.11, 3.12 --- 3.4, 3.7 slides Wed, Oct 31 Derivatives of exponentials and logarithms, and related rates 3.13, 3.15, 3.16, 3.17, 3.18, 3.19, 3.20 3.14 3.4, 3.6, 3.7, 4.7 slides

**Inverse functions and inverse trigonometric functions**Date Topics Required videos Supplementary videos Textbook sections Lecture slides Mon, Nov 12 Inverse functions 4.1, 4.2 --- 1.5, 1.7 slides Wed, Nov 14 One-to-one functions and inverse trigonometric functions 4.3, 4.4, 4.5, 4.6, 4.7, 4.8 --- 1.7, 3.5, 3.6 slides

**The Mean Value Theorem and applications**Date Topics Required videos Supplementary videos Textbook sections Lecture slides Mon, Nov 19 Local extrema 5.2, 5.3, 5.4 5.1 4.1 slides Wed, Nov 21 Rolle's Theorem and MVT 5.5, 5.6, 5.7, 5.8, 5.9 --- 4.2 slides Mon, Nov 26 Monotonocity 5.10, 5.11, 5.12 --- 4.3 slides

**Applications of the derivative**Date Topics Required videos Supplementary videos Textbook sections Lecture slides Wed, Nov 28 Applied optimization, Indeterminate forms and L'Hopital's Rule 6.1, 6.2, 6.4, 6.5, 6.7 6.3, 6.6 4.4, 4.5, 4.6, 4.8 slides Mon, Dec 3 Indeterminate forms and L'Hopital's Rule 6.8, 6.10 6.9 4.4, 4.5, 4.6 slides Wed, Dec 5 Concavity and Asymptotes 6.11, 6.12, 6.13, 6.14, 6.15 6.16 2.1, 4.9, slides Thu, Dec 6 Curve sketching --- --- 4.9 slides

**The definition of integral**Date Topics Required videos Lecture slides Mon, Jan 7 Sums and sigmas 7.1, 7.2 slides Wed, Jan 9 Suprema and infima, and integrable functions 7.3, 7.4, 7.5, 7.6, 7.7, 7.8, 7.9 slides Mon, Jan 14 More integrable functions 7.5, 7.6, 7.7, 7.8, 7.9 slides Wed, Jan 16 Riemann sums + second half (see next topic) 7.10, 7.11, 7.12 slides

**The Fundamental Theorem of Calculus**Date Topics Required videos Supplementary videos Textbook sections Lecture slides Wed, Jan 16 First half + antiderivatives, indefinite integrals 8.1, 8.2 --- 5.5, 5.6 slides Mon, Jan 21 FTC Part 1 8.3, 8.4 --- 5.6 slides Wed, Jan 23 FTC Part 2 + second half (see next topic) 8.5, 8.6 8.7 5.6 slides

**Integration methods**Date Topics Required videos Supplementary videos Textbook sections Lecture slides Wed, Jan 23 First half (see previous topic) + Integration by substitution 9.1 9.2-9.4 6.1 slides Mon, Jan 28 Integration by parts 9.6 9.5-9.9 6.2 slides Wed, Jan 30 Integration of trigonometric and rational functions 9.10,9.15 9.11-9.12 and 9.16-9.17 6.3, 6.5 slides

**Volumes**Date Topics Required videos Supplementary videos Textbook sections Lecture slides Special announcement Mon, Feb 4 Volumes 10.1 --- 7.4 slides --- Fri, Feb 8 Volumes + second half (see next topic) 10.2, 11.1,11.2 --- 7.5 slides Make up lecture at MP 102, 4-6pm

**Sequences**Date Topics Required videos Supplementary videos Textbook sections Lecture slides Special announcement Fri, Feb 8 Sequences + first half (see previous topic) 10.2, 11.1,11.2 --- 8.1,8.2 slides Make up lecture at MP 102, 4-6pm Mon, Feb 11 Properties of sequences 11.3,11.4 --- 8.1,8.2 slides --- Wed, Feb 13 Theorems about sequences 11.5-11.8 --- 8.2 slides ---

**Improper integrals**Date Topics Required videos Supplementary videos Textbook sections Lecture slides Mon, Feb 25 Improper integrals 12.1, 12.4 12.1--12.6 7.8, 7.9 Posted after lecture --- Wed, Feb 27 BCT and LCT for integrals 12.7--12.10 --- 7.8,7.9 Posted after lecture ---

**Series**Date Topics Required videos Supplementary videos Textbook sections Lecture slides Mon, March 4 Definition of series 13.2--13.4 13.1 8.3 Posted after lecture Wed, March 6 Properties of series 13.5--13.9 --- 8.3,8.4 Posted after lecture Mon, March 11 Integral and comparison tests 13.10--13.12 --- 8.5,8.7 Posted after lecture Wed, March 13 Alternating series and conditional and absolute convergence 13.13--13.15 13.16,13.17 8.6 Posted after lecture Mon, March 18 Ratio test 13.18--13.19 --- 8.7 Posted after lecture