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 Posted after lecture Wed, Jan 9 Suprema and infima, and integrable functions 7.3, 7.4, 7.5, 7.6, 7.7, 7.8, 7.9 Posted after lecture Mon, Jan 14 More integrable functions 7.5, 7.6, 7.7, 7.8, 7.9 Posted after lecture Wed, Jan 16 Riemann sums + second half (see next topic) 7.10, 7.11, 7.12 Posted after lecture

**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 Posted after lecture Mon, Jan 21 FTC Part 1 8.3, 8.4 --- 5.6 Posted after lecture Wed, Jan 23 FTC Part 2 + second half (TBD) 8.5, 8.6 8.7 5.6 Posted after lecture