Precalculus

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2 STUDENTS

Introduction to limits – Limit examples w/ brain malfunction on first prob – Squeeze theorem (sandwich theorem) – Proof: lim (sin x)/x – More limits – Sequences and Series – Permutations – Combinations – Binomial Theorem – Binomial theorem combinatorics connection – Introduction to interest – Introduction to compound interest and e – Exponential Growth – Polar coordinates – Parametric equations – Introduction to function inverses – Function inverse example – Basic complex analysis – Exponential form to find complex roots – Complex conjugates – Series sum example – Complex determinant example – 2003 AIME II problem 8 – Logarithmic scale – Vi and Sal explore how we think about scale – Vi and Sal talk about the mysteries of Benford’s law – Benford’s law explanation (sequel to mysteries of Benford’s law

Course Curriculum

 Introduction to limits Details 11:32 Introduction to limits 2 Details 7:39 Limit examples (part 1) Details 8:58 Limit examples (part 2) Details 6:58 Limit examples (part 3) Details 9:58 Limit examples w/ brain malfunction on first prob (part 4) Details 15:3 Squeeze theorem (sandwich theorem) Details 7:37 Proof: lim (sin x)/x Details 18:5 More limits Details 13:10 Sequences and Series (part 1) Details 9:49 Sequences and series (part 2) Details 10:4 Permutations Details 10:11 Combinations Details 10:16 Binomial Theorem (part 1) Details 12:38 Binomial Theorem (part 2) Details 14:20 Binomial theorem combinatorics connection Details 11:59 Introduction to interest Details 9:56 Interest (part 2) Details 8:2 Introduction to compound interest and e Details 10:11 Compound interest and e (part 2) Details 10:15 Compound interest and e (part 3) Details 10:4 Compound interest and e (part 4) Details 8:4 Exponential Growth Details 0:16 Polar coordinates 1 Details 10:20 Polar coordinates 2 Details 9:31 Polar coordinates 3 Details 7:37 Parametric equations 1 Details 11:8 Parametric equations 2 Details 9:46 Parametric equations 3 Details 12:52 Parametric equations 4 Details 13:5 Introduction to function inverses Details 9:6 Function inverse example 1 Details 6:44 Function inverses example 2 Details 7:12 Function inverses example 3 Details 7:35 Basic complex analysis Details 13:4 Exponential form to find complex roots Details 11:53 Complex conjugates Details 8:4 Series sum example Details 14:18 Complex determinant example Details 12:58 2003 AIME II problem 8 Details 12:8 Logarithmic scale Details 11:15 Vi and Sal explore how we think about scale Details 6:56 Vi and Sal talk about the mysteries of Benford’s law Details 8:5 Benford’s law explanation (sequel to mysteries of Benford’s law Details 6:28

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