Daily Topics

Here you'll find organized notes for each class session covering probability and statistics, functions and graphs, continuity, limits, and differentiation concepts.

Probability and Statistics Topics

• Introduction to Probability - Lecture 1

• Dependent vs Independent Events, Conditional Probability, and Continuous Distributions - Lecture 2

• Descriptive Statistics – Mean, Median, and Variance - Lecture 3

Functions and Graphs Topics

• Functions definition and basic examples (linear, quadratic) - Lecture 4

• Polynomial functions, graphs, and infinity behavior - Lecture 5

• Root and Rational Functions, Discontinuities, and Infinity Behavior - Lecture 6

• Exponential and Logarithmic Functions - Lecture 7

• Operations on Functions — Transformations and Composition - Lecture 8

• Operations on Functions — Inverses & Implicit vs. Explicit - Lecture 9

• Review Questions Answer Key - Lecture 10 Answer Key

• Review Questions - Lecture 10

Continuity Topics

• Types of Discontinuities (No Limits) - Lecture 11

Limits Topics

• Introduction to Limits - Lecture 12

• Existence of limits, one sided limits, and infinity limits. - Lecture 13

• Continuity, Laws of limits and Squeeze theorem - Lecture 14

• Algebraic manipulation of limits and asymptotes. Euler number $e$ and its properties. - Lecture 15

• Trigonometric functions and the unit circle - Lecture 16

• Limits Questions - Lecture 17

Differentiation Topics

• Introduction to Derivatives - Lecture 18

• Formal Definition of Derivatives, Derivatives as limits. - Lecture 19

• Rules of Derivatives 1 - Power, Exponential, Log, Addition and Subtraction Rules. - Lecture 20

• Derivatives rules 2 - multiplication and division rules - Lecture 21

• Derivatives rules 3 - Chain rule - Lecture 22

• Implicit Differentiation - Lecture 23

• Derivatives in Real Life and Optimization Problems - Lecture 24

• Optimization Problems and Related Rates - Lecture 25

• Derivatives Review - Lecture 26

• Quiz 3 Solutions - Quiz 3 Solutions