Lesson02 Vectors And Matrices Slides

Sep 21, 20071 like1,441 views

1. The document introduces vectors and matrices as ways to collectively represent multiple quantities or relationships between quantities. 2. Vectors are used to represent positions, food orders, prices, and other grouped data. Matrices are used to represent ingredient amounts for different foods and connections between rooms in a floorplan. 3. All of the examples can be expressed using vectors and matrices, with the key information being the numbers in the vectors and matrices.

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The document discusses curve sketching of functions by analyzing their derivatives. It provides: 1) A checklist for graphing a function which involves finding where the function is positive/negative/zero, its monotonicity from the first derivative, and concavity from the second derivative. 2) An example of graphing the cubic function f(x) = 2x^3 - 3x^2 - 12x through analyzing its derivatives. 3) Explanations of the increasing/decreasing test and concavity test to determine monotonicity and concavity from a function's derivatives.

Lesson 21: Curve Sketching (handout)Matthew Leingang

The document contains lecture notes on curve sketching from a Calculus I class. It discusses using the first and second derivative tests to determine properties of a function like monotonicity, concavity, maxima, minima, and points of inflection in order to sketch the graph of the function. It then provides an example of using these tests to sketch the graph of the cubic function f(x) = 2x^3 - 3x^2 - 12x.

Lesson 20: Derivatives and the Shapes of Curves (slides)Matthew Leingang

This document contains lecture notes on derivatives and the shapes of curves from a Calculus I class taught by Professor Matthew Leingang at New York University. The notes cover using derivatives to determine the intervals where a function is increasing or decreasing, classifying critical points as maxima or minima, using the second derivative to determine concavity, and applying the first and second derivative tests. Examples are provided to illustrate finding intervals of monotonicity for various functions.

Lesson 20: Derivatives and the Shapes of Curves (handout)Matthew Leingang

This document contains lecture notes on calculus from a Calculus I course. It covers determining the monotonicity of functions using the first derivative test. Key points include using the sign of the derivative to determine if a function is increasing or decreasing over an interval, and using the first derivative test to classify critical points as local maxima, minima, or neither. Examples are provided to demonstrate finding intervals of monotonicity for various functions and applying the first derivative test.

Lesson 19: The Mean Value Theorem (slides)Matthew Leingang

The document discusses the Mean Value Theorem (MVT) and Rolle's Theorem, providing their mathematical statements and proofs, as well as applications and examples. It outlines the importance of these theorems in understanding functions that are continuous and differentiable on certain intervals. Additionally, it addresses specific examples demonstrating the uniqueness of solutions to equations and the implications of theorems in real-world scenarios.