Lecture 7: Taylor Series Validity, Power Series, Vectors, Dot Products, and Cross Product.

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Presentation transcript:

Lecture 7: Taylor Series Validity, Power Series, Vectors, Dot Products, and Cross Product

Part I: Validity of Taylor Series

Taylor Series Failure

Taylor series remainder term

Part II: Power Series

Objectives Know what power series are and how to determine the radius of convergence of power series Know how power series can be manipulated within their radius of convergence Corresponding sections of Simmons: 14.2,14.3

Power Series

Radius of Convergence

Manipulating Power Series

Uniqueness of Power/Taylor Series

Part III: Vectors

Objectives Know what vectors are Know how find the magnitude, direction, dot product, and cross product of vectors. Corresponding sections in Simmons: 18.1, 18.2, 18.3

Vectors

Picture for vectors

Scalar Multiplication of Vectors and Vector Direction

Vector Addition and Subtraction

Displacement and Position Vectors

Dot Product

Properties of the dot product

Geometric Picture of the dot product

Connection between algebraic and geometric pictures a b c A B C PQ R

Condition for Perpendicular Vectors

Cross Product

Properties of the cross product

Geometric Picture of the Cross Product