'Differentiable function' diaporamas de présentation

Chapter 3 Application of Derivatives

Chapter 3 Application of Derivatives. 3.1 Extreme Values of Functions. Absolute maxima or minima are also referred to as global maxima or minima. Examples. Extreme Value Theorem. The requirements in Theorems 1 that the interval be closed and finite, and

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Introduction to Smoothing Splines

Introduction to Smoothing Splines. Tongtong Wu Feb 29, 2004. Outline. Introduction Linear and polynomial regression, and interpolation Roughness penalties Interpolating and Smoothing splines Cubic splines Interpolating splines Smoothing splines Natural cubic splines

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The Natural Logarithmic Function

The Natural Logarithmic Function. Differentiation Integration. Properties of the Natural Log Function. If a and b are positive numbers and n is rational, then the following properties are true:. The Algebra of Logarithmic Expressions. The Derivative of the Natural Logarithmic Function.

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Chapter 4

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Section 2.3 Product & Quotient Rules and Higher-Order Derivatives

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Standardization

Standardization. Standardization. The last major technique for processing your tree-ring data. Despite all this measuring, you can use raw measurements only rarely, such as for age structure studies and growth rate studies.

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Instabilities of SVD Small eigenvalues -> m+ sensitive to small amounts of noise Small eigenvalues maybe indistinguis

Instabilities of SVD Small eigenvalues -> m+ sensitive to small amounts of noise Small eigenvalues maybe indistinguishable from 0 Possible to remove small eigenvalues to stabilize solution -> Truncated SVD, TSVD Condition number cond(G)=s 1 /s k. TSVD

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Differentiability, Local Linearity

Differentiability, Local Linearity. Section 3.2a. How f ( a ) Might Fail to Exist. A function will not have a derivative at a point P ( a , f ( a )) where the slopes of the secant lines,. f ail to approach a limit as x approaches a . Four instances w here this occurs:.

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Derivatives and Differential Equations

Derivatives and Differential Equations. Differentiation. Differential change . Derivative Definition. Taylor Series. Taylor Series Graphically. Numerical Differentiation Based on Taylor Series . Forward finite-divided difference B ackward finite-divided difference

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Miss Battaglia AP Calculus

The Natural Logarithmic Function: Integration Objective: Use the Log Rule for Integration to integrate a rational function and integrate trig functions. Miss Battaglia AP Calculus. Log Rule for Integration. Let u be a differentiable function of x . 1. 2.

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Power, Sum, and Difference Rules, Higher-Order Derivatives

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Derivatives of the inverse trigonometric functions

Section 3.8. Derivatives of the inverse trigonometric functions. Derivatives of Inverse Functions. Theorem: If is differentiable at every point of an interval I and is never zero on I , then has an inverse and is differentiable at every point of the interval I.

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Section 2.3: Product and Quotient Rule

Section 2.3: Product and Quotient Rule. Students will be able to use the product and quotient rule to take the derivative of differentiable equations . Objective:. The derivative of f at x is given by.

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The Natural Log Function: Integration

The Natural Log Function: Integration. Lesson 5.7. Log Rule for Integration. Because Then we know that And in general, when u is a differentiable function in x: . Try It Out. Consider these . . . Finding Area. Given Determine the area under the curve on the interval [2, 4].

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Section 2.3

Section 2.3. Differentiation Formulas. DIFFERENTIATION FORMULAS FOR BASIC FUNCTIONS. 1. The derivative of a constant function, f ( x ) = c. 2. The derivative of the identity function, f ( x ) = x. THE POWER RULE.

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Differentiation Rules

Differentiation Rules. Chain Rule Let y be a differentiable function of u and u be differentiable function of x , then The Chain Rule is sometimes stated: Let y=f(x) and u=g(x) with f differentiable at u = g(x ) and and g differentiable at x , then .

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