PPT-Higher Derivative Scalars in

Supergravity JeanLuc Lehners Max Planck Institute for Gravitational Physics Albert Einstein Institute Based on work with Michael Köhn and Burt Ovrut Motivation Assume N 1 s upersymmetry. We have that AA 1 that is that the product of AA is the sum of the outer products of the columns of To see this consider that AA ij 1 pi pj because the ij element is the th row of which is the vector a a ni dotted with the th column of which is Notation dx dx y 00 f 00 Thus dx dx dy dx Example Find the second derivatives of the following functions a 2 x y 00 2 b y 00 c 5 4 5 y 00 The 64257rst derivative gives information about whether a funct ion increases or decreases In fact A d Section 3.1b. Remember, that in . graphical terms. , the derivative of a. function at a given point can be thought of as the . slope. of the curve at that point…. Therefore, we can get a good idea of what the graph of. Points of Inflection. Section 4.3a. Writing: True . or . False – A . critical point . of. a function always signifies . an . extreme. value . of the . function. Explain.. FALSE!!! – Counterexample???. define . scalar and vector quantities and . give . examples.. (. b) draw and use a vector triangle to . determine the resultant of two vectors such as displacement, velocity and force.. (c) Use trigonometry to determine the resultant of two vectors.. Which of the following is the odd one out?. Mass. Speed. Force. Temperature. Distance. Elephant. Which of the following is the odd one out?. Mass. Speed. Force. Temperature. Distance. Elephant. Scalars. Chapter 3.1. Definition of the Derivative. In the previous chapter, we defined the slope of the tangent line to a curve . at a point . as. When this limit exists, it is called the . derivative of . FGFOA Conference, Orlando FL,. Mark A. White, CPA, Partner, Purvis Gray & Company LLP. Jim Towne, Senior VP, DerivActiv. 1. Statement 53. Accounting and Financial Reporting for Derivative Instruments. VALUE THEOREMS. Derivability of a function :. A function . f . defined on [. a, b. ] is said to be derivable or differentiable at if exists. This limit is called derivative of . Distinguish between scalars and vectors.. Recognise quantities as either scalars or vectors.. HL: Find the resultant of perpendicular vectors.. HL: Describe how to find the resultant of two vectors.. nd. Derivative Test. Objectives:. To find Higher Order Derivatives. To use the second derivative to test for concavity. To use the 2. nd. Derivative Test to find relative . extrema. If a function’s derivative is . Slope of the Tangent Line. If . f. is defined on an open interval containing . c. and the limit exists, then . . and the line through (. c. , . f. (. c. )) with slope . m. is the line tangent to the graph of . The Product Rule. The derivative of a product of functions is NOT the product of the derivatives. . If . f. and . g. . are both differentiable, . then:. In other words, the derivative of a product of two functions is the first function times the derivative of the second function plus the second function times the derivative of the first function.. Examples should include: . velocity/speed, mass, force/weight, acceleration, displacement/distance. . Addition of vectors by calculation or scale drawing. . Calculations will be limited to two vectors at right angles. Scale drawings may involve vectors at angles other than .