Tangent planes Study guides, Revision notes & Summaries

Exercise 7.3.1 Why does the graph of a linear function have to pass through the origin? �(� + �) = �(�) + �(�) �(��) = ��(�), A linear function by definition needs to satisfy the following two conditions: Where � and � are vectors with the same number of elements and � is a scalar. �(�1, �2 … �� ) = �1�1 + �2�2 + ⋯ + ���� Thus, a linear function must be a linear combination of some number of independent variables: If (�1, �...

Exam (elaborations) TEST BANK FOR Mechanics of Materials An Integrated Learning System 3rd Edition By Timothy A. Philpot (Instructors Solution Manual) CONTENTS Philpot MoM 3rd 1. Stress 1.1 Introduction 1.2 Normal Stress Under Axial Loading 1.3 Direct Shear Stress 1.4 Bearing Stress 1.5 Stresses on Inclined Sections 1.6 Equality of Shear Stresses on Perpendicular Planes 2. Strain 2.1 Displacement, Deformation, and the Concept of Strain 2.2 Normal Strain 2.3 Shear Strain 2.4 Therm...

Calculus III

Essential Calculus 2nd Edition 2297 0875 0, 3, 4, 0, 2467, 3011, 9067, 6609 1: Functions and Limits 1.1: Functions and Their Representations 1.2: A Catalog of Essential Functions 1.3: The Limit of a Function 1.4: Calculating Limits 1.5: Continuity 1.6: Limits Involving Infinity 2: Derivatives 2.1: Derivatives and Rates of Change 2.2: The Derivative as a Function 2.3: Basic Differentiation Formulas 2.4: The Product and Quotient Rules 2.5: The Chain ...

Essential Calculus 2nd Edition 2297 0875 0, 3, 4, 0, 2467, 3011, 9067, 6609 1: Functions and Limits 1.1: Functions and Their Representations 1.2: A Catalog of Essential Functions 1.3: The Limit of a Function 1.4: Calculating Limits 1.5: Continuity 1.6: Limits Involving Infinity 2: Derivatives 2.1: Derivatives and Rates of Change 2.2: The Derivative as a Function 2.3: Basic Differentiation Formulas 2.4: The Product and Quotient Rules 2.5: The Chain ...

Multivariable Calculus

For exams June 2012 onwards For certification June 2012 onwards AQA Level 2 Certificate in Further Mathematics Specification Level 2 Specification Level 2 Certificate in Further Mathematics 8360 Our specification is published on our website (). We will let centres know in writing about any changes to the specification. We will also publish changes on our website. The definitive version of our specification will always be the one on our website, this may differ from printed versions...

1. Order of a matrix Number of rows by number of columns 2. Square matrix Matrix of order NxN 3. Leading diagonal Diagonal of matrix from top left to bottom right 4. Conditions for two matrices to be equal - must have same order - each element in one matrix must be equal to the corresponding ele- ment in the other 5. Matrices which you can't add are... non-conformable for addition 6. Matrices which you can't multiply are... non-conformable for multiplication 7. Matrix...

Strain - ANSWER-An alteration in the shape or volume of a soil related to stress. It is calculated as the ratio of the new shape compared to the original shape Effective Stress - ANSWER-The total amount of stress placed on a soil minus the pore-water pressure Normal Stress - ANSWER-The component of total stress that acts perpendicular to the plane. Shear stress - ANSWER-The component of total stress that acts parallel to any point in question. Dilatancy - ANSWER-Tendency of a materia...

define Enthalpy - answer-total energy of a system Which of the following is true of the electric field intensity about an isolated point charge? A. It varies directly as the distance to the charge. B. It varies inversely as the distance to the charge. C. It varies directly as the square of the distance to the charge. D. It varies inversely as the square of the distance to the charge. - answer-D. It varies inversely as the square of the distance to the charge. As a professional engin...