**Vector Calculus 2015-16 notes The University of Reading**

Vector Calculus: Grad, Div and Curl In vector calculus, div, grad and curl are standard differentiation1 operations on scalar or vector fields, resulting in a scalar or vector2 field. Scalar and Vector fields A scalar field is one that has a single value associated with each point in the domain. A simple example is a temperature distribution; every point in the domain has a single value. A... Vector Calculus deals with calculus in two and three dimensions, and develops the theory of curves, vector functions and partial derivatives, two and three dimensional 2. integration, line integrals and curl and divergence. [Applications include mechanics and dynamics, electrostatics, graphics and design.] Complex Analysis extends calculus from real numbers to complex numbers, and de-velops

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Then all of the operations of vector calculus can be written using indexed objects. 2 Algebraic relations 2.1 Free and dummy indices Any index that occurs precisely once on each side of an equation is a free index. An equation with a free index represents a vector equation, as it has to be satis ed for each value the index can take. So for example if A~and B~are vectors then A i = B i ()A~= B... Module Information Prerequisites MA1001 Multivariate Calculus MA1002 Vectors and ODEs MA1051 Newtonian Dynamics Assessment 2 hour examination: 60% 10 weekly problem sheets 20%

**Introduction to tensor calculus----Kees Dullemond & Kasper**

Introduction to Tensor Calculus Kees Dullemond & Kasper Peeters c 1991-2010. This booklet contains an explanation about tensor calculus for students of physics and engineering with a basic knowledge of linear algebra. The focus lies mainly on acquiring an understanding of the principles and ideas underlying the concept of ‘tensor’. We have not pursued mathematical strictness and pureness... A. Moiola, University of Reading 2 Vector calculus lecture notes, 2015–16 1 Fields and vector diﬀerential operators For simplicity, in these notes we only consider the 3-dimensional Euclidean space R3, and, from time to

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### Introduction to Tensor Calculus Kees Dullemond & Kasper Peeters c 1991-2010. This booklet contains an explanation about tensor calculus for students of physics and engineering with a basic knowledge of linear algebra. The focus lies mainly on acquiring an understanding of the principles and ideas underlying the concept of ‘tensor’. We have not pursued mathematical strictness and pureness

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- Then all of the operations of vector calculus can be written using indexed objects. 2 Algebraic relations 2.1 Free and dummy indices Any index that occurs precisely once on each side of an equation is a free index. An equation with a free index represents a vector equation, as it has to be satis ed for each value the index can take. So for example if A~and B~are vectors then A i = B i ()A~= B
- Vector Calculus: Grad, Div and Curl In vector calculus, div, grad and curl are standard differentiation1 operations on scalar or vector fields, resulting in a scalar or vector2 field. Scalar and Vector fields A scalar field is one that has a single value associated with each point in the domain. A simple example is a temperature distribution; every point in the domain has a single value. A
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