Green’s theorem - Study guides, Class notes & Summaries

INTRODUCTION Dear Student Welcome to MAT2615. We trust that you will find the mathematics studied in this module interesting and useful, and that you will enjoy doing it. THIS TUTORIAL LETTER CONTAINS INFORMATION TO FACILITATE YOUR STUDIES. PLEASE READ IT CAREFULLY AND KEEP IT FOR FUTURE REFERENCE. The delivery mode for this module is “blended”, which means that only some study material will be printed and posted to you. All study material which may include additional material will be...

Contents 1 First-Order Differential Equations 1 1.1 Terminology and Separable Equations 1 1.2 The Linear First-Order Equation 12 1.3 Exact Equations 19 1.4 Homogeneous, Bernoulli and Riccati Equa tions 28 2 Second-Order Differential Equations 37 2.1 The Linear Second-Order Equation 37 2.2 The Constant Coefficient Homogeneous Equation 41 2.3 Particular Solutions of the Nonhomogeneous Equation 46 2.4 The Euler Differential Equation 53 2.5 Series Solutions 58 3 The Laplace Transform 69 3.1 Definiti...

1. (10+5 points) Let F = P i + Qj be a vector field on a domain D in the plane. (a) Give two different characterizations for the vector field F to be conservative which are valid on ANY domain D. Solution. There are three different possible characterizations: – F = ∇f for some scalar function f. – F ds = 0 for all closed curves C in the domain of F. – For any curve C between points p and q, C F · ds depends only on the endpoints (p and q), not on the curve itself. (Path indep...

Department of Mathematics Courses of Study: Minor Major (B.A.) Combined B.A./M.A Master of Arts Doctor of Philosophy Objectives Undergraduate Major As our society becomes more technological, it is more affected by mathematics. Quite sophisticated mathematics is now central to the natural sciences, to ecological issues, to economics, and to our commercial and technical life. A student who takes such general level courses as MATH 5, 8, 10, 15, or 20 will better understand the world ...

Lecture notes were made while watching the recorded lectures assigned to watch. These notes include theory (theorems) and worked out examples from the lecturer. These specific notes cover Green's theorem.

Green’s Theorem, notes and solved examples

Exam (elaborations) TEST BANK FOR Functions of One Complex Variable I By Andreas Kleefeld Solutions Manual for Functions of One Complex Variable I, Second Edition1 © Copyright by Andreas Kleefeld, 2009 All Rights Reserved2 1by John B. Conway 2Last updated on January, 7th 2013 Contents 1 The Complex Number System 1 1.1 The real numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 The field of complex numbers . . . . . . . . . . . . . . . . . . . ...

Multivariable Calculus

Exam (elaborations) TEST BANK FOR Mathematics for Physical Science and Engineering Symbolic Computing Applications in Maple and Mathematica By Frank Harris (Solution Manual) Mathematics for Physical Science and Engineering: Symbolic Computing Applications in Maple and Mathematica Instructor’s Manual Frank E. Harris University of Utah, Salt Lake City, UT and University of Florida, Gainesville, FL Contents 0 Introduction 1 1 Computers, Science, and Engineering 3 1.1 Computing: Histori...

1 The Complex Number System 1 1.1 The real numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 The field of complex numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.3 The complex plane . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.4 Polar representation and roots of complex numbers . . . . . . . . . . . . . . . . . . . . . 5 1.5 Lines and half planes in the complex plane . . . . . . . . . . ...