Surface integrals - Study guides, Revision notes & Summaries

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 ...

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...

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 ...

Functions 1 1.1 Functions and Their Graphs 1 1.2 Combining Functions; Shifting and Scaling Graphs 8 1.3 Trigonometric Functions 19 1.4 Graphing with Calculators and Computers 26 Practice Exercises 30 Additional and Advanced Exercises 38 2 Limits and Continuity 43 2.1 Rates of Change and Tangents to Curves 43 2.2 Limit of a Function and Limit Laws 46 2.3 The Precise Definition of a Limit 55 2.4 One-Sided Limits 63 2.5 Continuity 67 2.6 Limits Involving Infinity; Asymptotes of Graphs ...

Summaries of Theme 2: 2.1) The fundamental theorem of calculus 2.2) Indefinite integrals and the net change theorem 2.3) Integration techniques 2.4) Trigonometric substitutions 2.5) Integration by partial fractions 2.6) Improper integrals 2.7) Area between two curves 2.8) Volume of a solid of revolution 2.9) Arc length 2.10) Area of a surface of revolution

Arc length in space - correct answer unit tangent vector formula - correct answer Find arc length parametrization - correct answer 1. find the arc length (s =xt) 2. solve for t 3. plug back into position equation to get r(s) Formula for curvature - correct answer unit normal vector formula - correc...

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 ...

Preface page ix 1 Preliminary algebra 1 2 Preliminary calculus 17 3 Complex numbers and hyperbolic functions 39 4 Series and limits 55 5 Partial differentiation 71 6 Multiple integrals 90 7 Vector algebra 104 8 Matrices and vector spaces 119 9 Normal modes 145 10 Vector calculus 156 11 Line, surface and volume integrals 176 v CONTENTS 12 Fourier series 193 13 Integral transforms 211 14 First-order ODEs 228 15 Higher-order ODEs 246 16 Series solutions of ODEs 269 17 Eigenfuncti...

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 ...