Engineering Calculus Notes 10

Engineering Calculus Notes 10 - x CONTENTS 4 Mappings and...

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x CONTENTS 4 Mappings and Transformations 413 4.1 Linear Mappings . . . . . . . . . . . . . . . . . . . . . . . . . 415 4.2 Differentiable Mappings . . . . . . . . . . . . . . . . . . . . . 424 4.3 Linear Systems of Equations . . . . . . . . . . . . . . . . . . . 438 4.4 Nonlinear Systems . . . . . . . . . . . . . . . . . . . . . . . . 450 5 Real-Valued Functions: Integration 485 5.1 Integration over Rectangles . . . . . . . . . . . . . . . . . . . 485 5.2 Integration over Planar Regions . . . . . . . . . . . . . . . . . 506 5.3 Changing Coordinates . . . . . . . . . . . . . . . . . . . . . . 527 5.4 Surface Integrals . . . . . . . . . . . . . . . . . . . . . . . . . 556 5.5 Integration in 3D . . . . . . . . . . . . . . . . . . . . . . . . . 578 6 Vector Fields and Forms 603 6.1 Line Integrals . . . . . . . . . . . . . . . . . . . . . . . . . . . 603 6.2 The Fundamental Theorem for Line Integrals . . . . . . . . . 621 6.3 Green’s Theorem . . . . . . . . . . . . . . . . . . . . . . . . . 644 6.4 2-forms in R 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . 663
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