Two-Dimensional Calculus

Two-dimensional calculus is vital to the mastery of the broader field, and this text presents an extensive treatment of this crucial subject. The book's advantages include the thorough integration of linear algebra and materials that aid the development of readers' geometric intuition. Problem sets appear at the end of each chapter, many of them with answers. 1986 edition. Copyright Foreword Preface to Reprint Edition Notation Contents Introduction Background 1 Vectors in the plane 2 Plane curves 3 Functions of two variables Differentiation 4 Partial derivatives and plane domains 5 Continuity 6 Directional derivatives and gradient 7 The chain rule 8 Level curves and the implicit function theorem 9 Maximum and minimum along a curve 10 Quadratic forms 11 Higher order derivatives 12 Taylor's theorem; maxima and minima Transformations 13 Pairs of functions; geometric representation 14 Linear transformations 15 Special linear transformations; composition 16 Differentiable transformations 17 Composition; inverse mappings 18 Functional dependence; conformal mapping 19 Vector fields 20 Change of coordinates Integration 21 Line integrals 22 Potential functions; independence of path 23 Area 24 The double integral 25 Green's theorem for a rectangle 26 Green's theorem for arbitrary figures; applications 27 Mean value theorem for the double integral; vector forms of Green's theorem 28 Transformation rule for double integrals References Answers to Selected Exercises Index