Tristan Needham (son of the distinguished social anthropologist Rodney Needham) grew up in Oxford, England. He studied physics at Merton College, Oxford, before moving to the Mathematical Institute, where he enjoyed the great privilege of studying black holes under the supervision of Sir Roger Penrose. Tristan received his DPhil in 1987 and joined the faculty of the University of San Francisco in 1989. His continuing mission is to seek out new intuitive forms of understanding, and new visualizations.

Visual Complex Analysis is a delight, and a book after my own heart. By his innovative and exclusive use of the geometrical perspective, Tristan Needham uncovers many surprising and largely unappreciated aspects of the beauty of complex analysis.

• 1: Geometry and Complex Arithmetic 2: Complex Functions as Transformations 3: Möbius Transformations and Inversion 4: Differentiation: The Amplitwist Concept 5: Further Geometry of Differentiation 6: Non-Euclidean Geometry 7: Winding Numbers and Topology 8: Complex Integration: Cauchy's Theorem 9: Cauchy's Formula and Its Applications 10: Vector Fields: Physics and Topology 11: Vector Fields and Complex Integration 12: Flows and Harmonic Functions

Tristan Needham (son of the distinguished social anthropologist Rodney Needham) grew up in Oxford, England. He studied physics at Merton College, Oxford, before moving to the Mathematical Institute, where he enjoyed the great privilege of studying black holes under the supervision of Sir Roger Penrose. Tristan received his DPhil in 1987 and joined the faculty of the University of San Francisco in 1989. His continuing mission is to seek out new intuitive forms of understanding, and new visualizations.

Visual Complex Analysis is a delight, and a book after my own heart. By his innovative and exclusive use of the geometrical perspective, Tristan Needham uncovers many surprising and largely unappreciated aspects of the beauty of complex analysis.

• 1: Geometry and Complex Arithmetic 2: Complex Functions as Transformations 3: Möbius Transformations and Inversion 4: Differentiation: The Amplitwist Concept 5: Further Geometry of Differentiation 6: Non-Euclidean Geometry 7: Winding Numbers and Topology 8: Complex Integration: Cauchy's Theorem 9: Cauchy's Formula and Its Applications 10: Vector Fields: Physics and Topology 11: Vector Fields and Complex Integration 12: Flows and Harmonic Functions

Tristan Needham (son of the distinguished social anthropologist Rodney Needham) grew up in Oxford, England. He studied physics at Merton College, Oxford, before moving to the Mathematical Institute, where he enjoyed the great privilege of studying black holes under the supervision of Sir Roger Penrose. Tristan received his DPhil in 1987 and joined the faculty of the University of San Francisco in 1989. His continuing mission is to seek out new intuitive forms of understanding, and new visualizations.

Visual Complex Analysis is a delight, and a book after my own heart. By his innovative and exclusive use of the geometrical perspective, Tristan Needham uncovers many surprising and largely unappreciated aspects of the beauty of complex analysis.

• 1: Geometry and Complex Arithmetic 2: Complex Functions as Transformations 3: Möbius Transformations and Inversion 4: Differentiation: The Amplitwist Concept 5: Further Geometry of Differentiation 6: Non-Euclidean Geometry 7: Winding Numbers and Topology 8: Complex Integration: Cauchy's Theorem 9: Cauchy's Formula and Its Applications 10: Vector Fields: Physics and Topology 11: Vector Fields and Complex Integration 12: Flows and Harmonic Functions