An introduction to complex analysis and the Laplace transform. (2021)

• Record Type: Book
• Further Information: Note: Vladimir Eiderman.
• Authors: Eiderman, V. Ya (Vladimir Ya.), 1952-
• Contents: Preface Introduction; 1. Complex Numbers and Their Arithmetic; Operations with Complex Numbers 2. Functions of a Complex Variable; Complex Plane; Sequences of Complex Numbers and Their Limits; Functions of Complex Variable. Limit and Continuity 3. Differentiation of Functions of a Complex Variable; Derivative and Differential; The Cauchy-Riemann Equations; Analytic Functions; Relations between Analytic and Harmonic Functions; Geometric Interpretation of a Derivative of a Function of Complex Variable; Notion of a Conformal Mapping 4. Conformal Mappings; Linear and Linear Fractional Functions; Power Function; Notion of a Riemann Surface; Exponential and Logarithmic Functions; General Power Function and Trigonometric Functions; Zukowski Function; General Properties of Conformal Mappings; An Application of Functions of Complex Variable in Hydrodynamics 5. Integration of Functions of a Complex Variable; Integral of a Function of Complex Variable; Cauchy Theorem; Indefinite Integral; Fundamental Theorem of Calculus; Cauchy’s Integral Formula and Their Applications 6. Series; Number Series; Functional Series; Uniform Convergence; Power series; Expansion of Functions in Power Series; Taylor Series; Uniqueness Property; Analytic Continuation; Complete Analytic Function; Loran Series 7. Isolated Singularities and Residues; Classification of Isolated Singular Points; Residue of a Function in an Isolated Singular Point; Evaluation of Integrals by Means of Residues; Logarithmic Residue and Argument Principle 8. The Laplace Transform; Laplace Transform; Basic Properties of the Laplace Transform; Application of the Laplace Transform to Solving Ordinary Differential Equations 9. Practicum; Solving of Typical Problems; Tasks for Self-Study Literature Index;
• Edition: 1st
• Publisher Details: Boca Raton : Chapman & Hall/CRC
• Publication Date: 2021
• Extent: 1 online resource, illustrations (black and white)
• Subjects: 515.9; Functions of complex variables; Mathematical analysis; Laplace transformation
• Languages: English
• ISBNs: 9781000511123; 9781000511116; 9780367810283
• Related ISBNs: 9780367409784
• Notes: Note: Description based on CIP data; resource not viewed.
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.