Basic Complex Analysis
Third Edition ©1999 Jerrold E. Marsden; California Institute of Technology; Michael J. Hoffman; California State University; Los Angeles Formats: Print
As low as $312.99
As low as $312.99
Authors
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Jerrold E. Marsden
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Michael J. Hoffman
Table of Contents
1.1 Introduction to Complex Numbers
1.2 Properties of Complex Numbers
1.3 Some Elementary Functions
1.4 Continuous Functions
1.5 Basic Properties of Analytic Functions
2. Cauchys Theorem
2.2 Cauchys Theorem-A First Look
2.3 A Closer Look at Cauchys Theorem
2.4 Cauchys Integral Formula
2.5 Maximum Modulus Theorem and Harmonic Functions
3. Series Representation of Analytic Functions
3.1 Convergent Series of Analytic Functions
3.2 Power Series and Taylors Theorem
3.3 Laurent Series and Classification of Singularities
4. Calculus of Residues
4.1 Calculation of Residues
4.2 Residue Theorem
4.3 Evaluation of Definite Integrals
5. Conformal Mappings
5.1 Basic Theory of Conformal Mappings
5.2 Fractional Linear and Schwarz-Christoffel Transformations
5.3 Applications of Conformal Mappings to Laplaces Equation, Heat Conduction, Electrostatics, and Hydrodynamics
6. Further Development of the Theory
6.1 Analytic Continuation and Elementary Riemann Surfaces
6.2 Rouche Theorem and Principle of the Argument
6.3 Mapping Properties of Analytic Functions
7. Asymptotic Methods
7.1 Infinite Products and the Gamma Function
7.2 Asymptotic Expansions and the Method of Steepest Descent
7.3 Stirlings Formula and Bessel Functions
8. Laplace Transform and Applications
Answers to Odd-Numbered Exercises
Index
Product Updates
Authors
-
Jerrold E. Marsden
-
Michael J. Hoffman
Table of Contents
1.1 Introduction to Complex Numbers
1.2 Properties of Complex Numbers
1.3 Some Elementary Functions
1.4 Continuous Functions
1.5 Basic Properties of Analytic Functions
2. Cauchys Theorem
2.2 Cauchys Theorem-A First Look
2.3 A Closer Look at Cauchys Theorem
2.4 Cauchys Integral Formula
2.5 Maximum Modulus Theorem and Harmonic Functions
3. Series Representation of Analytic Functions
3.1 Convergent Series of Analytic Functions
3.2 Power Series and Taylors Theorem
3.3 Laurent Series and Classification of Singularities
4. Calculus of Residues
4.1 Calculation of Residues
4.2 Residue Theorem
4.3 Evaluation of Definite Integrals
5. Conformal Mappings
5.1 Basic Theory of Conformal Mappings
5.2 Fractional Linear and Schwarz-Christoffel Transformations
5.3 Applications of Conformal Mappings to Laplaces Equation, Heat Conduction, Electrostatics, and Hydrodynamics
6. Further Development of the Theory
6.1 Analytic Continuation and Elementary Riemann Surfaces
6.2 Rouche Theorem and Principle of the Argument
6.3 Mapping Properties of Analytic Functions
7. Asymptotic Methods
7.1 Infinite Products and the Gamma Function
7.2 Asymptotic Expansions and the Method of Steepest Descent
7.3 Stirlings Formula and Bessel Functions
8. Laplace Transform and Applications
Answers to Odd-Numbered Exercises
Index
Product Updates
FAQs
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Are you a campus bookstore looking for ordering information?
MPS Order Search Tool (MOST) is a web-based purchase order tracking program that allows customers to view and track their purchases. No registration or special codes needed! Just enter your BILL-TO ACCT # and your ZIP CODE to track orders.
Canadian Stores: Please use only the first five digits/letters in your zip code on MOST.
Visit MOST, our online ordering system for booksellers: https://tracking.mpsvirginia.com/Login.aspx
Learn more about our Bookstore programs here: https://www.macmillanlearning.com/college/us/contact-us/booksellers
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Our courses currently integrate with Canvas, Blackboard (Learn and Ultra), Brightspace, D2L, and Moodle. Click on the support documentation below to find out more details about the integration with each LMS.
Integrate Macmillan courses with Blackboard
Integrate Macmillan courses with Canvas
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If you’re a verified instructor, you can request a free sample of our courseware, e-book, or print textbook to consider for use in your courses. Only registered and verified instructors can receive free print and digital samples, and they should not be sold to bookstores or book resellers. If you don't yet have an existing account with Macmillan Learning, it can take up to two business days to verify your status as an instructor. You can request a free sample from the right side of this product page by clicking on the "Request Instructor Sample" button or by contacting your rep. Learn more.
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Sometimes also referred to as a spiral-bound or binder-ready textbook, loose-leaf textbooks are available to purchase. This three-hole punched, unbound version of the book costs less than a hardcover or paperback book.
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We can help! Contact your representative to discuss your specific needs for your course. If our off-the-shelf course materials don’t quite hit the mark, we also offer custom solutions made to fit your needs.
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Basic Complex Analysis
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