Complex Analysis: A First Course with Applications 3rd edition

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Dennis G. Zill and Patrick D. Shanahan
Publisher: Jones and Bartlett Learning

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  • Chapter 1: Complex Numbers and the Complex Plane
    • 1.1: Complex Numbers and Their Properties (7)
    • 1.2: Complex Plane (7)
    • 1.3: Polar Form of Complex Numbers (5)
    • 1.4: Powers and Roots (5)
    • 1.5: Sets of Points in the Complex Plane (6)
    • 1.6: Applications (3)
    • 1: Review Quiz (6)

  • Chapter 2: Complex Functions and Mappings
    • 2.1: Complex Functions (8)
    • 2.2: Complex Functions as Mappings (6)
    • 2.3: Linear Mappings (7)
    • 2.4: Special Power Functions (5)
    • 2.5: Reciprocal Function (4)
    • 2.6: Applications (3)
    • 2: Review Quiz (3)

  • Chapter 3: Analytic Functions
    • 3.1: Limits and Continuity (8)
    • 3.2: Differentiability and Analyticity (6)
    • 3.3: Cauchy-Riemann Equations (4)
    • 3.4: Harmonic Functions (4)
    • 3.5: Applications (2)
    • 3: Review Quiz (4)

  • Chapter 4: Elementary Functions
    • 4.1: Exponential and Logarithmic Functions (8)
    • 4.2: Complex Powers (4)
    • 4.3: Trigonometric and Hyperbolic Functions (8)
    • 4.4: Inverse Trigonometric and Hyperbolic Functions (6)
    • 4.5: Applications
    • 4: Review Quiz (7)

  • Chapter 5: Integration in the Complex Plane
    • 5.1: Real Integrals (6)
    • 5.2: Complex Integrals (5)
    • 5.3: Cauchy-Goursat Theorem (4)
    • 5.4: Independence of Path (5)
    • 5.5: Cauchy's Integral Formulas and Their Consequences (5)
    • 5.6: Applications (5)
    • 5: Review Quiz (11)

  • Chapter 6: Series and Residues
    • 6.1: Sequences and Series (4)
    • 6.2: Taylor Series (6)
    • 6.3: Laurent Series (5)
    • 6.4: Zeros and Poles (4)
    • 6.5: Residues and Residue Theorem (5)
    • 6.6: Some Consequences of the Residue Theorem (10)
    • 6.7: Applications (3)
    • 6: Review Quiz (3)

  • Chapter 7: Conformal Mappings
    • 7.1: Conformal Mapping (3)
    • 7.2: Linear Fractional Transformations (5)
    • 7.3: Schwarz-Christoffel Transformations (4)
    • 7.4: Poisson Integral Formulas (2)
    • 7.5: Applications (2)
    • 7: Review Quiz (2)


Complex Analysis: A First Course with Applications, by Dennis G. Zill and Patrick D. Shanahan, is a truly accessible introduction to the fundamental principles and applications of complex analysis. Designed for the undergraduate student with a calculus background but no prior experience with complex analysis, this text discusses the theory of the most relevant mathematical topics in a student-friendly manner. The WebAssign component provides students with instant question feedback and links to the appropriate section of an eBook.

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Group Quantity Questions
Chapter 1: Complex Numbers and the Complex Plane
1.R 6 006 024 026 031 032 036
1.1 7 002a 007 013 023 029 037 043
1.2 7 005 011 013 015 022 024 031
1.3 5 003 017 019 025 035
1.4 5 001 006 011 017 026
1.5 6 004 005 015 020 022 032
1.6 3 009 013 019
Chapter 2: Complex Functions and Mappings
2.R 3 010 021 029
2.1 8 001 007 011 013 016 019 024 037
2.2 6 003 006 009 013 018 022
2.3 7 001 003 006 009 012 025 028
2.4 5 003 022 027 035 051
2.5 4 001 009 011 016
2.6 3 003 011 022
Chapter 3: Analytic Functions
3.R 4 001 024 027 031
3.1 8 001 011 016 021 023 030 038 058
3.2 6 011 013 015 017 025 027
3.3 4 001 007 017 024
3.4 4 003 011 015 017
3.5 2 006 011
Chapter 4: Elementary Functions
4.R 7 001 012 019 023 024 026 035
4.1 8 001 007 010 016 023 027 035 046
4.2 4 002 009 012 016
4.3 8 002 005 010 018 024 026 033 038
4.4 6 001 004 006 009 011 015
Chapter 5: Integration in the Complex Plane
5.R 11 003 008 009 010 011 012 025 032 033 034 037
5.1 6 003 005 007 011 018 027
5.2 5 001 008 015 018 022
5.3 4 009 011 017 025
5.4 5 003 006 011 021 025
5.5 5 001 009 012 017 021
5.6 5 001 005 010 013 025
Chapter 6: Series and Residues
6.R 3 007 023 038
6.1 4 001 016 019 023
6.2 6 002 010 017 026 027 037
6.3 5 001 005 007 013 022
6.4 4 005 013 015 022
6.5 5 001 007 018 025 030
6.6 10 003 007 011 012 015 022 026 031 060 070
6.7 3 003 010 019
Chapter 7: Conformal Mappings
7.R 2 016 021
7.1 3 001 004 015
7.2 5 001 005 017 021 025
7.3 4 001 008 009 011
7.4 2 001 007
7.5 2 012 014
Total 235