Math 241 Calculus, Part IV (4h. 1c.u.) Text: Zill, Dennis and Cullen ...

Core Maple
Chapter Section & Topic Problems Problems
Complex Analysis 785
17 Functions of a Complex Variable 789
17.3 Sets of Points in the Complex Plane 798 3, 5, 11, 13, 17, 25
17.4 Functions of a Complex Variable; Analyticity 800 1, 5, 9, 17, 21, 23, 31, 33, 37, 43
17.5 Cauchy-Riemann Equations 806 1, 5, 11, 15, 20, 27
17.6 Exponential and Logarithmic Functions 811 3, 11, 15, 17, 25, 37, 45, 47
17.7 Trigonometric and Hyperbolic Functions 818 3, 9, 13, 17, 24
17.8 Inverse Trigonometric and Hyperbolic Functions 822 1, 5, 11, 13
18 Integration in the Complex Plane 827
18.1 Contour Integrals 828 3, 5, 13, 19, 23, 25, 29, 33
18.2 Cauchy-Goursat Theorem 833 3, 9, 13, 19, 21, 23
18.3 Independence of Path 838 2, 4, 9, 15, 19, 23
18.4 Cauchy's Integral Formula 845 3, 5, 11, 17, 21, 23
19 Series and Residues 851
19.1 Sequences and Series 852 3, 7, 11, 15, 19, 23, 27
19.2 Taylor Series 857 3, 11, 17, 21, 27, 31
19.3 Laurent Series 863 3, 9, 15, 21, 25, 27
19.4 Zeros and Poles 870 1, 5, 9, 13, 19, 23
19.5 Residues and Residue Theorem 873 3, 9, 13, 17, 21, 27, 31
19.6 Evaluation of Real Integrals 879 3, 7, 11, 17, 27, 31, 35
OLD EXAM QUESTIONS also form a part of the core.
The core problems indicate the kind of basic problems you will need to be able to solve by hand. They also provide a guide to
the basic level of difficulty to be expected on the final exam.
Note: All sections of Math 241 have a COMMON FINAL EXAM
The following sections contain material covered in previous courses. Students are encouraged to review this
material as needed.
17 Functions of a Complex Variable 789
17.1 Complex Numbers 790
17.2 Form of Complex Numbers; Powers and Roots 793