MATH 135: COMPLEX NUMBERS
(WINTER, 2008)
The introduction of complex numbers in the 16th century made it possible to solve the equation x2 + 1 = 0. These notes1 present one way of defining complex numbers. 1. The Complex Plane A complex number z is given
Math 135A, Winter 2008
Midterm #2 (Solutions)
cosh x - cos x . sin x2 (1 + x2 /2! + O(x3 ) - (1 - x2 /2! + O(x3 ) cosh x - cos x x2 + O(x3 ) = Solution: = 2 1 as x 0. sin x2 x2 + O(x3 ) x + O(x3 ) (1) Evaluate lim
x0
(2) Is the series
(-1)k
k=1
ln k abso
Math 135A, Winter 2008
Homework #8 (due 2/29/2008)
Routine problems: 9.3: #11, #13, #23, #26, #10, #19, #21, #37;
To hand in:
(1) Show tht
k=0
sin k converges. Evaluate it exactly bu using the fact that sin k = 2k
1 a+ib
(eik ).
Hint: It will be useful
Math 135A, Winter 2008
Homework #7 (due 2/22/2008)
Routine problems: 12.6: #1, #2, #5, #9, #10, #11, #13, #17; 12.7: #3, #7, #20, #31, #34; 12.8: #1, #3, #4, #5, #8, #19, #27, #41, #44. Also, make use of the material in the notes More on Taylor Polynomia
MATH 134: Honors Calculus
Professor: Jack Lee
Department: Math
Calculus Week 1 Notes
For this course, we will take the following fundamental notions as primitive
undefined terms
The only facts about them that can be used in proofs are the ones expressed i