Math 1d: Sequences and Series Week 7
California Institute of Technology
Winter 2014
Jay Daigle
1
Fourier Series
In the past week weve looked at ways to approximate functions using polynomials. If you have
an innitely-dierentiable function, its Taylor seri
Math 1d: Sequences and Series Week 6
California Institute of Technology
Winter 2014
Jay Daigle
Recall that last time, for an innitely dierentiable function f , we dened Taylor polynomials and the Taylor series:
Denition 0.1. The n-th order approximation t
Math 1d: Sequences and Series Week 5
California Institute of Technology
Winter 2014
Jay Daigle
1
Power Series
We left o last class with a discussion of the function, k=0 xk , which had a number of nice
properties, most of which came from the fact that it
Math 1d: Sequences and Series Week 4
California Institute of Technology
Winter 2014
Jay Daigle
We start this week by nishing our discussion of complex calculus. (Because last terms
calculus was so simple, right?).
Denition 0.1. If f : C C is a function, w
Math 1d: Sequences and Series Week 3
California Institute of Technology
Winter 2014
Jay Daigle
1
Complex Numbers and Series
1.1
Complex Numbers
We often want to ask for the solution to a polynomial equation, such as x2 1 = 0. Many
of these equations had s
Math 1d: Sequences and Series Week 2
California Institute of Technology
Winter 2014
Jay Daigle
1
Series of Positive Real Numbers
n
1
Example 1.1. Let an = k=0 k2 . We claim that limn an exists. Assuming
m
1
(without loss of generality) that m > n, we see
Math 1d: Sequences and Series Week 1
California Institute of Technology
Winter 2014
Jay Daigle
1
Sequences of Real Numbers
The rst section of this course will cover a mathematical object called a sequence.
Denition 1.1. A sequence of real numbers is a (us
Math 1d
Instructor: Jay Daigle
Homework 7
Due Friday, 28 at noon
Caltech Winter 2014
Instructions
The rst problem is mandatory, and no collaboration is allowed. Be as clean as you can in
your writeup; but remember you can resubmit as often as you like. Yo
Math 1d
Instructor: Jay Daigle
Homework 6
Due Tuesday, February 18 at noon
Caltech Winter 2014
Instructions
The rst problem is mandatory, and no collaboration is allowed. Be as clean as you can in
your writeup; but remember you can resubmit as often as yo
Math 1d
Instructor: Jay Daigle
Homework 5
Due Tuesday, February 11 at noon
Caltech Winter 2014
Instructions
The rst problem is mandatory, and no collaboration is allowed. Be as clean as you can in
your writeup; but remember you can resubmit as often as yo
Math 1d
Instructor: Jay Daigle
Homework 4
Due Tuesday, February 4 at noon
Caltech Winter 2014
Instructions
The rst problem is mandatory, and no collaboration is allowed. Be as clean as you can in
your writeup; but remember you can resubmit as often as you
Math 1d
Instructor: Jay Daigle
Homework 3
Due Tuesday, January 28 at noon
Caltech Winter 2014
Instructions
The rst problem is mandatory, and no collaboration is allowed. Be as clean as you can in
your writeup; but remember you can resubmit as often as you
Math 1d
Instructor: Jay Daigle
Homework 2
Due Tuesday, January 21 at noon
Caltech Winter 2014
Instructions
The rst problem is mandatory, and no collaboration is allowed. Be as clean as you can in
your writeup; but remember you can resubmit as often as you
Math 1d
Instructor: Jay Daigle
Homework 1
Due Tuesday, January 14 at noon
Caltech Winter 2014
Instructions
The rst problem is mandatory, and no collaboration is allowed. Be as clean as you can in
your writeup; but remember you can resubmit as often as you
Math 1d
Instructor: Jay Daigle
Homework 1 Solutions
Caltech Winter 2014
Instructions
The rst problem is mandatory, and no collaboration is allowed. Be as clean as you can in
your writeup; but remember you can resubmit as often as you like. You may consult