7/25/2013 SECOND HOURLY PRACTICE VIII
2013
Maths 21a, O.Knill, Summer
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7/11/2013 FIRST HOURLY
Maths 21a, O.Knill, Summer 2013
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7/25/2013 SECOND HOURLY
Maths 21a, O.Knill, Summer 2013
Name:
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Try to answer each question on the same page as the question is asked. If needed, use
the back or the next empty page for work. If you need addit
7/11/2013 FIRST HOURLY Practice II
Maths 21a, O.Knill, Summer 2013
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8/8/2013 PRACTICE EXAM I
Maths 21a, O. Knill, Summer 2013
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7/25/2013 SECOND HOURLY PRACTICE VI Maths 21a, O.Knill, Summer 2013
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Math 1A: introduction to functions and calculus
Oliver Knill, 2014
Lecture 23: Improper integrals
In this lecture, we look at integrals on innite intervals or integrals, where the function can get
innite at some point. These integrals are called improper
Math 1A: introduction to functions and calculus
Oliver Knill, Spring 2014
4/8/2014: Second midterm practice C
Your Name:
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7/25/2013 SECOND HOURLY PRACTICE IV Maths 21a, O.Knill, Summer 2013
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8/8/2013 PRACTICE EXAM V
Maths 21a, O. Knill, Summer 2013
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8/8/2013 PRACTICE EXAM VI
Maths 21a, O. Knill, Summer 2013
Name:
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Math 1A: introduction to functions and calculus
Oliver Knill, 2014
Lecture 10: Worksheet
The chain rule
The rule(f (g(x) = f (g(x)g (x) is called the chain rule.
For example, the derivative of sin(log(x) is cos(log(x)/x.
We have also seen that we can comp
7/25/2013 SECOND HOURLY PRACTICE V Maths 21a, O.Knill, Summer 2013
Name:
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Math 1A: introduction to functions and calculus
Oliver Knill, 2014
Lecture 11: Worksheet
Critical points and extrema
In this worksheet we want to nd out which rectangle of xed area
xy = 1 has minimal circumference 2x + 2y.
To solve this problem we have to
Math 1A: introduction to functions and calculus
Oliver Knill, 2014
Lecture 20: Worksheet
Anti derivatives
Here are some trickier anti derivative puzzles. We still have no integration techniques and must rely on intuition and experiments to nd
the derivati
8/8/2013 PRACTICE EXAM III
Maths 21a, O. Knill, Summer 2013
Name:
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the back or the next empty page for work.
Do not detac
Math 1A: introduction to functions and calculus
Oliver Knill, Spring 2014
4/8/2014: Second midterm practice B
Your Name:
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8/8/2013 PRACTICE EXAM VIII
Maths 21a, O. Knill, Summer 2013
Name:
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Try to answer each question on the same page as the question is asked. If needed, use
the back or the next empty page for work.
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7/25/2013 SECOND HOURLY PRACTICE III Maths 21a, O.Knill, Summer 2013
Name:
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the back or the next empty page for work. If y
Math 1A: introduction to functions and calculus
Oliver Knill, Spring 2014
4/8/2014: Second midterm practice D
Your Name:
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7/25/2013 SECOND HOURLY PRACTICE II Maths 21a, O.Knill, Summer 2013
Name:
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Math 1A: introduction to functions and calculus
Oliver Knill, 2014
Lecture 13: Worksheet
Hopitals rule
1
What does lHopitals rule say about
exp(2x) 1
?
x0
x
lim
3
2
1
1.0
0.5
0.5
1
1.0
2
Apply lHopitals rule to get the limit of
f (x) =
for x 0.
sin(200x)
Math 1A: introduction to functions and calculus
Oliver Knill, 2014
Lecture 19: Fundamental theorem
In this lecture we come back to the fundamental theorem of calculus for dierentiable functions. This will allow us in general to compute integrals of functi
Math 1A: introduction to functions and calculus
Oliver Knill, 2014
Lecture 16: The mean value theorem
In this lecture, we look at the mean value theorem and a special case called Rolles theorem.
Unlike the intermediate value theorem which applied for cont
Math 1A: introduction to functions and calculus
Oliver Knill, 2014
Lecture 34: Calculus and Statistics
In this lecture, we look at an application of calculus to statistics. We have already dened the
probability density function f called PDF and its anti-d
Math S21a: Multivariable calculus
Oliver Knill, Summer 2016
Lecture 9: Partial derivatives
If f (x, y) is a function of two variables, then x
f (x, y) is defined as the derivative of
the function g(x) = f (x, y) with respect to x, where y is considered a
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Differential Calculus
Complex Numbers
z = a + ib
Where:
z = rcis = r(cos + i sin )
Where r is the modulus |z| and the argument arg z .
University of Sydney
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8001A SEMESTER 1 2011
THE UNIVERSITY OF SYDNEY
SCHOOL OF MATHEMATICS AND STATISTICS
MATH 1001
DIFFERENTIAL CALCULUS
June 2011 LECTURERS: R. Howlett, X. Liu, N. Saunders, Z. Zhang.
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