Mathematical Methods for Physics 1, Autumn 2012 Department of Mathematics, University
of Sussex
Exercise Sheet 3 Due on Thursday, 8th November 2012, 3pm
Submit to the School Oce
The marks scored on problems listed in this exercise sheet are used for asses
Mathematical Methods for Physics 1, Autumn 2012 Department of Mathematics, University
of Sussex
Workshop Sheet 8
The problems on this workshop sheet relate to Chapter 8 of the lectures and lecture notes.
1. Let z1 = 2 i 2 and z2 =
3 + i.
(a) Plot the comp
Mathematical Methods for Physics 1, Autumn 2012 Department of Mathematics, University
of Sussex
Workshop Sheet 9
The problems on this workshop sheet relate to Chapter 9 of the lectures and lecture notes.
1. Suppose that the vectors a and b satisfy a + b =
Mathematical Methods for Physics 1, Autumn 2012 Department of Mathematics, University
of Sussex
Workshop Sheet 7
The problems on this workshop sheet relate to Chapter 7 of the lectures and lecture notes.
If you are asked to compute a Maclaurin or Taylor s
Mathematical Methods for Physics 1, Autumn 2012 Department of Mathematics, University
of Sussex
Workshop Sheet 6
The problems on this workshop sheet relate to Chapter 5 and Chapter 6 of the lectures and
lecture notes.
1. Use integration by parts to evalua
Mathematical Methods for Physics 1, Autumn 2012 Department of Mathematics, University
of Sussex
Workshop Sheet 5
The problems on this workshop sheet relate to Chapter 5 of the lectures and lecture notes.
1. Find the area under the graph of the function
1
Mathematical Methods for Physics 1, Autumn 2012 Department of Mathematics, University
of Sussex
Workshop Sheet 4
The problems on this workshop sheet relate to Chapter 3 and Chapter 4 of the lectures and
lecture notes.
1. Compute the rst and second order d
Mathematical Methods for Physics 1, Autumn 2012 Department of Mathematics, University
of Sussex
Workshop Sheet 3
The problems on this workshop sheet relate to Chapter 3 of the lectures and lecture notes.
1. For each of the following functions, plot the fu
Mathematical Methods for Physics 1, Autumn 2012 Department of Mathematics, University
of Sussex
Workshop Sheet 2
The problems on this workshop sheet relate to Chapter 1 and 2 of the lectures and lecture
notes.
1. For the quadratic function
1
g ( x) = x2 +
Mathematical Methods for Physics 1, Autumn 2012 Department of Mathematics, University
of Sussex
Workshop Sheet 10
The problems on this workshop sheet relate to Chapter 10 of the lectures and lecture notes.
1. Show that if a = (a1 , a2 , a3 ), b = (b1 , b2
1
Mathematical Methods for Physics 1, Solutions to Workshop Sheet 1
Mathematical Methods for Physics 1, Autumn 2012 Department of Mathematics, University
of Sussex
Solutions to Workshop Sheet 2
1. For the quadratic function
1
g (x) = x2 + 1
2
do the follo
1
Mathematical Methods for Physics 1, Solutions to Workshop Sheet 8
Mathematical Methods for Physics 1, Autumn 2012 Department of Mathematics, University
of Sussex
Solutions to Workshop Sheet 8
1. Let z1 = 2 i 2 and z2 =
3 + i.
(a) Plot the complex number
Mathematical Methods for Physics 1, Solutions to Workshop Sheet 7
1
Mathematical Methods for Physics 1, Autumn 2012 Department of Mathematics, University
of Sussex
Solutions to Workshop Sheet 7
1. Write down the 10th and 19th terms of the arithmetic progr
1
Mathematical Methods for Physics 1, Solutions to Workshop Sheet 9
Mathematical Methods for Physics 1, Autumn 2012 Department of Mathematics, University
of Sussex
Solutions to Workshop Sheet 9
1. Suppose that the vectors a and b satisfy a + b = (2, 3, 4)
1
Mathematical Methods for Physics 1, Solutions to Workshop Sheet 5
Mathematical Methods for Physics 1, Autumn 2012 Department of Mathematics, University
of Sussex
Solutions to Workshop Sheet 6
1. Use integration by parts to evaluate the following integra
Mathematical Methods for Physics 1, Solutions to Workshop Sheet 3
1
Mathematical Methods for Physics 1, Autumn 2012 Department of Mathematics, University
of Sussex
Solutions to Workshop Sheet 3
1. For each of the following functions, plot the function and
Mathematical Methods for Physics 1, Solutions to Workshop Sheet 5
1
Mathematical Methods for Physics 1, Autumn 2012 Department of Mathematics, University
of Sussex
Solutions to Workshop Sheet 5
1. Find the area under the graph of the function
f (x) =
1
,
1
Mathematical Methods for Physics 1, Solutions to Workshop Sheet 4
Mathematical Methods for Physics 1, Autumn 2012 Department of Mathematics, University
of Sussex
Solutions to Workshop Sheet 4
1. Compute the rst and second order derivative of each of the
Mathematical Methods for Physics 1, Solutions to Workshop Sheet 1
1
Mathematical Methods for Physics 1, Autumn 2012 Department of Mathematics, University
of Sussex
Solutions to Workshop Sheet 1
1. Sketch the graphs of the following functions f : R R.
(i)
Mathematical Methods for Physics 1, Solutions to Exercise Sheet 4
1
Mathematical Methods for Physics 1, Autumn 2012 Department of Mathematics, University
of Sussex
Solutions to Exercise Sheet 4
1. Find the sum of the following series
(a)
1 + 3.5 + 6 + 8.5
Mathematical Methods for Physics 1, Solutions to Exercise Sheet 5
1
Mathematical Methods for Physics 1, Autumn 2012 Department of Mathematics, University
of Sussex
Solutions to Exercise Sheet 5
1. Write the complex numbers below in the form x + i y with x
Chapter 5
Basic Integration
Integration is the reverse operation to dierentiation. In this chapter we
will introduce integration and discuss all standard techniques of integration. In
Chapter 6, we will use integration to tackle various applications, such
Chapter 2
Classical Functions
In this chapter we discuss the classical functions. In Section 2.1, we discuss briey
polynomials, the easiest classical functions. In the last chapter we have already
encountered polynomials of degree zero, one, and two, that
Chapter 1
Introduction to Functions
Functions are of paramount importance in physics and engineering in order to describe physical phenomena such as movement and speed over a period of time, the
change of the temperature over a period of time, as well as
Mathematical Methods for Physics 1, Autumn 2012 Department of Mathematics, University
of Sussex
Exercise Sheet 5 Due on Thursday, 6th December 2012, 3pm
Submit to the School Oce
The marks scored on problems listed in this exercise sheet are used for asses
Chapter 3
Dierentiation
In this chapter we learn more properties of functions, namely continuity and dierentiability. In Section 3.1, we briey discuss continuity. If a function is continuous,
then its graph is one continuous curve. The functions that you
Mathematical Methods for Physics 1, Autumn 2012 Department of Mathematics, University
of Sussex
Exercise Sheet 1 Due on Thursday, 11th October 2012, 3pm
Submit to the School Oce
The marks scored on problems listed in this exercise sheet are used for asses
Mathematical Methods for Physics 1, Autumn 2012 Department of Mathematics, University
of Sussex
Exercise Sheet 4 Due on Thursday, 22nd November 2012, 3pm
Submit to the School Oce
The marks scored on problems listed in this exercise sheet are used for asse
Mathematical Methods for Physics 1, Autumn 2012 Department of Mathematics, University
of Sussex
Exercise Sheet 2 Due on Thursday, 25th October 2012, 3pm
Submit to the School Oce
The marks scored on problems listed in this exercise sheet are used for asses
Chapter 6
Further Integration
In this chapter we learn several applications of integration that are important
for engineering and physics. The rst such application is nding the average of a
function which is discussed in Section 6.1. For example we may wa