ENGI 5432 Final Exam 2009 - Solutions Page 1 of 14
ENGI 5432 Advanced Calculus
Final Examination, 2009 Solutions
Note: You need the Symbo; font (68 1:3) in order to display various symbols correctly, such as
yr, p, .51 and g (otherwise they appear asp,
ENGI 5432
2.
2. Surface Integrals
Page 2.01
Surface Integrals
This chapter introduces the theorems of Green, Gauss and Stokes.
Two different
methods of integrating a function of two variables over a curved surface are developed.
The sections in this chapt
ENGI 5432
1.
1. Vector Fields and the Gradient Operator
Page 1-01
Vector Fields and the Gradient Operator
In this chapter, a review of vectors from previous courses is followed by the introduction
of lines of force. The gradient operator is extended to di
ENGI 5432
3.
3. Fourier Series
Page 3.01
Fourier Series
This short chapter offers a very brief review of [discrete] Fourier series.
The Fourier series of f (x) on the interval (L, L) is
a
f ( x) = 0 +
2
n x
n x
+ bn sin
L
L
an cos
n =1
where
an
5.
Suggestions for the Formula Sheets
Below are some suggestions for many more formulae than can be placed easily on both
sides of the two standard 8"11" sheets of paper for the final examination. It is
strongly recommended that students compose their own
ENGI 5432
4.
Lecture Notes 4 - PDEs
Page 4.01
Partial Differential Equations
Partial differential equations (PDEs) are equations involving functions of more than one
variable and their partial derivatives with respect to those variables.
Most (but not all