Goals: This course is de signed to teach students
to:
(i) Develop mathematical formulations for engineering problems
(ii) Apply appropriate analytical and numerical approximations
(iii) Learn and apply elementary numerical algorithms
(iv) Improve problem solving skills
This course contributes to B.S. program objectives 1, 2, 3, and 11.
TEXT: Numerical Methods for Engineers , SC Chapra and RP Canale 5th
Edition
TOPICS (43 lectures)
Topics that will be covered are listed be low . The numerical references are to
sections in
Chapra & Canale; a useful (but more advanced source) of material for sections
1.1 and 1.2 is
Wikipedia . These references are not necessarily
complete; in some cases your classroom notes may be the only source or you may
need to consult
more advanced texts. Asterisked sections are for your personal study; they are
part of the syllabus
even though they are not lecture topics.
1. Linear Algebra (14 lectures)
An algebra is a set of rules for manipulating symbols . Linear Algebra then is a
set of rules for
manipulating and solving linear systems of equations: i.e.
Linear algebra is the foundation of numerical computing, because linear
equations are the only
ones a computer can solve directly. More complicated equations, such as
non-linear algebraic
equations, ordinary differential equations , and partial differential equations
are typically reduced to
repeated solutions of linear algebraic equations. Thus linear algebra is at the
core of numerical
analysis. Read sections PT3.1.1 and PT3.3 first.
1.1 Vectors (2 lectures)
1.1.1. Definitions and operations
1.1.2. Vector space and basis vectors
1.1.3. Linear dependence
1.1.4. Linear transformations
1.2 Matrices (4 lectures)
1.2.1. Matrix re presentations of linear transformations
1.2.2. Sequences of transformations: matrix-matrix multiplication (PT3.2.2)
1.2.3. Matrix de terminants (9.1.2)
1.2.4. Matrix inverse
1.2.5. Special matrices* (Box PT3.1)
1.3Solving linear systems (4 lectures)
1.3.1. Gauss elimination (9.2)
1.3.2. GaussJordan elimination* (9.7)
1.3.3. Scaling and pivoting (9.4)
1.3.4. LU decomposition (10.1)
1.3.5. Vector and matrix norms, and matrix condition (10.3.1 & 10.3.2)
1.3.6. Using Excel functions (11.3.1)
1.4Applications (2 lectures)
1.4.1. A reactor system (12.1)
1.4.2. A resistor ne twork (12.3)
1.4.3. A spring network* (12.4)
1.5Programming VBA (2 lectures)
1.5.1. Basic concepts (Environment, operations, I/O)
1.5.2. Loops, conditions, subprograms
2.Uncertainty and statistics (5 lectures)
Data is always accompanied by uncertainty. In some cases, for example the speed
of light, the
uncertainty is so small that it can be neglected for practical purposes.
However, in many cases the
uncertainty in measurement is significant and we need a language to express
this; this is called
statistics. Here we will introduce some elementary ideas and applications of
statistical methods.
2.1Probability, mean, and standard deviation (PT5.2)
2.2Central limit theorem, normal distribution and confidence intervals (Box
PT5.1)
2.3Linear regression (17.1)
2.4 Multiple regression (17.3 & 17.4)
2.5Application of linear regression (20.1)
