Western University (Ontario)  Also known as University of Western Ontario
Applied Mathematics for Engineers I
AM 1413

Fall 2013
Chapter 2: Differentiation
Methods for detonating differential equations:
f `(x ) = Df(x)=Dxf(x)=Dx1f(x)= d/dx*f(x)
f `(x)=D2f(x)=D2xf(x)=d2/dx*f(x)
*Note, go back to first principles for any derivative
2.1 Tangent lines and their slopes:
Definition of a
Western University (Ontario)  Also known as University of Western Ontario
Applied Mathematics for Engineers I
AM 1413

Fall 2013
MIDERM REVIEW
L`Hopital's Rule:
Suppose the functions f and g are differentiable on the open interval (a,b) and
g`(x)0 (but can be at a) there. suppose also that:
Must write down the lim of g(x) and f(x), and then determine the form of these limits. see c
Western University (Ontario)  Also known as University of Western Ontario
Applied Mathematics for Engineers I
AM 1413

Fall 2013
TRIG REVIEW
the trig ration can be
thought of a circle of
radius of one. This has
a right angle triangle
within it. it is this
triangle that the trig
ratios come from and
can be solved from.
The acute angle is labelled "t" and is measured in radians (), 2
Western University (Ontario)  Also known as University of Western Ontario
Applied Mathematics for Engineers I
AM 1413

Fall 2013
Chapter 4: More
Applications of
Differentiation
4.1: Related Rates
When two or more quantities that change with time are linked by an
equation, that equation can be differentiated with respect to time to
produce an equation linking the rates of change of
Western University (Ontario)  Also known as University of Western Ontario
Applied Mathematics for Engineers I
AM 1413

Fall 2013
Chapter 5: Integration
5.1: Sums and sigma Notation
is used to denote the sum of
sequence values.
Ex:
m is the lower limit and n is the upper limit of the summing values, Ie start at m, m+1, m+2,. n1, n
i, is the index of the sequence and has no effect
Western University (Ontario)  Also known as University of Western Ontario
Applied Mathematics for Engineers I
AM 1413

Fall 2013
Chapter 8: Conics, Parametric Curves and Polar Curves
8.2: Parametric Curves
Breaking down the curve, into functions of x=f(r), and y=g(r)
Allows for curves and vertical lines to be possible.
The parameter r, is independent from the axis,
Parameter of a s
Western University (Ontario)  Also known as University of Western Ontario
Applied Mathematics for Engineers I
AM 1413

Fall 2013
Chapter 7: Applications of Integration
7.1: Volumes by slicingSolids of Revolution
By taking slices of a cylinder, the volume of a shape can be determined.
V=A(x)x
V=A(x)dx
Rotation of a function around an axis:
Determine the area of a cross section, det
Western University (Ontario)  Also known as University of Western Ontario
Applied Mathematics for Engineers I
AM 1413

Fall 2013
Chapter 6: Techniques of integration
6.1: Integration by parts
Suppose that U(x) and V(x) are tow differentiable functions: than according to chain rule:
Than the inverse of this will be given by:
Which simplifies to
Ex: xexdx, let U=x, than dU=dx, V=ex,
Western University (Ontario)  Also known as University of Western Ontario
Applied Mathematics for Engineers I
AM 1413

Fall 2013
Chapter 3: Transcendental Functions
3.1: Inverse functions:
The function must be a onetoone function. This means that for any f(x) there is only a single x value that will give that f(x) y. Value. If it does not meet this the
function must be broken apa
Western University (Ontario)  Also known as University of Western Ontario
Applied Mathematics for Engineers I
AM 1413

Fall 2013
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