Review of basic algebra and calculus

The study of geophysics requires mathematics to describe various physical phenomena and systems. Throughout this course, formulas will be provided that give such a mathematical framework. Although students will not be responsible for being able to derive them, it is essential for students have the skills to combine, manipulate and simplify these mathematical expressions. Many of the assigned problems can be solved by isolating a single variable and finding its value, given other known values.

Some basic rules used in mathematical manipulations in the following:

1. Factoring formulas

ab + ac = a(b + c) common factor
a2 - b2 = (a + b)(a - b) difference of squares
a2 + 2ab + b2 = (a + b)2 perfect square
a2 - 2ab + b2 = (a - b)2

2. Properties of Logarithms

logb xy = logb x + logb y
logb (x/y) = logb x - logb y
logb xr = r logb x
logb 1 = 0
logb b = 1
logb x = logax/logab Change of base

3. Properties of Exponents

a-n = 1/an , a!=0
aman = am+n
am/an = am - n , a!=0
(ab)n = anbn
(a/b)n = an/bn , b!=0
a0 = 1 , a!=0

4. Quadratic Formula

5. Trigonometry



Law of sines:



Law of cosines:



Angle measurements:

6. Calculus:

Differentiation:

Product rule:


Division rule:


Chain rule:

Integration:

Integration by parts: