Author Archives: Sybil Shaver

Topics: • Finding the sum of the first k terms of an arithmetic sequence (also called the kth partial sum) • Geometric sequences and the general formula for the nth term of a geometric sequence • Finding the sum of … Continue reading →

(after Test 4)   Topics: • Sequences in general and some notation: introduction to arithmetic and geometric sequences • Arithmetic sequences • The general formula for the nth term of an arithmetic sequence: We multiply d by (n-1) because we … Continue reading →

Here is the beautiful video riffing off Fibonacci numbers, the Golden Ratio, and related things, which I mentioned in class: https://www.youtube.com/v/kkGeOWYOFoA?fs=1&hl=en_US

  Announcement from the Mathematics Department:  All students, without exception, are expected to appear at the scheduled time and place for their final examination in mathematics. [For this course, that means Thursday 22 May 2014, 8:00 AM, in our normal … Continue reading →

Topics: • Vectors in the plane • Magnitude and direction angle of a vector • Unit vectors • Scalar multiplication • Vector addition     Homework: • Review the definitions, terminology, and notation in the examples regarding vectors. Most of … Continue reading →

Topics: • The geometric representation of complex numbers: we represent the complex number a+bi as the point (a,b) in the coordinate plane (called “the complex plane” when we are talking about complex numbers). Better: we really think of a+bi as … Continue reading →

Topics: • Solving the basic trig equations: , , . The methods are developed in these examples: Example 20.1 for  Example 20.4 for  Example 20.7 for  Examples 20.3, 20.6, and 20.9 use the developed methods to solve other basic trig equations.   … Continue reading →

Topics: • The addition, subtraction, and double angle identities for tangent • Proving identities • The inverse trig functions (Session 19)   Homework: • Review the examples discussed in class • Review the definitions of the inverse trig functions and … Continue reading →

Topics: • Finding exact values for the trig functions using knowledge of basic triangles and points on the coordinate axes • Basic graphs of sine, cosine, and tangent and their properties • Transformed graphs of sine and cosine functions Here … Continue reading →

Topics: • Exponential functions in applications where the rate of growth or decay (decrease) per unit time is known. (See Examples 15.6, 15.7, and 15.8) Exponential growth and decay occur when the rate of change is a percentage of the … Continue reading →