Syllabus Stuff

Below you'll find the required parts of a syllabus, so that I can print this and send it to admin to make them happy. You're welcome to peruse it... but it's dry and not terribly informative in terms of what the course will be like or how I am as an instructor. (It probably won't make much sense either unless you've previously taking precalc.)

Reliable internet access and way to get on Canvas - whether that going to a lab on campus or doing so off campus. You will not be able to complete this course using a smartphone only. If you need help getting these materials, the campus has a laptop loan program.

You may also want to consider having the following apps downloaded to your smartphone, if you have space:

• Desmos - their graphing software and calculators are legit.

• Kahoot - then it plays music at you? You can also just access it from a browser.

• Canvas Student - we are part of the San Diego Community College District

• Pronto - the messaging system where you can easily send me questions including videos, pictures, etc...

MATH 104 with a grade of "C" or better, or equivalent

This course is a study of numerical, analytical, and graphical properties of functions. The course content includes polynomial, rational, irrational, exponential, logarithmic, and trigonometric functions. Additional topics include: inverse functions, complex numbers, polar coordinates, matrices, conic sections, sequences, series and the binomial theorem. This course is designed as a preparation for calculus and is intended for the transfer student planning to major in mathematics, engineering, economics, or disciplines included in the physical or life sciences.

Students successfully completing this course will be able to:

• Define and distinguish between higher order polynomial functions and non-polynomial functions and relations, and analyze the graphs of functions by determining their domains and ranges.

• Analyze properties of functions and their graphs, including symmetries, intervals where the function is increasing or decreasing, and its asymptotic behavior.

• Prove algebraically and justify graphically when a function is one-to-one.

• Graph a variety of algebraic, rational, exponential, logarithmic, and trigonometric functions, and where applicable, use rigid and non-rigid transformations, intercepts and asymptotes.

• Perform algebraic operations on various functions including composition of functions, and determine the domain of the resulting function.

• Calculate the inverse of a one-to-one function, determine the domain and range of the inverse and describe the relation between their graphs.

• Solve equations and application problems involving exponential and logarithmic functions

• Simplify difference quotients involving a variety of functions including polynomial, rational, trigonometric, exponential, and logarithmic functions.

• Apply a variety of root finding theorems and tests in order to factor polynomials or solve polynomial equations whose degree is higher than quadratic.

• Simplify rational expressions and expressions involving radicals that arise from calculus operations, such as those from the product or quotient rules.

• Determine the partial fraction decomposition of rational functions.

• Define, evaluate, describe and graph all trigonometric and inverse trigonometric functions, and solve equations involving these functions.

• Derive and prove fundamental trigonometric identities including the sum, difference, double and half angle identities.

• Apply the laws of sines and cosines in solving oblique triangles and application problems

• Represent complex numbers in rectangular, trigonometric and exponential forms and perform arithmetic operations with each.16.Perform algebraic operations involving matrices

• Apply matrices in solving linear systems of equations.

• Compute the determinant of a square matrix, and apply determinants to various applications.

• Apply vector algebra to problems involving vector quantities.

• Perform various vector operations, including the dot and cross products, and formulate their geometric interpretations.

• Analyze, identify, and graph the four conic sections.

• Solve systems of non-linear equations and inequalities, including those involving conic sections.

• Define and analyze sequences and series, including arithmetic and geometric sequences and series, find the sum of finite and infinite geometric series.

• Apply the binomial theorem to expand powers of binomial expressions.

• Prove elementary mathematical statements that require the use of the Principle of Mathematical Induction.

1. Given the representation a graph 𝑓(𝑥), students will identify the 𝑎, ℎ and 𝑘 variables in the expression 𝑎𝑓(𝑥−ℎ)+𝑘 for a variety of transformations.

2. Students will be able to calculate the difference quotient for a variety of functions and simplify it.