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 a calculus course.)

🚩 Note: This course is TWO classes, you must remain enrolled in both to stay in the class.

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

• 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 141 with a grade of "C" or better, or equivalent 

This course is an introduction to university-level calculus requiring a strong background in algebra and trigonometry. The topics of study include analytic geometry, limits, differentiation and integration of algebraic and transcendental functions, and applications of derivatives and integrals. Emphasis is placed on calculus applications involving motion, optimization, graphing, and applications in the physical and life sciences. This course incorporates the use of technology. Analytical reading and problem solving are strongly emphasized in this course. This course is intended for students majoring in mathematics, computer science, physics, chemistry, engineering, or economics.

Students successfully completing this course will be able to:

• Evaluate various types of limits graphically, numerically, and algebraically, and analyze properties of functions applying limits including one-sided, two-sided, finite and infinite limits.

• Develop a rigorous epsilon-delta limit proof for simple polynomials.

• Recognize and evaluate the "limit" using the common limit theorems and properties.

• Analyze the behavior of algebraic and transcendental functions by applying common continuity theorems, and investigate the continuity of such functions at a point, on an open or closed interval.

• Calculate the derivative of a function using the limit definition.

• Calculate the slope and the equation of the tangent line of a function at a given point.

• Calculate derivatives using common differentiation theorems.

• Calculate the derivative of a function implicitly.

• Solve applications using related rates of change.

• Apply differentials to make linear approximations and analyze propagated errors.

• Apply derivatives to graph functions by calculating the critical points, the points of non-differentiability, the points of inflections, the vertical tangents, cusps or corners, and the extrema of a function.

• Calculate where a function is increasing, or decreasing, concave up or concave down by applying its first and second derivatives respectively, and apply the First and Second Derivative Tests to calculate and identify the function's relative extrema.

• Solve optimization problems using differentiation techniques.

• Recognize and apply Rolle's Theorem and the Mean-Value Theorem where appropriate.

• Apply Newton's method to find roots of functions.

• Analyze motion of a particle along a straight line.

• Calculate the anti-derivative of a wide class of functions, using substitution techniques when appropriate.

• Apply appropriate approximation techniques to find areas under a curve using summation notation.

• Calculate the definite integral using the limit of a Riemann Sum and the Fundamental Theorem of Calculus. Apply the Fundamental Theorem of Calculus to investigate a broad class of functions.

• Apply integration in a variety of application problems: including areas between curves, arclengths of a single variable function, and volumes.

• Estimate the value of a definite integral using standard numerical integration techniques which may include the Left-Endpoint Rule, the Right-Endpoint Rule, the Midpoint Rule, the Trapezoidal Rule and Simpson's Rule.

• Calculate derivatives of inverse trigonometric functions, and hyperbolic functions.

• Calculate integrals of hyperbolic functions and of functions whose anti-derivatives give inverse trigonometric functions.

1. Students will evaluate a definite integral with a non-polynomial algebraic integrand by using a u substitution with correct form and notation. 

2. Students demonstrate a knowledge of the connection between a derivative and an integral.