Course Syllabus

Course Description:

This course explores the basic concepts of analytic geometry, limits (including indeterminate forms), derivatives, and integrals. The topics covered will include graphs, derivatives, and integrals of algebraic, trigonometric, exponential, logarithmic, and hyperbolic functions. Standard proofs will be covered, such as delta-epsilon proofs and proofs of some theorems. Applications will be covered, including those involving rectilinear motion, differentials, related rates, graphing, and optimization.

Student Learning Outcomes:

Upon successful completion of the course, students will be able to:

• compute limits of algebraic, exponential, logarithmic, and trigonometric functions.
• calculate derivatives of algebraic, exponential, logarithmic, and trigonometric functions.
• evaluate integrals of algebraic, exponential, logarithmic, and trigonometric functions.
• apply derivatives and integrals to solve physics, economic, geometric, and/or other problems.
• prove basic theorems related to limits, continuity, and differentiability, including delta-epsilon proofs.

Course Content:

• Real numbers, coordinate systems in two dimensions, lines, functions
• Introduction to limits, definition of limits, theorems on limits, one-sided limits, computation of limits using numerical, graphical, and algebraic approaches, delta-epsilon proofs; continuity and differentiability of functions, determining if a function is continuous at a real number; limits at infinity, asymptotes; introduction to derivatives and the limit definition of the derivative at a real number and as a function
• Use of differentiation theorems, derivatives of algebraic, trigonometric, inverse trigonometric, exponential, logarithmic, and hyperbolic functions, the chain rule, implicit differentiation, differentiation of inverse functions, higher order derivatives, use derivatives for applications including equation of tangent lines and related rates, and differentials
• Local and absolute extrema of functions; Rolle's theorem and the Mean Value Theorem; the first derivative test, the second derivative test, concavity; graphing functions using first and second derivatives, concavity, and asymptotes; applications of extrema including optimization, antiderivatives, indeterminate forms, and L'Hopital's rule
• Sigma notation, area, evaluating the definite integral as a limit, properties of the integral, the Fundamental Theorem of Calculus including computing integrals, and integration by substitution

Textbook:

Great news: your textbook for this class is available for free online!
Calculus, Volume 1 from OpenStax, ISBN 1-947172-13-1

You have several options to obtain this book:

• View online (Links to an external site.) (Links to an external site.)
• Download a PDF (Links to an external site.) (Links to an external site.)

You can use whichever formats you want. Web view is recommended -- the responsive design works seamlessly on any device.

Important Notes:

• All first week assignments need to be completed and submitted by the due date to avoid possibly being dropped from the class. These are important "sign up on supporting websites" assignments that will allow you to complete the course, and are vital to your success
• Academic integrity is important, and if you are caught cheating on any assessment you will have the grade for that assessment automatically be a zero.
• HOWEVER--- I emphasize that we ALL need to learn the material.  Classwork, Homework, extra work is encouraged to be done with others, as your peers can often explain things to you better than I can.  So the ONLY time I will not want you discussing presented problems will be during formal tests and quizzes.  AT ALL OTHER TIMES HELP EACH OTHER!!!