Course Syllabus

Course Description:

Our course adheres to the scope and sequence of most general calculus courses nationwide. With this objective in mind, the content has been developed and arranged to provide a logical progression from fundamental to more advanced concepts, building upon what you all have already learned and emphasizing connections between topics and between theory and applications. The list below provides the three big ideas around which the course is built. The goal of each module is to enable you not just to recognize concepts, but work with them in ways that will be useful in later courses and future careers.  The hope is that your mastery of and understanding of the big ideas will help you retain and transfer the knowledge and skills you acquire for years to come.

This course will cover the following big three ideas: BIG IDEA 1: CHANGE Using derivatives to describe rates of change of one variable with respect to another or using definite integrals to describe the net change in one variable over an interval of another allows students to understand change in a variety of contexts. It is critical that students grasp the relationship between integration and differentiation as expressed in the Fundamental Theorem of Calculus—a central idea in AP Calculus. Upon successful completion of the course, students will be able to: calculate derivatives of polynomial, radical, rational, exponential, logarithmic, and trigonometric functions. evaluate integrals of algebraic, exponential, logarithmic, and trigonometric functions. BIG IDEA 2: LIMITS  Beginning with a discrete model and then considering the consequences of a limiting case allows us to model real-world behavior and to discover and understand important ideas, definitions, formulas, and theorems in calculus: for example, continuity, differentiation, integration, and series bc only. Upon successful completion of the course, students will be able to: compute limits of polynomial, radical, rational, exponential, logarithmic, and trigonometric functions algebraically and graphically. BIG IDEA 3: ANALYSIS OF FUNCTIONS Calculus allows us to analyze the behaviors of functions by relating limits to differentiation, integration, and infinite series and relating each of these concepts to the others. Upon successful completion of the course, students will be able to: apply derivatives and integrals to solve physics, economic, geometric, and/or other problems. analyze and interpret the behavior of functions

Course Content:

Throughout the textbook, you will find examples and exercises that present classical ideas and techniques as well as modern applications and methods. Derivations and explanations strive for a balance of clarity and rigor. Motivational applications cover important topics in probability, biology, ecology, business, and economics, as well as areas of physics, chemistry, engineering, and computer science. Projects in each chapter give you opportunities to explore interesting sidelights in pure and applied mathematics, from determining a safe distance between the grandstand and the track at a Formula One racetrack, to calculating the center of mass of the Grand Canyon Skywalk or the terminal speed of a skydiver. Opening Applications pose problems that are solved later in the chapter, using the ideas covered in that chapter. Problems include the hydraulic force against the Hoover Dam, and the comparison of relative intensity of two earthquakes.  Definitions, Rules, and Theorems are highlighted throughout the text, including over 60 Proofs of theorems.

• 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

Feedback

We will have a few types of assignments that will anchor the daily practice of what you have learned and we will have check-ins as well as overarching assessments  by each "chapter" or "module."  

Digital and Paper-Based Assignments (25%):

We will rely on Khan Academy, Desmos, and DeltaMath for some extending practice digitally, but we also do some assignments using pencil and paper.  All assignments not embedded within Canvas and are not an assessment will fall in this category. 

Canvas Problem Sets (25%):

These problem sets are a bit longer and more closely follow all the problem types shown in the text and videos.  They are intended to provide comprehensive exposure to all the relevant information and give you a look at the variety of ways we will engage with the mathematics on a particular topic.  

Assessments and Check-ins (50%):

This is one way we will check for understanding of your learning.   Each module will have several different types of assessments that cover all the topics within the module.  Some of these will be embedded in Canvas and look similar to the assignments you have been completing, while others may be paper-based or occur on DeltaMath as well as Khan Academy.  Check-ins will be as a group as well as an individual.  It may be a virtual meeting where I listen and watch you all work together on a set of problems or it might be one-on-one check-ins.  In whatever form it may occur, these will be ways to check in more deeply about the content and your learning.

Textbook:

The 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 (highly recommend and you can save your highlights and notes)
• Download a PDF

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

Volume 1 [Students working at a faster pace or continuing on will extend their work into Volume 2]

Important Links

• How to be Successful in this Course

• Getting Started with Canvas

• Canvas Quick Links

• Online Learning Resources

Important Notes:

• Academic dishonesty and plagiarism will result in a one-on-one conversation with Nooha and yourself and may result in a failing grade on the assignment. Using someone else's ideas or phrasing and representing those ideas or phrasing as our own, either on purpose or through carelessness, is a serious offense known as plagiarism. "Ideas or phrasing" includes written or spoken material, from whole papers and paragraphs to sentences, and, indeed, phrases but it also includes statistics, worked problems, graphs/images, etc.  
• Work will be a mixture of online assignments delivered within Canvas, as well as digital and paper-based problems that will need to be completed outside of the Canvas environment.