Calculus I

Welcome to Students

Who is the target audience and what will they learn?
This college-level calculus course serves students with a strong background in mathematics or science. Topics include limits and graphs of real-valued functions, continuity, differentiation, linear approximation, optimization, related rates, Riemann sums, area functions and their connection to derivatives, integration techniques, and applications of definite integrals.
Should I be afraid if most of those terms sound like Greek to me?
Your instructor doesn't expect you to know all the terminology before the semester even begins. You'll start on familiar territory and gradually work your way up to the new concepts.
How can I determine whether I'm meeting the desired learning outcomes?
As the semester proceeds, periodically refer to the checklist below, asking yourself whether you can:
2.1T Recognize and sketch tangent lines in various situations
2.1V Estimate instantaneous velocity from average velocity by selecting appropriate points
2.2L Estimate limits and one-sided limits graphically and numerically, and also recognize when they do not exist
2.3L Evaluate limits and one-sided limits algebraically
2.3C Determine at which points on its graph a function is discontinous and describe the type of discontinuity
2.4IVT Apply the Intermediate Value Theorem to show where a root of an equation exists
2.5L Recognize and evaluate limits of infinity or negative infinity graphically, algebraically, and numerically
2.5AS Use limits to determine where a function has a vertical or horizontal asymptote
2.6DI Interpret the derivative as the slope of the tangent line and as the instantaneous rate of change
2.6DC Calculate the derivative of simple algebraic functions from the limit definition
2.7-8R Recognize f, f', f'' from given graphs
2.7-8SF Use the graph of f to sketch a graph of f'
2.7-8D Determine where a function is differentiable graphically and algebraically, and describe why it is not differentiable
2.7-8SF Use the graph of f' to sketch a graph of f
Classes of functions you should be able to analyze: algebraic functions, circular and inverse circular functions, exponential and logarithmic functions, and parametric functions
3.1-7B Memorize derivatives of the basic functions in each class
3.1-7DR Differentiate sum, difference, product, quotient, and composition of functions from these classes
3.1-7LD Recognize and apply logarithmic differentiation when appropriate
3.1-7ID Recognize and apply implicit differentiation when appropriate
3.1-7T Determine where a curve has a horizontal or vertical tangent (for explicit or implicit functions, and parametric curves)
3.1-7T Calculate the equation of the tangent line at a point on a parametric curve or an implicit function
3.8M Derive velocity and acceleration from the position function for an object in motion
3.8O Optional standards for other applications: chemistry, biology, economics, etc.
3.9L Calculate the tangent line approximation for a function and determine whether it is an over- or an underapproximation
3.9D Use differentials to approximate change and error
4.1RR Model related rates as a mathematical equation and solve the problem using calculus
4.2MM Use calculus to determine the local and absolute extrema of a function on a given interval
4.3MVT Understand the consequences of the Mean Value Theorem graphically and identify points on the graph whose existence satisfies the conclusion of the MVT
4.3G Use the functions f' and f'' to answer questions about the graph of f
4.5IF Recognize all indeterminate forms: 0/0, inf/inf, 0*inf, inf-inf, 1^inf, inf^0, 0^0
4.5LH Evaluate limits of the form 0/0 and inf/inf
4.5LO Evaluate limits of the difference, product, and exponential indeterminate forms
4.6O Model a quantity to be optimized as a function of one variable and solve the optimization problem
4.7NA Apply Newton's Method to approximate zeros to a given degree of accuracy
4.7NF Recognize when Newton's Method fails to converge to the desired zero
4.8M Memorize the antiderivatives of basic functions
4.8C Calculate families of antiderivatives and solutions of initial value problems
5.1RS Express areas as limits of Riemann sums, including the use of sigma notation
5.2DI Express and evaluate a definite integral as the limit of a Riemann sum
5.2RS Compute left, right, and midpoint approximations of definite integrals and state (if possible) whether the approximations are over- or underestimates
5.2P Use the properties of definite integrals to compute new integrals from old integrals
5.3ET Evaluate definite integrals using the Evaluation Theorem
5.3EI Recognize and evaluate indefinite integrals
5.3M Set up and evaluate integrals to find displacement and total distance traveled from a velocity function
5.4AF Sketch the graph of an "area under f" function from a graph of f
5.4FTC State both parts of the FTC and explain their meaning and importance
5.4D Use FTC (and chain rule) to find the derivative of area functions
6.1A Set up integrals (with respect to x and y) representing the area between two curves
6.1P Set up integrals representing the area enclosed by parametric curves
(Codes refer to the Stewart textbook's numbering of sections, as of the 4th edition. Standards with a dark blue background are considered advanced/optional.)
How can I estimate my chances of success in this course?
Have a look at the thread Prerequisites for Calculus, which outlines the best predictors of success in the first semester of university calculus sequence.

Practice Materials