This page contains some links to pages with material relevant to the
introductory calculus course.
You will also find links to *Mathematica* notebooks which you
can download and modify for further exploration.
Some of the links on this page are to Portable Document Format (PDF)
files.
A PDF viewer such as the free Acroread application are available
here.

- Section 01 current semester syllabus
- A preview of two important themes which will be explored in first semester calculus.
- An introduction to the concept of a limit.
- Some properties of limits and theorems for evaluating them.
- Graphs of the inverse trigonometric functions.
- Continuity and the bisection method.
- Limits involving infinity and asymptotes.
- Loss-of-significance errors and the computation of limits.
- Finding the slope of the tangent line to the graph of a function.
- An introduction to the derivative of a function of a single variable.
- Some rules for the computation of derivatives, also the notation for and interpretation of higher order derivatives.
- The product and quotient rules for derivatives.
- The chain rule for derivatives and differentiating inverse functions.
- The derivatives of the trigonometric functions.
- The derivatives of the exponential and logarithmic functions.
- Implicit differentiation and the derivatives of the inverse trigonometric functions.
- An introduction to the Mean Value Theorem.
- An introduction to linear approximation and Newton's Method.
- l'Hopital's Rule for limits of indeterminate forms.
- Maximum and minimum values of a function.
- Increasing and decreasing properties of a function.
- Concavity and the Second Derivative Test.
- An overview of curve sketching. Two example problems for testing your skills at graphing are also available.
- Employing the tools of calculus on problems involving optimization.
- Using Implicit differentiation to solve related rates problems.
- An introduction to antiderivatives and antidifferentiation.
- Sums and sigma notation.
- Area under a curve and Riemann sums.
- The definite integral and its properties.
- The Fundamental Theorem of Calculus, parts I and II.
- Using the technique of integration by substitution to evaluate indefinite and definite integrals.
- An introduction to numerical integration featuring the Midpoint and Trapezoidal Rules.
- A rigorous treatment of the natural logarithm function and the exponential function.
- Modeling with differential equations.
- Separable differential equations and the logistic equation.
- A review sheet of exercises for the final examination. Solutions are also available.