The following table lists the minimum set of topics to be included in this course. The number of lectures listed for each chapter is only a suggestion and will vary across instructors and semesters.
There are typically 42-43 lecture days in a semester, so lecture periods are available for exams.
|1.1 – 1.6||Limits and Continuity||10|
|2.1 – 2.8||Derivatives||8|
|3.1-3.5, 3.7||Applications of Derivatives||8|
|4.1 – 4.5||Integrals||8|
|5.1 – 5.5||Log and Exp||6|
OPTIONAL TOPICS (time permitting)
- The epsilon/delta definition of limits from early Ch 1
- Section 3.6 on Newton’s Method of approximation
- Section 5.6 on Inverse Trig Functions
- Section 5.7 on Hyperbolic Functions
- Section 6.4 on Integration with Tables or CAS
- Section 7.7 on Differential Equations
- Other outside topics, readings, videos, or materials the Instructor deems relevant
If all course instructors in a given semester cover a particular topic, they may choose to include that topic in the common final exam.
By the end of this course, students should be able to:
- Understand the fundamental concepts of calculus, including limits, continuity, and the definition of derivatives.
- Compute limits algebraically and graphically to evaluate indeterminate forms and understand the behavior of functions at specific points.
- Differentiate algebraic, trigonometric, exponential, and logarithmic functions using various differentiation rules.
- Apply the chain rule, product rule, and quotient rule to find derivatives of composite functions and functions involving products and quotients.
- Use derivatives to analyze the behavior of functions, including identifying critical points, extrema, and points of inflection.
- Apply the first derivative test and the second derivative test to determine the intervals of increase, decrease, and concavity of functions.
- Solve optimization problems using derivatives to find maximum and minimum values of functions.
- Understand the concept of antiderivatives and find them for simple functions and apply the power rule and integration by substitution.
- Calculate definite integrals using the concept of Riemann sums and interpret the integral as the area under a curve.
- Apply the fundamental theorem of calculus to evaluate definite integrals and compute areas between curves.
- Use integration to find the total change, average value, and displacement of a function over a specified interval.
- Apply the concept of integration to solve real-world problems, such as problems in physics, engineering, and economics.
- Utilize computational tools and software (e.g., MATLAB, Python) to perform calculus calculations and visualize functions and their derivatives.
- Understand the application of calculus in various fields and appreciate its significance in modeling and analyzing real-world phenomena.