Math 125 is a coordinated course and a common final exam is offered at the end of each semester.
You can find past common finals here.

REQUIRED TEXTBOOK

Stewart, Essential Calculus (2nd ed.)

SECTION COVERAGE

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.

 Sections Topics Lectures 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 Total 40

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.

MEASURABLE OBJECTIVES

By the end of this course, students should be able to:

1. Understand the fundamental concepts of calculus, including limits, continuity, and the definition of derivatives.
2. Compute limits algebraically and graphically to evaluate indeterminate forms and understand the behavior of functions at specific points.
3. Differentiate algebraic, trigonometric, exponential, and logarithmic functions using various differentiation rules.
4. Apply the chain rule, product rule, and quotient rule to find derivatives of composite functions and functions involving products and quotients.
5. Use derivatives to analyze the behavior of functions, including identifying critical points, extrema, and points of inflection.
6. Apply the first derivative test and the second derivative test to determine the intervals of increase, decrease, and concavity of functions.
7. Solve optimization problems using derivatives to find maximum and minimum values of functions.
8. Understand the concept of antiderivatives and find them for simple functions and apply the power rule and integration by substitution.
9. Calculate definite integrals using the concept of Riemann sums and interpret the integral as the area under a curve.
10. Apply the fundamental theorem of calculus to evaluate definite integrals and compute areas between curves.
11. Use integration to find the total change, average value, and displacement of a function over a specified interval.
12. Apply the concept of integration to solve real-world problems, such as problems in physics, engineering, and economics.
13. Utilize computational tools and software (e.g., MATLAB, Python) to perform calculus calculations and visualize functions and their derivatives.
14. Understand the application of calculus in various fields and appreciate its significance in modeling and analyzing real-world phenomena.