For students planning to pursue a course of study involving a concentration in mathematics. Topics include limits, continuity, the derivative, differentiation of algebraic, exponential, logarithmic, trigonometric and inverse trigonometric functions, applications of the derivative, antidifferentiation, and the definite integral. Numerical, graphical and algebraic approaches are used whenever possible. Credit cannot be earned for both MATH 153 and 180. Requires a graphing calculator, with the TI-84 Plus series recommended. Also requires access to an online homework management system.
Goals, Topics, and Objectives
- To study the nature and significance of calculus for students of science, technology, engineering, and mathematics disciplines.
- To demonstrate various applications of calculus to problems from the social sciences, physical sciences, and engineering.
- To present an exposition of calculus that incorporates graphical, numerical, and algebraic analysis, without undue emphasis on theoretical abstraction or routine mechanical manipulation.
- To use technology to illustrate calculus concepts and verify calculus solutions to application problems.
- To provide students with an exposure to the logical reasoning of mathematics.
- Introduction to Limits
- Determine limits of functions using numerical, algebraic and graphical methods.
- Determine infinite limits and limits at infinity.
- Determine continuity or discontinuity using the limit.
- Derivatives of Functions
- Find the derivative of functions using the limit definition of the derivative.
- Differentiate algebraic, logarithmic, exponential, trigonometric and inverse trigonometric functions using derivative rules.
- Differentiate composite functions using the chain rule.
- Find the derivative of a function defined implicitly.
- Applications of the Derivative
- Use the derivative to find instantaneous rates of change and related rates of change in application problems.
- Use the derivative to find properties of functions: maxima and minima, increasing, decreasing, concavity, points of inflection and use this information to sketch the graph of functions.
- Solve optimization problems using the derivative.
- Determine the linear approximation of functions using the derivative.
- Apply the Mean Value Theorem.
- Use the derivative to define and check the antiderivative function.
- Integration of Functions
- Approximate the area under a curve using the Riemann Sum with left endpoint, right endpoint, and midpoint.
- Find the antiderivatives (indefinite integrals) of algebraic, logarithmic, exponential, trigonometric and inverse trigonometric functions using integration rules.
- Approximate the definite integral using the Riemann Sum with left endpoint, right endpoint, and midpoint.
- Find the definite integral using the Fundamental Theorem of Calculus.
- Use the integral to find the average value of a function.
- Determine the integral of composite functions using the substitution rule.
- Applications of Integration
- Find the position and velocity functions from the acceleration function using integration.
- Find the net rate of change of a function using integration.
- Determine the area between two curves by integration with respect to x or y.
Assessment and Requirements
- All students will be required to complete a comprehensive final examination that assesses the learning of all course objectives.
- This final exam must be weighted in a manner so that this exam score is worth a minimum of fifteen percent (15%) of the final course grade. In selected semesters this final exam may be a common final exam administered to all sections of Math 180.
- All students will be required to complete online homework. This online homework must be weighted in such a manner so that it is worth between six percent (6%) and twelve percent (12%) of the final course grade.
- Additional assessment of student achievement may include assignments, quizzes, and exams.
- Application problems must not only be included on chapter exams but also on the final exam.
- Some exam problems should require the use of a graphing calculator.
- A graphing calculator is required of each student and the Mathematics Department recommends and uses the TI-84 Plus series.
- Access to an online homework management system is also required.
- Application problems must be covered in all mathematics courses. Every section in any course outline that includes application problems must be covered.
- Quantitative Literacy
- Category 3: Mathematics (College Algebra Track)
Credit for Prior College-Level Learning
A student may receive credit for MATH-180 by earning one of the minimum scores from the following exams:
- At least 50 on the CLEP Calculus exam, or
- At least 3 on the Advanced Placement (AP) Calculus AB test,
- At least 3 on the Advanced Placement (AP) Calculus BC test,
- At least 5 on the International Baccalaureate-Standard Level (IB-SL) Mathematics Exam (IB-SL-based credit awarded only after completion of MATH-183 with a grade of C or higher), or
- At least 5 on the International Baccalaureate-Higher Level (IB-HL) Mathematics Exam.