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Oct 23, 2026
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MATH 1401 - Calculus II
Credits: 5
Catalog Description
A continuation of MATH 1400 , this is a transfer course intended for bachelor programs in technology, engineering, mathematics, or science, including natural, physical, and social sciences. Topics include the theory and techniques of integration, application problems involving integration, an introduction to differential equations, and infinite sequences and series, polar coordinates, and parametric curves.
Prerequisite(s) (must have a grade of C or better): MATH 1400 with a grade of C or better, or equivalent
Minnesota Transfer Curriculum (MnTC) Goal Area(s) fulfilled: Goal 04: Mathematical/Logical Reasoning
Additional fee to student: No
Learner Outcomes
- Integrate using integration by parts, miscellaneous substitutions, partial fractions, or tables of integrals.
- Approximate the value of a definite integral by using on each sub-interval the left-hand or right-hand endpoint, the mid-point rule, trapezoidal rule, or Simpson’s rule, and find the error in approximation when using each of these rules.
- Use a definite integral to find the area between graphs.
- Find the volume of a solid.
- Use integration to find the length of an arc.
- Find the moment of a system about the origin, the x-axis, or the y-axis.
- Find the total mass and center of mass of a system or lamina.
- Solve applications of integration such as surface area of a surface of revolution, work, fluid pressure, fluid force or the mean and median of a probability density function, as well as simple probabilities.
- Solve a separable differential equation.
- Solve an exponential equation.
- Solve a logarithmic equation.
- Solve a system of linear equations with row reduction.
- State the definition of an infinite sequence.
- Find a particular term or sequence of terms for a particular infinite sequence.
- State the definition of an arithmetic sequence and give examples thereof.
- State the definition of a geometric sequence and give examples thereof.
- Work back and forth readily between expanded and closed forms of summation notation.
- Apply the concepts of experiment, outcome, and sample space to a given model.
- State the definition of probability of an event for a given sample space and apply such to simple problems.
- Differentiate and integrate a power series.
- Find a Taylor polynomial of a function at a real number and estimate the error in using that polynomial as an approximation of the function.
- Use a binomial series to approximate a function.
- Find the slope of a tangent line to a curve given by a set of parametric equations.
- Find the arc length of a curve given by a set of parametric equations.
- Use appropriate technology (graphing calculator, computer algebra system, etc.) where applicable in the above outcomes and interpret the results.
Major Areas of Course Content
- Techniques of integration
- Numerical integration
- Improper integrals
- Applications of the definite integral including area, volume, arc length, and centroids
- Solving separable differential equations
- Applications of separable differential equations
- Slopes, areas, and lengths in polar coordinates
- Sequences
- Series and power series
- Taylor polynomials
- Approximations of functions
- Slopes, areas, and lengths of parametric curves
Credit for Prior Learning Options
Course-Specific Exam
Credit for Prior Learning Option Procedure(s)
- The student should contact an instructor currently teaching or scheduled to teach the desired course.
- The instructor will provide and schedule an exam date.
- The student is to bring the Credit by Exam form to the scheduled exam.
- The faculty member will notify the student and Records Office of the results.
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