Common Course Outline

Catalog Description

Course Description

This course is a second semester calculus course including topics of: inverse functions (exponential, logarithmic, trigonometric, etc.), techniques of integration, applications including arc length, surface area, force, and centers of mass, differential equations, parametric and polar forms, sequences and series including Taylor series.

Date Last Revised (Month, year)

February, 2026

Outline of Major Content Areas

1. Calculus of inverse functions
2. Calculus of exponential and logarithmic functions
3. Calculus of inverse trigonometric functions
4. Calculus of hyperbolic functions and their inverses
5. Integration Techniques
6. Applications of integration including arc length, surface area of rotation, hydrostatic force, and centroids of mass, expected values, and variances.
7. Calculus of Parametric and Polar curves
8. Infinite sequences and series, convergence and divergence, including Taylor series.
9. Separable and Linear First Order Differential Equations, Logistic and Natural growth models.
10. Numerical Approximation Methods

Learning Outcomes (General)

The student will be able to:

1. Differentiate and integrate various functions and their inverses including trigonometric, exponential, logarithmic and hyperbolic.
2. Recognize and integrate functions using u-substitution, integration by parts, trigonometric forms, trigonometric substitution, partial fractions with linear, quadratic and repeated factors, and other miscellaneous function substitutions.
3. Apply L’Hopitals rule to evaluate indeterminate forms of limits.
4. Evaluate convergence and divergence of improper integrals.
5. Solve differential equations including separation of variables and first order linear differential equations with applications including position-velocity-acceleration, mixing, growth and decay, logistic growth.
6. Recognize sequence and series patterns and apply tests for convergence and divergence.
7. Derive and use Taylor and McLaurin series for differentiable functions.
8. Use parametric forms and polar forms of graphing as compared to Cartesian with respect to symmetries, area, tangent lines, arc length, and surface area.
9. Calculate numerical estimates of calculus operations using tools such as Newton’s Method, Midpoint Rule, Trapezoid Rule, and Simpson’s Rule.

Learning Outcomes (MnTC)

Goal 4/Mathematics/Logical Reasoning

The student will be able to:

1. Illustrate historical and contemporary applications of mathematics/logical systems.
2. Clearly express mathematical/logical ideas in writing.
3. Explain what constitutes a valid mathematical/logical argument (proof).
4. Apply higher-order problem solving and/or modeling strategies.

Methods for Evaluation of Student Learning

Methods may include but are not limited to:

• Quizzes
• Homework
• Projects
• Papers
• Group work
• Examinations

RCTC Core Outcome(s)

This course contributes to meeting the following RCTC Core Outcome(s):

Critical Thinking

Students will think systematically and explore information thoroughly before accepting or formulating a position or conclusion.

Special Information (if any)

Graphing Calculator required. (Texas Instruments Recommended)