Math 112: Calculus 1

Catalog Information

Title

Calculus 1.

(Credit Hours:Lecture Hours:Lab Hours)

(4:5:0)

Offered

F, W, Sp, Su

Prerequisite

Math 110 and 111 or equivalent.

Description

Differential and integral calculus: limits; continuity; the derivative and applications; extrema; the definite integral; fundamental theorem of calculus; L'Hopital's rule.

Note

Honors also.

Desired Learning Outcomes

This course is designed for students majoring in the mathematical and physical sciences, engineering, or mathematics education and for students minoring in mathematics or mathematics education. Calculus is the foundation for most of the mathematics studied at the university level. The mastery of calculus requires well-developed skills, clear conceptual understanding, and the ability to model phenomena in a variety of settings. Calculus 1 develops the concepts of limit, derivative, and integral, and is fundamental for many fields of mathematics. This course contributes to all the expected learning outcomes of the Mathematics BS (see [1]).

Prerequisites

Students are expected to have completed a high school course in college algebra and trigonometry sometimes called pre-calculus or to take Math 110 and 111.

Minimal learning outcomes

Students should achieve mastery of the topics below. This means that they should know all relevant definitions, full statements of the major theorems, and examples of the various concepts. Further, students should be able to solve non-trivial problems related to these concepts, and prove simple theorems in analogy to proofs given by the instructor. Previous final exams (see [2]) give specific examples of the level of understanding that is expected.

1. Limits and derivatives
   • The limit of a function
   • Laws for calculating limits
   • The definition of a limit
   • Continuity
   • The derivative as the slope of a tangent line
   • The derivative as a rate of change
2. Differentiation rules
   • Standard rules for derivatives including power, sum, product, and quotient rules
   • The chain rule
   • Derivatives of trigonometric functions
   • Derivatives of exponential and logarithmic functions
     
3. Applications of differentiation
   • Exponential growth and decay
   • Related rates problems
   • Linear approximations
   • Maximum and minimum values
   • The Mean Value Theorem
   • L’Hospital’s Rule
   • Curve sketching
4. Integrals
   • Indefinite integrals
   • Basic formulas for antiderivatives that come from derivative rules
   • The substitution rule for integration
   • Definite integrals
   • Area under a curve
   • Fundamental Theorem of Calculus

Textbooks

Possible textbooks for this course include (but are not limited to):

Additional topics

These are at the instructor's discretion as time allows. Some suggested topics are hyperbolic functions, Newton’s method, and velocity and acceleration problems.

Courses for which this course is prerequisite

This course is required for Math 113, Math 290 (or concurrent enrollment), Math 313, and Math 362.