MTH 252 Integral Calculus

Lecture Hours: 5
Credits: 5

Covers the development of definite and indefinite integrals, the fundamental theorem of calculus, applications of integrals, constructing functions from their rates of change, and techniques of integration. Introduces differential equations.

Prerequisite: Placement into WR 115 (or higher), or completion of WR 090 (or higher); and completion of MTH 251 (or higher) or equivalent course as determined by the instructor; or consent of instructor. (All prerequisite courses must be completed with a grade of C or better.)
Student Learning Outcomes:

Create mathematical models of abstract and real-world situations using anti-derivative functions.
Use inductive reasoning to develop mathematical conjectures involving anti-derivative function models. Use deductive reasoning to verify and apply mathematical arguments involving these models.
Use mathematical problem-solving techniques involving integrals and anti-derivative functions, including the use of graphical, symbolic, narrative and tabular representations.
Make mathematical connections and solve problems from other disciplines involving integrals and anti-derivative functions.
Use oral and written skills to individually and collaboratively communicate about integrals and anti-derivative function models.
Use appropriate technology to enhance mathematical thinking and understanding, to solve mathematical problems involving integrals and anti-derivative functions and judge the reasonableness of results.

Statewide General Education Outcomes:

Use appropriate mathematics to solve problems.
Recognize which mathematical concepts are applicable to a scenario, apply appropriate mathematics and technology in its analysis, and then accurately interpret, validate, and communicate the results.

Content Outline

Constructing Anti-Derivatives from Their Rates of Change
- The Definite Integral
  - Riemann Sums
  - Definition of Definite Integral
  - Definite integral as area
  - Definite integral as distance
  - Interpretations of the definite integral
  - Fundamental Theorem of Calculus
  - Properties of Integrals
- Constructing anti-derivatives
  - Graphically
  - Numerically
  - Analytically
Integration Techniques
- Integration by substitution
- Integration by parts
- Tables of integrals
- Numerical Approximations
- Approximation errors
- Improper integrals
Using the Definite Integral
- Average Value of a function
- Arc Length
- Applications from geometry
- Applications from a variety of disciplines
  - Physics
  - Economics
  - Biology
  - Statistics and probability
Differential Equations
- Recognizing differential equations
- Slope fields
- Euler’s Method
- Separation of variables
- Growth and decay