Survey of Calculus II

General

Prefix

MATH

Course Number

212

Course Level

Undergraduate

Department/Unit(s)

College/School

College of Science and Engineering

Description

Differentiation and integration of trigonometric functions, integration techniques and applications, three-dimensional analytic geometry, multivariable calculus, differential equations.

Prerequisites

Credits

Min

3

Max

3

Repeatable

No

Goals and Diversity

MN Goal Course

No

Cultural Diversity

No

Learning Outcomes

Outcome

Evaluate definite integrals and antiderivatives by using a variety of techniques of integration including substitution, integration by parts, and partial fractions.

Outcome

Differentiate and integrate functions that are the product, quotient, and composition of trigonometric and inverse trigonometric functions with other functions.

Outcome

Approximate solutions using numerical techniques including the Newton-Raphson Method, Euler's Method, and numerical integration techniques.

Outcome

Set up and solve applications of the definite integral including finding volumes of solids and calculating work and hydrostatic force.

Outcome

Calculate partial derivatives of functions of several variables and interpret the results.

Outcome

Find extrema of functions of several variables using the Second Derivative Test, the Extreme Value Theorem (extended to functions of two variables), and Lagrange Multipliers.

Outcome

Set up and evaluate double integrals to find the volume under a surface and above the x-y plane.

Outcome

Derive Taylor Polynomials and Maclaurin Series for variations of familiar functions.

Outcome

Sketch solutions to the differential equation for various initial values (given a slope field).

Outcome

Solve first-order, separable differential equations with and without initial values.

Outcome

Sketch a qualitative solution to a differential equation without solving that equation explicitly.

Outcome

Determine whether a differential is exact and if so find the function of two variables that generates such a differential.

Dependencies

Courses

MATH212 is a prerequisite for:

Programs

MATH212 is a completion requirement for: