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: