# Survey of Calculus II

## General

MATH

212

### 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.

3

3

No

No

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: