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## MATH 211 *Advanced Calculus 1 for Electrical and Computer Engineers*

# Calendar Description

# Prerequisites, Co-requisites, and Post-requisites

# Prerequisite Knowledge

# Purpose

*Fourier series. Ordinary differential equations. Laplace transform.
Applications to linear electrical systems.*

A proposed wording would be:

*Ordinary differential equations,
the Laplace transform,
Fourier series, and
partial-differential equations
applied to electrical and computer engineering
with emphasis on 1st- and 2nd-order linear systems,
oscillations, resonance, and the heat and Laplace equations.
The laboratories use numeric and symbolic computation techniques applied
to these problems.*

The prerequisites to MATH 211 include MATH 119 *Calculus 2 for Engineering*, ECE 140 *Linear Circuits*, and ECE 150 *Fundamentals of Programming*.

The co-requisite to MATH 211 is MATH 115 *Linear Algebra*.

The following courses have MATH 211 (or ECE 342/207 or MATH 213) as a prerequisite:

- MATH 212
- ECE 207
*Signals and Systems* - ECE 316
*Probability Theory and Random Processes* - ECE 318
*Communication Systems* - ECE 380
*Analog Control Systems* - ECE 413
*Digital Signal Processing* - ECE 414
*Wireless Communication* - ECE 418
*Communication Networks* - ECE 443
*Circuit Analysis and Filter Design*

As MATH 211 is tightly associated with ECE 342/207, I have included courses which explicitly call for ECE 342 as prerequisite.

- Basic complex arithmetic including the roots of quadratic polynomials.
- Euler's formula
*e*= cos(^{jt}*t*) +*j*sin(*t*). - Integration and differentiation of polynomial, rational polynomial, exponential, logarithmic, and trigonometric functions.
- Integration by parts and by substitution.
- Polynomial factoring.
- Polynomial division.
- Partial fraction decomposition.
- Proper and improper integration.
- Taylor series.
- RLC circuits.
- Structured programming: repetition and conditional statements, and functions (for the laboratories).

Without a 1st-year course in linear algebra, one concept which must be taught is that of linearity—not that this is difficult; however, some instructors may expect students to know this from first year.

When the ECE 140 *Linear Circuits* description is complete,
we should consider additional prerequisite knowledge.

This course will introduce students to ordinary differential equations, initial-value problems, their solutions through the use of Laplace transforms, the Fourier series representation of periodic functions and how Fourier series naturally interact with the Laplace transform, and an introduction to partial differential equations.