Syllabus
1701.235 Mathematics for Engineering Analysis I
 

CATALOG DESCRIPTION:

1701.235 Mathematics for Engineering Analysis I
(Prerequisite: 1701.131 Calculus II) 4 s.h.

This course gives a comprehensive introduction to functions of several variables, linear algebra, vector calculus and ordinary differential equations. It includes partial derivatives, double integrals, matrices, matrix operations, eigenvalues and eigenvectors, dot and cross products, divergence, curl, first order ordinary differential equations and numerical methods. A computer algebra system such as Mathematica is required.

OBJECTIVES:

Students will demonstrate the ability to:

i. evaluate the partial derivatives and gradient functions of several variables, evaluate double and triple integrals;

ii. compute the dot and cross product of vectors;

iii. compute divergence and curl of a vector field;

iv. perform matrix operations, evaluate determinant, eigenvalues and eigenvectors of a matrix;

v. solve separable and exact differential equations;

vi. use integrating factors to solve first order differential equations;

vii. use numerical methods to solve linear systems and differential equations.

CONTENTS:

Functions of Several Variables

Introduction to Functions of Several Variables

Partial Derivatives

Chain Rule

Directional Derivatives and Gradient

Double Integrals and Volume

Change of Variables, Polar Coordinates

Triple Integrals and Applications

Vector Differential Calculus, Grad, Div, Curl

Vector Algebra in 2-Space and 3-Space

Inner Product (Dot Product)

Vector Product (Cross Product)

Vector and Scalar Functions and Fields, Derivatives

Curves, Tangents, Arc Length

Velocity and Acceleration

Curvature and Torsion of a Curve

Gradient of a Scalar Field, Directional Derivative

Divergence of a Vector Field

Curl of Vector Field

Grad, Div, Curl in Curvilinear Coordinates.

Linear Algebra: Matrices, Vectors, Determinants

Basic Concepts

Matrix Addition, Scalar Multiplication

Matrix Multiplication

Linear Systems of Equations, Gauss Elimination

Linear Independence, Vector Space, Rank of a Matrix.

Linear Systems: General Properties of Solutions

Inverse of a Matrix

Determinants

Rank in Terms of Determinants, Cramer's Rule

Eigenvalues, Eigenvectors

Some Applications of Eigenvalue Problems

Properties of Eigenvectors, Diagonalization

Numerical Methods including Gauss Elimination, Iteration and Norms.

First-Order Differential Equations

Basic Concepts and Ideas

Separable Differential Equations

Modeling: Separable Equations

Reduction to Separable Form

Exact Differential Equations

Integrating Factors

Linear Differential Equations

Numerical Methods including Euler, Improved Euler and Runge-Kutta

TEXT:
Kreyszig, Erwin, Advanced Engineering Mathematics, 8th edition, John Wiley and Sons Inc., New York, 1999 and accompanying Mathematica manual.