Courses

Arithmetic and algebra; solving equations; introduction to trigonometry; introduction to exponential and logarithmic functions

Rational and Irrational Expressions and Equations

Trigonometric Functions

Geometric and Trigonometric Angles
Trigonometric Functions for Acute Angles
Trigonometric Functions for Arbitrary Angles
Solving Oblique Triangles – Law of Sines

Solving Oblique Triangles – Law of Cosines
Radian Measure of Angles
Graphs and Simplest Equations for Basic Trigonometric Functions
Trigonometric Identities and None-Simplest Equations

Exponential and Logarithmic Functions

Logarithms
Exponential and Logarithmic Functions
Compound Interest and Number e

Functions and their graphs; polynomial, rational, trigonometric, exponential, and logarithmic functions.

Functions and graphs

Polynomials and rational functions
Exponential and logarithmic functions
Trigonometric functions
Complex numbers, sequences, and the binomial theorem

Functions, limits, differentiation, and tangent lines, L’Hôpital’s Rule, Fundamental Theorem of Calculus and applications.

Limits

Derivatives

Instantaneous Rate of Change
Interpretations of the Derivative
Basic Differential Rules
The Product and Quotient Rules

The Chain Rule
Implicit Differentiation
Derivatives of Inverse Functions
L’Hôpital’s Rule

Graphs of Functions

Extreme Values
The Mean Value Theorem
Increasing and Decreasing Functions

Concavity and the Second Derivative
Curve Sketching

Applications of Derivatives

Related Rates
Optimization

Differentials

Integration

Antiderivatives and Indefinite Integration
The Definite Integral

Riemann Sums
The Fundamental Theorem of Calculus

A continuation of MAT 1475. Topics include Taylor polynomials, Mean Value Theorem, Taylor and Maclaurin series, tests of convergence, techniques of integration, improper integrals, areas, volumes and arc lengths.

Integration

Techniques of Antidifferentiation

Substitution
Integration by Parts
Trigonometric Integrals

Trigonometric Substitution
Partial Fraction Decomposition
Improper Integration

Sequences and Series

Taylor Polynomials
Sequences
Infinite Series
Integral and Comparison Tests

Ratio and Root Tests
Alternating Series and Absolute Convergence
Power Series
Taylor Series

Applications of Integration

Areas Between Two Curves
Volume by Cross-Sectional area; Disk and Washer Methods

The Shell Method
Arc Length and Surface Area

An introduction to solving ordinary differential equations. Applications to various problems are discussed.

First Order Equations

Applications of First Order Equations

Growth and Decay
Cooling and Mixing

Elementary Mechanics

Numerical Methods

Euler’s Method
The Improved Euler Method and Related Methods

The Runge-Kutta Method

Linear Second Order Equations

Homogeneous Linear Equations
Constant Coefficient Homogeneous Equations
Nonhomogeneous Linear Equations

The Method of Undetermined Coefficients
Reduction of Order
Variation of Parameters

Applcations of Linear Second Order Equations

Spring Problems

The RLC Circuit

Series Solutions of Linear Second Order Equations

Review of Power Series
Series Solutions Near an Ordinary Point

Regular Singular Points Euler Equations

Laplace Transforms

Introduction to the Laplace Transform
The Inverse Laplace Transform

Solution of Initial Value Problems
Convolutions

Topics include sample spaces and probabilities, discrete probability distributions (Binomial, Hypergeometric), expectation and variance, continuous probability distributions (Normal, Student, Chi-Square), confidence intervals, hypothesis testing, and correlation and regression. Spreadsheets are used throughout the semester.

The study of discrete and continuous probability distributions including the Binomial, Poisson, Hypergeometric, Exponential, Chi-Squared and Normal Distribution. Conditional distributions, covariance and correlation, confidence intervals, least square estimation, chi-square goodness of fit distribution and test for independence and randomness. Ends with an application to queuing.

This course introduces the foundations of discrete mathematics as they apply to computer science, focusing on providing a solid theoretical foundation for further work. Topics include functions, relations, sets, simple proof techniques, Boolean algebra, propositional logic, elementary number theory, writing, analyzing and testing algorithms.

This course continues the discussion of discrete mathematical structures and algorithms introduced in MAT 2440. Topics in the second course include predicate logic, recurrence relations, graphs, trees, digital logic, computational complexity and elementary computability.

An introductory course in Linear Algebra. Topics include vectors, vector spaces, systems of linear equations, linear transformations, properties of matrices, determinants, eigenvalues and eigenvectors.