# Math Topics

Here you can find a directory of the content developed by the Engineering Math Resource Center for the various engineering mathematics topics you will learn in your math courses. Reference these to brush-up on topics that you have spent time learning and practicing or to give you some specific context into how these topics will be used in future engineering courses. Each of these pages will first give you a general overview of how that specific mathematical topic is used in engineering before providing a description of the topic in mathematical terms. Specific applications of the topic will then be given for each of the majors in engineering offered at USU. Finally, external resources will be provided so that additional practice and understanding can be found easily for the interested student.

## Mathematics Foundations

- Reading and Writing Mathematics
- Integers
- Fractions
- Decimals
- Properties of Real Numbers
- Properties of Complex Numbers

## Algebra

- Functions
- Domain and Range
- The Rectangular Coordinate System and Graphs
- Equations and Inequalities
- Solving Linear Equations
- Systems of Linear Equations
- Polynomials
- Factoring
- Rational Expressions
- Roots and Radicals
- Quadratic Equations
- Exponential and Logarithmic Functions
- Conics
- Sequences
- Series
- Binomial Theorem
- Absolute Value
- Inverses
- Fitting Models to Data
- Partial Fraction Decomposition

## Trigonometry

- Angles
- Right Triangles
- The Unit Circle
- Trigonometric Functions
- Inverse Trigonometric Functions
- Trigonometric Identities
- The Law of Sines
- The Law of Cosines
- Polar Coordinates
- Polar Form of Complex Numbers
- Parametric Equations
- Vectors
- Analytic Geometry
- Rotations of Axes

## Calculus I

- Limits
- The Limit Laws
- Continuity
- Derivatives
- Differentiation Rules
- Derivatives of Trigonometric Functions
- The Chain Rule
- Derivatives of Inverse Functions
- Implicit Differentiation
- Derivatives of Exponential and Logarithmic Functions
- Linear Approximations
- Differentials
- Maxima and Minima
- The Mean Value Theorem
- Asymptotes
- L’Hopital’s Rule
- Newton’s Method
- Antiderivatives
- Integration
- Definite Integrals
- The Fundamental Theorem of Calculus
- Integration Rules
- Substitution
- Integrals Involving Exponential and Logarithmic Functions
- Integrals Resulting in Inverse Trigonometric Functions

## Calculus II

- Integration by Parts
- Trigonometric Integrals
- The Divergence and Integral Tests for Sequences and Series
- Comparison Tests for Sequences and Series
- Ratio and Root Tests for Sequences and Series
- Properties of Power Series
- Taylor and Maclaurin Series
- Calculus of Parametric Curves

## Calculus III (Multivariable Calculus)

- Vectors in 2D
- Vectors in 3D
- Vector Products
- Lines and Planes in Space
- Cylindrical and Spherical Coordinates
- Vector-Valued Functions and Space Curves
- Calculus of Vector-Valued Functions
- Functions of Several Variables
- Limits and Continuity
- Partial Derivatives
- Tangent Planes
- Linear Approximations
- The Chain Rule
- Directional Derivatives and the Gradient
- Maxima and Minima
- Lagrange Multipliers
- Double Integrals
- Triple Integrals
- Change of Variables in Multiple Integrals
- Vector Fields
- Line Integrals
- Green’s Theorem
- Divergence
- Curl
- Surface Integrals
- Stokes’ Theorem
- The Divergence Theorem
- Scalar Triple Product

## Linear Algebra

- Systems of Linear Equations
- Matrix Properties
- Gauss Elimination
- Matrix Inverses

## Differential Equations

- First-Order Linear Equations
- Second-Order Linear Equations
- Nonhomogeneous Linear Equations