Elementary Engineering Mathematics

This page contains links to notes, equation sheets, and recommended exercises for topics in elementary engineering mathematics. The material covers the application of mathematics to introductory engineering problems. Topics include mechanical and electrical engineering applications using algebra and trigonometry, vectors, sinusoids and harmonic functions, systems of equations and matrices, simple derivatives and integrals, and simple linear differential equations.

The course material is intended to help students:

  1. Learn to apply mathematics in the solution of introductory engineering problems
  2. Learn how mathematics is used throughout their engineering curriculum
  3. Strengthen their basic mathematical skills

These course materials were developed based on EGR 101 Introductory Mathematics for Engineering Applications; a course taught at Wright State University. EGR 101 was developed under a Course, Curriculum and Laboratory Improvement (CCLI) grant from the National Science Foundation (NSF). In Phase 3 of this project entitled “A National Model for Engineering Mathematics Education,” similar courses were developed and taught in engineering programs at various universities.

Golfer’s Approach Shot to the Green


Applications of Two-Dimensional Vectors

Application of 2D Vectors in Statics, Mechanics of Materials, Elementary Dynamics

Applications of Harmonic and Exponential Functions

  1. Exponential and Natural Logarithm Functions
  2. Sine and Cosine Functions of Time
  3. Application of Sine, Cosine, and Exponential Functions in Control Systems
  4. Application of Sine and Cosine Functions in Electrical Engineering

Applications of Derivatives

  1. Introduction to Derivative of a Function
  2. Derivatives of Functions as Functions
  3. Application of Derivatives in Statics, Mechanics of Materials
  4. Application of Derivatives in Electrical Engineering

Applications of Integrals

  1. Introduction to Integrals of Functions
  2. Integrals of Functions as Functions
  3. Application of Integration in Elementary Dynamics
  4. Application of Integration in Statics, Mechanics of Materials
  5. Application of Integration in Electrical Engineering

Applications of Differential Equations

Introduction to Differential Equations in Mechanical Engineering

Equation Sheets

  1. Algebra and Trigonometry
  2. Vectors and Complex Numbers
  3. Systems of Equations and Exponential, Sine, and Cosine Functions
  4. Spring-Mass-Damper Systems
  5. Electric Circuits
  6. Derivatives and Differentiation
  7. Integrals and Integration
  8. Differential Equations for Spring-Mass-Damper Systems


  1. Algebra – Lines          (Answers)
  2. Algebra – Quadratic Equations          (Answers)
  3. Geometry/Trigonometry          (Answers)
  4. Two-Dimensional Vectors          (Answers)
  5. Complex Numbers          (Answers)
  6. Two-Dimensional Vectors & Simultaneous Equations          (Answers)
  7. Exponential, Natural Log, and Trigonometric Functions          (Answers)
  8. Derivatives #1          (Answers)
  9. Derivatives #2          (Answers)
  10. Integrals          (Answers)