Elementary Engineering Math

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.

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.

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

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Notes

Applications of Algebra

  1. Application of Lines in Elementary Dynamics
  2. Application of Lines in Statics, Mechanics of Materials, and Elementary Dynamics
  3. Application of Lines in Electric Circuits
  4. Application of Quadratic Equations in Elementary Dynamics
  5. Application of Quadratic Equations in Electric Circuits

Applications of Geometry and Trigonometry

  1. Geometry: Some Useful Concepts and Definitions
  2. Application of Trigonometric Functions in Mechanical Engineering: Part I
  3. Application of Trigonometric Functions in Mechanical Engineering: Part II
  4. Application of Geometry/Trigonometry in Elementary Dynamics

Applications of Two-Dimensional Vectors

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

Application of Complex Numbers

  1. Introduction to Complex Numbers
  2. Application of Complex Numbers in Electric Circuits

Applications of Systems of Equations and Matrices

  1. Application of Systems of Equations and Matrices in Statics
  2. Application of Systems of Equations and Matrices in Electrical Engineering

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

  1. 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/Differentiation
  7. Integrals/Integration
  8. Differential Equations for Spring-Mass-Damper Systems

Recommended Exercises

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