Essential Engineering Mathematics

Contents

Introduction

Preliminaries

1.3 Complex Numbers 17

• 1.3.1  Imaginary Numbers 17
• 1.3.2  The Complex Number System and its Arithmetic
• 1.3.3  Solving Polynomial Equations Using Complex Numbers
• 1.3.4  Geometry of Complex Numbers

2. Vectors and Matrices

• 2.1  Vectors
• 2.2  Matrices and Determinants

• 2.2.1  Arithmetic of Matrices
• 2.2.2  Inverse Matrices and Determinants
• 2.2.3  The Cross Product

2.3 Systems of Linear Equations and Row Reduction

• 2.3.1  Systems of Linear Equations
• 2.3.2  Row Reduction
• 2.3.3  Finding the Inverse of a Matrix using Row Reduction

• 2.4  Bases
• 2.5  Eigenvalues and Eigenvectors

3. Functions and Limits

3.1 Functions

4. Calculus of One Variable Part 1: Differentiation

• 4.1  Derivatives
• 4.2  The Chain Rule
• 4.3  Some Standard Derivatives
• 4.4  Dierentiating Inverse Functions
• 4.5  Implicit Differentiation
• 4.6  Logarithmic Differentiation

1. 4.7  Higher Derivatives
2. 4.8  L’Hôpital’s Rule
3. 4.9  Taylor Series

5. Calculus of One Variable Part 2: Integration

• 5.1  Summing Series
• 5.2  Integrals
• 5.3  Antiderivatives
• 5.4  Integration by Substitution
• 5.5  Partial Fractions
• 5.6  Integration by Parts
• 5.7  Reduction Formulae
• 5.8  Improper Integrals

6. Calculus of Many Variables

• 6.1  Surfaces and Partial Derivatives
• 6.2  Scalar Fields
• 6.3  Vector Fields
• 6.4  Jacobians and the Chain Rule
• 6.5  Line Integrals
• 6.6  Surface and Volume Integrals

7. Ordinary Differential Equations

8. Complex Function Theory

• 8.1  Standard Complex Functions
• 8.2  The Cauchy-Riemann Equations
• 8.3 Complex Integrals