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Essential Engineering Mathematics

PDF Civil Engineering 5 years ago 0 77

Contents

Introduction

Preliminaries

  • 1.1  Number Systems: The Integers, Rationals and Reals
  • 1.2  Working with the Real Numbers
  • 1.2.1  Intervals
  • 1.2.2  Solving Inequalities
  • 1.2.3  Absolute Value
  • 1.2.4  Inequalities Involving Absolute Value

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

  • 3.1.1  Denition of a Function
  • 3.1.2  Piping Functions Together
  • 3.1.3  Inverse Functions
  • 3.2  Limits
  • 3.3  Continuity

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

  • 7.1  First Order Dierential Equations Solvable by Integrating Factor
  • 7.2  First Order Separable Differential Equations
  • 7.3 Second Order Linear Differential Equations with Constant Coefficients: The Homogeneous Case
  • 7.4  Second Order Linear Differential Equations with Constant Coefficients:
    The Inhomogeneous Case
  • 7.5  Initial Value Problems

8. Complex Function Theory

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

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