Essential Engineering Mathematics
Publisher: Bookboon.com
Published: 2013
ISBN-13: 9788776817350
Table of contents: title: Content; title: 0. Introduction; title: 1. Preliminaries; title: 1.1 Number Systems: The Integers, Rationals and Reals; title: 1.2 Working with the Real Numbers; title: 1.2.1 Intervals; title: 1.2.2 Solving Inequalities; title: 1.2.3 Absolute Value; title: 1.2.4 Inequalities Involving Absolute Value; title: 1.3 Complex Numbers; title: 1.3.1 Imaginary Numbers; title: 1.3.2 The Complex Number System and its Arithmetic; title: 1.3.3 Solving Polynomial Equations Using Complex Numbers; title: 1.3.4 Geometry of Complex Numbers; title: 2. Vectors and Matrices; title: 2.1 Vectors; title: 2.2 Matrices and Determinants; title: 2.2.1 Arithmetic of Matrices; title: 2.2.2 Inverse Matrices and Determinants; title: 2.2.3 The Cross Product; title: 2.3 Systems of Linear Equations and Row Reduction; title: 2.3.1 Systems of Linear Equations; title: 2.3.2 Row Reduction; title: 2.3.3 Finding the Inverse of a Matrix using Row Reduction; title: 2.4 Bases; title: 2.5 Eigenvalues and Eigenvectors; title: 3. Functions and Limits; title: 3.1 Functions; title: 3.1.1 Denition of a Function; title: 3.1.2 Piping Functions Together; title: 3.1.3 Inverse Functions; title: 3.2 Limits; title: 3.3 Continuity; title: 4. Calculus of One Variable Part 1: Differentiation; title: 4.1 Derivatives; title: 4.2 The Chain Rule; title: 4.3 Some Standard Derivatives; title: 4.4 Dierentiating Inverse Functions; title: 4.5 Implicit Differentiation; title: 4.6 Logarithmic Differentiation 4.7 Higher Derivatives; title: 4.8 L’Hôpital’s Rule; title: 4.9 Taylor Series; title: 5. Calculus of One Variable Part 2: Integration; title: 5.1 Summing Series; title: 5.2 Integrals; title: 5.3 Antiderivatives; title: 5.4 Integration by Substitution; title: 5.5 Partial Fractions; title: 5.6 Integration by Parts; title: 5.7 Reduction Formulae; title: 5.8 Improper Integrals; title: 6. Calculus of Many Variables; title: 6.1 Surfaces and Partial Derivatives; title: 6.2 Scalar Fields; title: 6.3 Vector Fields; title: 6.4 Jacobians and the Chain Rule; title: 6.5 Line Integrals; title: 6.6 Surface and Volume Integrals; title: 7. Ordinary Differential Equations; title: 7.1 First Order Dierential Equations Solvable by Integrating Factor; title: 7.2 First Order Separable Differential Equations; title: 7.3 Second Order Linear Differential Equations with Constant Coefficients: The Homogeneous Case; title: 7.4 Second Order Linear Differential Equations with Constant Coefficients: The Inhomogeneous Case; title: 7.5 Initial Value Problems; title: 8. Complex Function Theory; title: 8.1 Standard Complex Functions; title: 8.2 The Cauchy-Riemann Equations; title: 8.3 Complex Integrals; title: Index