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Essential Engineering Mathematics by Michael Batty
Descriptions
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This textbook covers topics such as functions, single variable calculus, multivariate calculus, differential equations and complex functions. The necessary linear algebra for multivariate calculus is also outlined. More advanced topics which have been omitted, but which you will certainly come across, are partial differential equations, Fourier transforms and Laplace transforms.
Contents
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0. Introduction
1. 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
1.3.1 Imaginary Numbers
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 4.7 Higher Derivatives
4.8 L’Hôpital’s Rule
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
About The Author
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Michael Batty was born in 1970 in Durham, England. He gained his Ph.D. in mathematics (geometric group theory) from Warwick University in 1998. Having spent many years in academia researching and teaching mathematics and computer science, he now works as a server-side web developer. His research interests include group theory and algorithms, and he is also a keen artist in his spare time.
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