Essential Engineering Mathematics
A clear, practical refresher of core engineering mathematics.
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- • Refresh key techniques in algebra, functions, and calculus quickly
- • Gain clarity on topics often seen as difficult, like differentiation
- • Build essential linear algebra tools for multivariate work
- • Learn core methods for integration, series, ODEs, and complex functions
الوصف
Essential Engineering Mathematics is a short, undergraduate-focused guide designed to refresh algebraic and calculus techniques while easing the transition from school-level to university-level mathematics. It is not a comprehensive survey, but it highlights areas that engineers commonly find difficult—especially calculus—while building the necessary foundations along the way. The book begins with preliminaries on number systems, real and complex numbers, inequalities, and absolute value, then moves through vectors and matrices, systems of linear equations, eigenvalues and eigenvectors, and function basics. Later chapters develop single-variable differentiation and integration, including series and Taylor expansions, then extend to multivariable calculus, ordinary differential equations, and an introduction to complex function theory and complex integration.
فهرس المحتويات
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 Index
معاينة
Trinity College Dublin between 1998 and 2000. It is by no means a
comprehensive guide to all the mathematics an engineer might encounter during the course of his or her degree. The aim is more to
highlight and explain some areas commonly found difficult, such
as calculus, and to ease the transition from school level to university level mathematics, where sometimes the subject matter is
similar, but the emphasis is usually different. The early sections
on functions and single variable calculus are in this spirit. The
later sections on multivariate calculus, differential equations and
complex functions are more typically found on a first or second
year undergraduate course, depending upon the university.
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