A Mathematics Boot Camp for Science and Engineering Students

Cover
Half Title
Title
Copyright
Contents
Preface
Notes from the Author
Topic 1 Physical Meaning and Units
	1.1 Physical Meaning
	1.2 Physical Quantities, Units, and Dimensions
		1.2.1 Base Quantities and Derived Quantities
		1.2.2 Units and Dimensions
		1.2.3 Unit Conversions
	1.3 Systems of Units
		1.3.1 Coherent Systems of Units
		1.3.2 The International System of Units
		1.3.3 Some Common Non-SI Systems
	1.4 Dimensional Homogeneity
	1.5 Recommendations on the Proper Use of Units
	Exercise Problems
Topic 2 Solution Procedure and Significant Figures
	2.1 The Five-Stage Solution Procedure
	2.2 Significant Figures
		2.2.1 Uncertainty in Measurements and Significant Figures
		2.2.2 Counting Significant Figures
		2.2.3 Significant Figures in Calculations
		2.2.4 Guidelines for Using Significant Figures in Calculations
	2.3 Summary and Recommendations
	Exercise Problems
Topic 3 Derivatives
	3.1 Derivatives of Single-Variable Functions
		3.1.1 Definition of Derivatives
		3.1.2 Application of Derivatives
	3.2 Derivatives of Multivariable Functions
		3.2.1 Definition of Partial Derivatives
		3.2.2 Application of Partial Derivatives
	3.3 Introduction to Differential Equations
		3.3.1 Newton’s Second Law
		3.3.2 The Heat Equation
		3.3.3 The Wave Equation
		3.3.4 The Laplace Equation
		3.3.5 The Schrödinger Equation
	Exercise Problems
Topic 4 Differentials
	4.1 Differentials of Single-Variable Functions
	4.2 Differentials of Multivariable Functions
	4.3 Applications of Differentials
		4.3.1 Application in Uncertainty Analysis
		4.3.2 Application in Thermodynamics
		4.3.3 Interpreting Differentials
	Exercise Problems
Topic 5 Integrals
	5.1 Integrals of Single-Variable Functions
		5.1.1 Indefinite Integrals
		5.1.2 Definite Integrals
	5.2 Integrals of Multivariable Functions
		5.2.1 Multiple Integrals
		5.2.2 Line and Surface Integrals
		5.2.3 Integrating Thermodynamic Functions
	Exercise Problems
Topic 6 Coordinate Systems
	6.1 Cartesian Coordinate Systems
	6.2 Polar Coordinate System
	6.3 Cylindrical and Spherical Coordinate Systems
	6.4 The Line, Area, and Volume Elements
	Exercise Problems
Topic 7 Vectors
	7.1 Graphical and Algebraic Representation of Vectors
	7.2 Vector Operations
		7.2.1 Addition and Subtraction
		7.2.2 Multiplications
	7.3 Vector Calculus
		7.3.1 Vector Functions and Space Curves
		7.3.2 Vector Fields
	7.4 Solving Problems Involving Vectors
	Exercise Problems
Topic 8 Complex Numbers and Functions
	8.1 Definitions and Basic Operations
	8.2 Complex Numbers in the Polar Form
	8.3 Complex Functions and Their Applications
		8.3.1 Complex Functions and Euler’s Formula
		8.3.2 Harmonic Motions
		8.3.3 Complex Impedance
		8.3.4 Other Applications
	Exercise Problems
Topic 9 Approximation Techniques and Numerical Problem Solving
	9.1 Data Interpolation and Extrapolation
	9.2 Estimating from a Figure
	9.3 Numerical Techniques
		9.3.1 Solving Equations
		9.3.2 Numerical Differentiation
		9.3.3 Numerical Integration
	Exercise Problems
Topic 10 Mixed Exercises
	Exercise Problems
Appendices
Index