Essentials and Examples of Applied Mathematics (Pearson Original Edition)

Essentials and Examples of Applied Mathematics
Title Page
Copyright
About the Author
Common Formulas and Rules
Preface (second edition)
General Study Guide
Table of Contents
CHAPTER 1: Review of Basic Algebra
	1.1 Numbers and Operations
		1.1.1 Summary of real numbers and arithmetic operations
		1.1.2 Summary of exponents and roots with real numbers
		1.1.3 Summary of logarithmic operations with real numbers
	1.2 Algebraic Expressions and Operations
		1.2.1 Summary of algebraic expressions and basic operations
		1.2.2 Multiplication and division with algebraic expressions
	1.3 Factorising Algebraic Expressions
	1.4 Algebraic Fraction Operations
	1.5 Equations
		1.5.1 Equations and general properties
		1.5.2 Solving linear and quadratic equations
		1.5.3 Systems of linear equations
	Chapter 1: Exercises Answers
CHAPTER 2: Review of Triangles and Trigonometry
	2.1 Plane Angles and General Properties of Triangles
		2.1.1 Plane angles
		2.1.2 Triangles and general properties
		2.1.3 Right triangles and trigonometric functions of acute angles
		2.1.4 Applications of right triangles
	2.2 General Trigonometric Functions and Identities
		2.2.1 Trigonometric functions of general angles
		2.2.2 Trigonometric identities and relationships
	2.3 Oblique Triangles and Laws of Sines and Cosines
		2.3.1 Oblique triangles and laws of sines and cosines
		2.3.2 Solving oblique triangles
	2.4 Summary of Basic Geometry
	Chapter 2: Exercises Answers
CHAPTER 3: Inequalities and Sequences
	3.1 Inequalities
		3.1.1 Linear inequalities
		3.1.2 Applications of inequalities
	3.2 Absolute Values, Equations and Inequalities
		3.2.1 Absolute values
		3.2.2 Absolute-value equations
		3.2.3 Absolute-value inequalities
	3.3 Sequences and Series
		3.3.1 Concepts of sequences and series
		3.3.2 Arithmetic sequences
		3.3.3 Geometric sequences
	Chapter 3: Exercises Answers
CHAPTER 4: Functions and Graphs
	4.1 Introduction to Functions and Graphs
		4.1.1 The concept of functions and graphic presentations
		4.1.2 General properties of functions
		4.1.3 Translations and reflections of functions
	4.2 Special Functions and Inverse Functions
		4.2.1 Symmetric functions
		4.2.2 Special functions
		4.2.3 Implicit and parametric functions
		4.2.4 Inverse functions
	4.3 Multivariable Functions and the Cartesian System
		4.3.1 Basics of multivariable functions and the Cartesian system
		4.3.2 3D functions and graphs in the Cartesian system
	Chapter 4: Exercises Answers
CHAPTER 5: Polynomial Functions
	5.1 Linear Functions
		5.1.1 Expressions of linear functions
		5.1.2 Properties of linear functions
		5.1.3 Applications of linear functions
	5.2 Quadratic Functions
		5.2.1 Expressions and features of quadratic functions
		5.2.2 Applications of quadratic functions
	5.3 Higher Order Polynomials
	Chapter 5: Exercises Answers
CHAPTER 6: Exponential and Logarithmic Functions
	6.1 Exponential Functions
		6.1.1 Exponential functions and properties
		6.1.2 Special exponential functions
	6.2 Logarithmic Functions
		6.2.1 Logarithmic functions and properties
		6.2.2 Logarithmic scales
	6.3 Applications of Exponential and Logarithmic Functions
		6.3.1 Exponential and logarithmic equations
		6.3.2 Compound interest
		6.3.3 Population growth
		6.3.4 Earthquake energy
		6.3.5 Radioactive decay
		6.3.6 Charging capacitors
	Chapter 6: Exercises Answers
CHAPTER 7: Trigonometric and Hyperbolic Functions
	7.1 General Trigonometric Functions
		7.1.1 Characteristics of general trigonometric functions
		7.1.2 Generic sine and cosine functions and combinations
	7.2 Inverses of Trigonometric Functions
	7.3 Trigonometric Equations
	7.4 Hyperbolic Functions
		7.4.1 Hyperbolic functions
		7.4.2 Hyperbolic Identities and Relationships
	Chapter 7: Exercises Answers
CHAPTER 8: Essentials of Vectors
	8.1 Vectors and Operations
		8.1.1 The concept and properties of vectors
		8.1.2 Addition and subtraction of plane vectors
		8.1.3 Multiplications of two plane vectors
	8.2 Applications of vectors
	Chapter 8: Exercises Answers
CHAPTER 9: Essentials of Complex Numbers
	9.1 Complex Numbers in Rectangular System
		9.1.1 The concept and representation in rectangular system
		9.1.2 Operations in rectangular system
	9.2 Complex Numbers in Polar System
		9.2.1 Representation of complex numbers in polar system
		9.2.2 Operations of complex numbers in polar system
	9.3 Complex Numbers in Exponential Form
	9.4 Applications of Complex Numbers
		9.4.1 Quadratic equations with complex roots
		9.4.2 Complex numbers for operations of plane vectors
		9.4.3 Ohm’s law for alternating current by complex numbers
	Chapter 9: Exercises Answers
CHAPTER 10: Essentials of Derivatives
	10.1 Limits and Continuities of Functions
		10.1.1 Limits of functions
		10.1.2 Continuities of functions
	10.2 Derivatives of Continuous Functions
		10.2.1 The concept and meanings of derivatives of functions
		10.2.2 Derivatives of common functions and basic rules
	10.3 Advanced Techniques of Differentiation
		10.3.1 The extended product rule
		10.3.2 The chain rule
		10.3.3 The logarithmic rule
	10.4 Higher Order Derivatives
	10.5 Derivatives of Special Functions
		10.5.1 Derivatives of parametric functions
		10.5.2 Derivatives of implicit functions
	Chapter 10: Exercises Answers
CHAPTER: 11 Applications of Derivatives
	11.1 Tangent and Normal Lines
	11.2 Limits of Indeterminate Forms (L’Hospital’s Rule)
	11.3 Critical Points and Extreme Values of Functions
		11.3.1 Concepts of critical points and extreme values
		11.3.2 Determining the nature of extreme values
	11.4 Applications of Derivatives in Science and Engineering
	Chapter 11: Exercises Answers
CHAPTER 12: Derivatives for Approximation
	12.1 Solving Nonlinear Equations by Newton’s Method
	12.2 Taylor Polynomials
	12.3 Taylor and Maclaurin Series
	Chapter 12: Exercises Answers
CHAPTER 13: Differentials and Applications
	13.1 Differentials of Functions
		13.1.1 Small changes and differentials of functions
		13.1.2 Estimation of small changes of a function at a given point
	13.2 Applications of Differentials
		13.2.1 Error estimation in numeric computation
		13.2.2 Linear approximation
	Chapter 13: Exercises Answers
CHAPTER 14: Indefinite Integration
	14.1 Fundamentals of Indefinite Integration
		14.1.1 The concept of indefinite integrals
		14.1.2 Basic rules for indefinite integrals
	14.2 Advanced Techniques for Indefinite Integration
		14.2.1 Integration by substitution
		14.2.2 Integration by parts
		14.2.3 Integration by complete differentials
		14.2.4 Integration by partial fractions
	Chapter 14: Exercises Answers
CHAPTER 15: Applications of Indefinite Integration
	15.1 Applications of Indefinite Integration in Sciences
	15.2 Applications of Indefinite Integration in Engineering
	Chapter 15: Exercises Answers
CHAPTER 16: Definite Integration and Applications
	16.1 Essentials of Definite Integration
		16.1.1 The concept and essential formulae of definite integrals
		16.1.2 Handling the limits in definite integration
		16.1.3 Operational rules for definite integration
	16.2 Applications of Definite Integration
		16.2.1 Geometric applications
		16.2.2 Applications in physics and engineering
	Chapter 16: Exercises Answers
CHAPTER 17: Special and Numeric Integration
	17.1 Improper Integration
		17.1.1 Definite integration over infinite limit(s)
		17.1.2 Definite integration of integrands with undefined points
	17.2 Integration of Special Functions
		17.2.1 Integration of segmented (piecewise) functions
		17.2.2 Integration of rational functions of sine or cosine
	17.3 Numeric Integration
		17.3.1 Trapezium method
		17.3.2 Simpson’s method
		17.3.3 Numeric integration by Maclaurin series
	Chapter 17: Exercises Answers
CHAPTER 18: Systems of Linear Equations
	18.1 Fundamentals of Matrices and Vectors
		18.1.1 Matrices and vectors
		18.1.2 Special matrices
		18.1.3 Addition and scalar multiplication of matrices and vectors
		18.1.4 Matrix multiplications
	18.2 Determinants
	18.3 Solving Systems of Linear Equations
		18.3.1 Systems of linear equations
		18.3.2 Solving systems of linear equations by Cramer’s rule
		18.3.3 Elementary row operations and Gauss elimination
	Chapter 18: Exercises Answers
General References
Appendix: Formulae of Indefinite Integration