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