Table of Contents - Discovering Mathematics with Excel

Discovering Mathematics with Excel

TABLE OF CONTENTS

1. Discovering Mathematics
	1.1 What is Mathematics
	1.2 Euclid’s Elements
	1.3 Finding the Circumference of a Circle
	1.4 Golden Ratio and Fibonacci Sequence
	1.5 Circular Functions
	1.6 Exponents and Logarithms
	1.7 Slopes and Derivatives
	1.8 Areas and Integrals
	1.9 Complex Numbers and Euler’s Equation
	1.10 Summary and More Discoveries
	Problems
2. Discovering the World of Numbers
	2.1 Counting and Number Systems
	2.2 Arithmetic Series and Triangular Numbers
	2.3 Squares and Square Roots
	2.4 Multiplications and Geometric Series
	2.5 Prime Numbers
	2.6 Counting and Choosing
	2.7 The Binomial Theorem
	2.8 Recurrence Sequences
	2.9 Modular Arithmetic
	2.10 Continued Fractions
	2.11 Public-key Cryptography
	Problems
3. Discovering Trigonometry
	3.1 Trigonometric Functions
	3.2 Sine and Cosine Waves
	3.3 Trigonometric Identities
	3.4 Congruent and Similar Triangles
	3.5 Area of Triangles
	3.6 Power Series and Trigonometric Functions
	3.7 Excel Plots of Trigonometric Functions
	3.8 Inverse Trigonometric Functions
	Problems
4. Discovering Probability and Statistics
	4.1 Flipping a Coin
	4.2 The Normal Distribution
	4.3 The Central Limit Theorem
	4.4 Rolling Dice
	4.5 Surprising Probabilities
	4.6 Conditional Probabilities
	4.7 Hypothesis Testing
	4.8 Bayesian Inference
	Problems
5. Discovering Logic and Algorithms
	5.1 Logical Operations
	5.2 Logic Gates
	5.3 Positive and Negative Logic:
		De Morgan's Theorem
	5.4 Design of Digital Circuits
	5.5 Boolean Algebra
	5.6 Design of Multiplexers
	5.7 Algorithms
	5.8 A GCD Algorithm
	5.9 A Sorting Algorithm
	Problems
6. Discovering Algebra
	6.1 The Quadratic Equation
	6.2 Solving Linear Equations
	6.3 Solving Cubic Equations
	Problems
7. Discovering Geometry
	7.1 Triangles and Circles
	7.2 Conic Sections
	7.3 The Volume of a Cone and a Sphere
	7.4 Doubling the Cube
	7.5 Trisecting an Angle
	7.6 Fractal Geometry
	Problems
8. Discovering Vectors
	8.1 Addition and Subtraction of Vectors
	8.2 The Scalar or Dot Product
	8.3 The Vector or Cross Product
	8.4 The Index Notation
	8.5 Orthogonal Curvilinear Coordinate Systems
	Problems
9. Discovering Calculus
	9.1 The Fundamental Theorem of Calculus
	9.2 Differentiation
	9.3 Integration
	9.4 Implicit Differentiation
	Problems
10. Discovering Vector Differentiation
	10.1 Linear Motion
	10.2 Projectile Motion
	10.3 Circular Motion
	10.4 Plane Curvilinear Motion
	Problems
11. Discovering Differential Equations
	11.1 Another Look at the Exponential Function
	11.2 Computer Solutions of Differential Equations
	11.3 Analytic Solutions of Differential Equations
	11.4 Second-Order Differential Equations
	11.5 Linear Systems of Differential Equations
	11.6 Eigenvalues and Eigenvectors
	11.7 Classifying Linear Systems Solutions
	11.8 A General Second-Order Differential Equation
	11.9 Predator-Prey Differential Equations
	11.10 Discovering Chaos
	Problems
Index

(377 pages)