New Book:"Exploring
Mathmematics with Scientific Notebook", Published by Springer Verlag, ISBN
#981-3083-88-3. Co-authored with Professor Jonathan
Lewin . The topics range from college algebra, precalculus, calculus,
differential equations, linear algebra, advanced calculus and etc.
Table of Contents:
(Wei-Chi Yang and Jonathan Lewin)
Chapter 1. Getting to Know Scientific WorkPlace
1.1. Scientific
WorkPlace: A Brief Introduction
1.2. Some Elementary
Exercises
1.2.1. Operations with Algebra And Trigonometry
1.2.2. Solving Equations and Inequalities
1.2.3. An Application:
Calculus Operations
1.3.Making Definitions
1.3.1 Some Examples of Definitions
1.3.2 Evaluating A Function at a Column of Numbers
1.3.3 Iterations of Functions
1.4.Graphs in
Scientific WorkPlace
1.4.1. Drawing and Revising Graphs
1.4.2. Multiple Rectangles Plots
1.4.3. Implicit Plots: Some Conic Sections; A Smiling Face
1.4.4. Polar Plots: A Simple Polar Plot; A Complicated Polar Plot.
1.4.5. Parametric Plots
1.4.6 .Exploring A Parametric Curve
1.4.7. 3D Parametric Plots
A Parametric Cone with Maple and Mathematica
Drawing The Cone with Maple
Drawing The Cone with Mathematica
A Parametric Sphere
A Knotted Tube
A Mobius Band (with an animation)
1.4.8. Some Miscellaneous Exercises
Chapter 2. Derivatives
2.1. Objective
2.1.1. A Graphical Approach to The Derivative
2.1.2. A Numerical Approach to The Derivative
2.1.3. An Algebraic Approach to The Derivative
2.1.4. Some Exercises
2.1.5. Using Multiple Plots to Illustrate Derivatives
2.1.6. A Real World Problem.
Chapter 3. Riemann Sums
3.1. Introduction
3.2. The Approximating
Sums
3.3. A Simple
Example
3.4. A More
Complicated Example
3.5. A Convergent
Improper Integral
3.6. Remark
3.7. An Indefinite
Integral
3.8. The Fundamental
Theorem of Calculus
3.9. Using the
Graphs of Riemann Sums
Chapter 4. Calculating Volumes
4.1. Rotation
of A Graph about An Axis
4.2. Applications
of double integrals.
A Region Bounded by Planes
A Region Bounded by Two Surfaces
Describing A Region with Cylindrical Polar Coordinate
Chapter 5. Sequences and Series
5.1. Infinite
Series with Scientific Workplace
5.1.1. Example
5.1.2. Example
5.1.3. Example
5.1.4. Exercise
5.1.5. Exercise
5.1.6. Example
5.1.7. Exercise
5.1.8. Exercise
Chapter 6. Fixed Point Thorems
6.1. Objective:
6.1.1. The Existence Theorem
6.1.2. Existence and Uniquness Theorem
6.1.3. Fixed Point Iteration Theorem and Algorithm.
6.1.4. Example
6.1.5. Remark
Chapter 7. Logistic Growth
7.1. Discrete
model
7.2. Continuous
Model
Chapter 8. Rate of Convergence
8.1. Example
Chapter 9. Multivariable Calculus
9.1. Optimization:
9.1.1. Theorem
9.1.2. Theorem
9.1.3. Example
9.1.4. Example
9.2. Lagrange
Multipliers
9.2.1. Theorem
9.2.2. Example
9.2.3. Example
9.2.4. Example
Chapter 10. Maclaurin Series:
Chapter 11. Linear Algebra with Scientific Workplace
11.0. Introduction
11.0.1. Using the Matrices Menue:
11.0.2. Some Exercises on Matrix Operations
11.1. Characteristic
Polynomial and Minimum Polynomial
11.1.1. Definition of A Characteristic Polynomial
11.1.2. Definition of A Minimum Polynomial
11.2. Link with
Maple
Chapter 12. Markov Chains
12.0 Definitions
and Theorems
12.0.1. Definition of Transition Probability
12.0.2. Definition of A Transition Matrix
12.0.3. State Vectors of A Markov Process
12.0.4. Theorem
12.0.5. Example
12.1. Limiting
Behavior
12.1.1. Definition of a Regular Transition Matrix
12.1.2. Theorem
12.1.3. Theorem
12.1.4. Theorem
12.1.5. Example
12.1.6. Remark
12.2. Rabbits
and Foxes
12.2.1. Example
Chapter 13. Some Curve Fitting Problems
13.1. Objective
13.1.1. Traditionally:
13.1.2. Example
13.1.3. Innovative way by using Statistics Package
Chapter 14. An Application to The Natural Logarithm
14.1. Introduction
Chapter 15. Limits of Functions:
15.1. Example
15.2. Example
Chapter 16. Maximizing A Probability Function
16.1. Remark
16.2. Exercises:
Chapter 17. A Function with A Positive Derivative
17.1. Objective:
17.1.1. Theorrem
Chapter 18. Fourier Polynomials
18.1. An animation
18.2. Exercise
Chapter 19. An Area Problem
19.1. Equal Areas:
19.1.1. Remark
Chapter 20. Differential Equations:
20.1. Exact Method:
20.2. Laplace
Method:
20.3. Series
Method:
20.4. Numerical
Methods
20.5. Graphical
Solutions to initial-Value Problems
20.6. Exercises:
Chapter 21. Application to The Theory of Chaos
21.1. An Example:
21.1.1. Case 1: Proposition
21.1.2. Case 2: Proposition
Chapter 22. Sequences of Functions
22.1. Objective
22.1.1. Theorem: Uniform Convergence And Continuity
22.1.2. Example
22.1.3. Example
22.1.4. Example
22.1.5. Example
22.1.6. Exercise
Chapter 23. The Integral Test
23.1. Objective
23.1.1. The Integral Test: Derivative Form
23.1.2. Corollary
23.1.3. Exercise
23.2. Integral
Test and Abel's Test
23.2.1. Theorem: Abel's Test
Chapter 24. Nowhere Differentiable Functions
24.1. Objective
24.2. Experimenting
the graphs of partial sums
31.2.1. Remark
Chapter 25. Application to Fourier Series
25.1. Comparisons
of Absolutely Convergent Trigonometric Series
25.1.1. Example
25.1.2. Theorem