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Making calculus
practical, useful, visual, hands-on, safe and Entertaining

 

 

 

 

 

 

 

  • Dialogue format:  Incorporated throughout the entire text, the dialogue format provides a thought-provoking forum for students to initiate intellectual discussions and also renders problem-solving strategies more transparent.

  • Numerous real-world applications:  A central emphasis on applications makes this text unique and plays an important role in the development of the main mathematical themes that it presents. The variety of topics is far ranging, from mechanics and the laws of motion to electric circuits and even a rather careful introduction to elementary probabilistic phenomena.

  • Historical chapters and philosophical discussions:  Chapters such as the Origins of Modern Mathematics (Descartes and Fermat), Miraculous Insights (Newton), and Galileo Galilei and the Copernican Revolution are scattered throughout the text to provide historical context and open up channels of teacher/student communication beyond the ordinary.

  • Comprehensive coverage of topics with numerous exercises:  The text covers all the standard material typically covered in an applied calculus course and offers a sufficient number of exercises in the text and in separate sections at the end of each chapter. The authors make the material highly accessible by developing topics from a numerical, algebraic and geometric point of view.


TEXT - TABLE OF CONTENTS

Part I: DIFFERENTIATION
1. Functions
2. Limits of Functions
3. Limits Made More Precise
4. The Derivative
5. The Origins of Modern Mathematics
6. Designing a Radar Antenna (Part 1)
7. A Theoretical Matter: Continuity
8. Newton's Laws and Rocket Motion (Part 1)
9. Miraculous Insights
10. Rules of Differentiation
11. Graphs of Functions
12. Optimization (Part 1)
13. Newton's Method of Approximation

PART II: INTEGRATION
14. Introduction to Integration
15. Galileo Galilei and the Copernican Revolution
16. Computing Volumes and the Hydrostatic Principle
17. The Definite Integral
18. Bernhard Riemann and the Spirit of Pythagoras
19. The Fundamental Theorem of Calculus
20. New Horizons

PART III: SPECIAL FUNCTIONS
21. The Natural Logarithm and Newton's Law of Cooling (Part 1)
22. Inverse Functions, the Exponential Function, and the Law of Cooling (Part 2)
23. The General Exponential Function and Fruit Flies
24. The General Logarithm and Power Functions
25. Honeycombs (Part 1)
26. Trigonometric Functions
27. Trigonometric Inverse Functions and Honeycombs (Part 2)
28. Explaining the Rainbow
29. Relative Growth and Decay

PART IV: METHODS OF INTEGRATION
30. Integration by Substitution and Rocket Motion (Part 2)
31. Inverse Integration by Substitution and Designing a Radar Antenna (Part 2)
32. Ellipses and Kidney Stones
33. Integration of Rational Functions and the Physics of Sky Diving
34. Tossing Coins (Part 1)
35. Integration by Parts and Tossing Coins (Part 2)
36. Simple Random Experiments
37. Trapezoid Estimates and Stirling's Formula
38. Improper Integrals and Infinite Trumpets

PART V: TAYLOR APPROXIMATION
39. Taylor Polynomials
40. Taylor's Theorem
41. Infinite Series
42. Taylor Series

PART VI: DIFFERENTIAL EQUATIONS
43. Separable and Homogeneous Differential Equations
44. First-Order Linear Differential Equations and Electric Circuits (Part 1)
45. Complex Numbers
46. Second-Order Linear Differential Equations and Electric Circuits (Part 2)
47. Difference Equations and Fibonacci Numbers
48. The Laplace Transform
49. Applications of the Laplace Transform to Differential Equations
50. Numerical Solutions of Differential Equations and Falling Bodies
51. Power Series Solutions

PART VII: LINEAR ALGEBRA
52. Conditional Probability (Part 1)
53. Matrices and Conditional Probability (Part 2)
54. Systems of Linear Equations, Inverse Matrices, and Conditional Probability
     (Part 3)
55. Resistor Networks and Conditional Probability (Part 4)
56. Determinants, Cramer's Rule, and Characteristic Values
57. Vector Spaces

PART VIII: SYSTEMS OF DIFFERENTIAL EQUATIONS
58. Linear Systems and Mechanical Systems (Part 1)
59. First-Order Linear Systems
60. Homogeneous Systems with Constant Coefficients and Mechanical Systems
     (Part 2)
61. Nonhomogeneous Systems and Mechanical Systems (Part 3)
62. Application of the Laplace Transform to Linear Systems
63. R-C-L Networks
64. Higher-Order Linear Differential Equations

PART IX: VECTOR CALCULUS
65. The Geometry of Two and Three-Dimensional Space
66. Statics and the Sagging Problem (Part 1)
67. Curves, Parameterizations, and the Sagging Problem (Part 2)
68. Velocity, Acceleration, and the Laws of Motion
69. Multivariable Functions, Vector Fields, and the Law of Gravitation
70. A Project: the Laws of Celestial Mechanics
71. Partial Derivatives, Gradients, and Conservation of Energy
72. Path Integrals, Work, and the Coulomb Field
73. Optimization (Part 2) and Linear Regression
74. Integration of Multivariable Functions and Electrostatics
75. Change of Variables and the Gravitational Field of the Earth
76. The Motion of a Rigid Body
77. The Normal Distribution and Tossing Coins (Part 3)
78. Parameterized Surfaces, Flux Integrals, and Flowing Liquids
79. The Divergence Theorem and the Law of Gauss
80. Stokes' Theorem and the Speed of Light

 

 

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