A Mathematica Approach to Calculus

by Gresser, John T.; Bradley, Gerald L.; Smith, Karl J.

• ISBN13: 9780130105868
• ISBN10: 0130105864
• Edition: 2nd
• Format: Paperback
• Copyright: 1999-06-01
• Publisher: Pearson Prentice Hall

Summary

Ideally suited for use with either Bradley/Smith or Varberg/Purcell/Rigdon, this manual may also be used in conjunction with other calculus texts. Many of the exercise sets have additional problems labeled projects which are somewhat more involved. These projects are designed to enhance problem-solving skills by making use of not only topics currently under discussion, but, occasionally, a wide variety of previously discussed topics as well.

Table of Contents

Some Preliminaries	1	(8)
Mathematica Notebooks	1	(3)
Opening Old Notebooks	4	(1)
Frequent Saving	5	(1)
Mathematica's On-Line-Help	5	(4)
Basic Mathematica	9	(32)
Mathematica as a Calculator	9	(5)
Assigned and Unassigned Names	14	(3)
Functions and Expressions	17	(3)
Algebra	20	(4)
Plotting Graphs	24	(2)
The Differential Calculus	26	(3)
Solving Problems in Mathematica	29	(7)
Exercise Set	36	(5)
Basic Integration	41	(18)
Area and the Definite Integral	41	(4)
Integration and the Fundamental Theorem of Calculus	45	(4)
Integration by Substitution	49	(2)
Numerical Integration	51	(5)
Exercise Set	56	(3)
Applications of Integration	59	(12)
Sample Problems	60	(6)
Exercise Set	66	(5)
The Transcendental Functions	71	(28)
Inverse Functions	71	(5)
Logarithmic and Exponential Functions	76	(7)
The Inverse Trigonometric Functions	83	(4)
Exponential Growth and Decay	87	(3)
The Hyperbolic Functions and Their Inverses	90	(1)
Indeterminate Forms and L'Hopital's Rule	91	(2)
Exercise Set	93	(6)
Techniques of Integration	99	(20)
Integration by Substitution Revisited	101	(4)
Integration by Parts	105	(2)
Reduction Formulas	107	(1)
Inverse Trigonometric Substitutions	108	(2)
Rational Functions	110	(1)
Improper Integrals	111	(5)
Exercise Set	116	(3)
Sequences and Series	119	(26)
Mathematica's Limit Command	120	(2)
Sequences	122	(7)
Series	129	(2)
Positive Term Series	131	(3)
Alternating Series and Absolute Convergence	134	(2)
Power Series	136	(4)
Exercise Set	140	(5)
Plane Curves and Polar Coordinates	145	(26)
Conic Sections	145	(8)
Parametrically Defined Planar Curves	153	(5)
Polar Coordinates	158	(7)
Exercise Set	165	(6)
Vectors and Analytic Geometry	171	(26)
Vectors, Addition, and Scalar Multiplication	171	(4)
The Dot and Cross Products	175	(4)
Lines and Planes	179	(3)
Surfaces in Space	182	(8)
Exercise Set	190	(7)
Vector Valued Functions	197	(14)
Curves in Space	197	(5)
Motion in Space	202	(3)
Geometry of Curves	205	(2)
Exercise SEt	207	(4)
Multivariate Differential Calculus	211	(46)
Functions of Several Variables	211	(4)
Limits with Two or More Variables	215	(2)
Partial Derivatives	217	(7)
Directional Derivatives and the Gradient	224	(8)
Optimization	232	(16)
Exercise Set	248	(9)
Multiple Integration	257
Double Integrals	257
Applications of Double Integrals	265
Triple Integrals	268
Applications of Triple Integrals	274
Exercise Set	280