Basic Training in Mathematics: A Fitness Program for Science Students

Front Cover
Springer Science & Business Media, Apr 30, 1995 - Science - 366 pages
1 Review
Based on course material used by the author at Yale University, this practical text addresses the widening gap found between the mathematics required for upper-level courses in the physical sciences and the knowledge of incoming students. This superb book offers students an excellent opportunity to strengthen their mathematical skills by solving various problems in differential calculus. By covering material in its simplest form, students can look forward to a smooth entry into any course in the physical sciences.
 

What people are saying - Write a review

User Review - Flag as inappropriate

Later after I study

Selected pages

Contents

DIFFERENTIAL CALCULUS OF ONE VARIABLE
1
13 Exponential and Log Functions
5
14 Trigonometric Functions
19
15 Plotting Functions
23
16 Miscellaneous Problems on Differential Calculus
25
17 Differentials
29
18 Summary
30
INTEGRAL CALCULUS
33
75 Scalar Field and the Gradient
167
76 Curl of a Vector Field
172
77 The Divergence of a Vector Field
182
78 Differential Operators
186
79 Summary of Integral Theorems
188
711 Applications from Electrodynamics
192
712 Summary
202
MATRICES AND DETERMINANTS
205

22 Some Tricks of the Trade
44
23 Summary
49
CALCULUS OF MANY VARIABLES
51
32 Integral Calculus of Many Variables
61
33 Summary
72
INFINITE SERIES
75
42 Tests for Convergence
77
43 Power Series in x
80
44 Summary
87
COMPLEX NUMBERS
89
52 Complex Numbers in Cartesian Form
90
53 Polar Form of Complex Numbers
94
54 An Application
98
55 Summary
104
FUNCTIONS OF A COMPLEX VARIABLE
107
62 Analytic Functions Defined by Power Series
116
63 Calculus of Analytic Functions
126
64 The Residue Theorem
132
65 Taylor Series for Analytic Functions
139
66 Summary
144
VECTOR CALCULUS
149
72 Time Derivatives of Vectors
155
73 Scalar and Vector Fields
158
74 Line and Surface Integrals
159
82 Matrix Inverses
211
83 Determinants
215
84 Transformations on Matrices and Special Matrices
220
85 Summary
227
LINEAR VECTOR SPACES
229
92 Inner Product Spaces
237
93 Linear Operators
247
94 Some Advanced Topics
252
95 The Eigenvalue Problem
255
96 Applications of Eigenvalue Theory
266
97 Function Spaces
277
98 Some Terminology
294
910 Summary
300
DIFFERENTIAL EQUATIONS
305
102 ODEs with Constant Coefficients
307
First Order
315
Second Order and Homogeneous
318
105 Partial Differential Equations
329
106 Greens Function Method
345
107 Summary
347
ANSWERS
351
INDEX
359
Copyright

Other editions - View all

Common terms and phrases

Popular passages

Page iii - ... at great cost to herself. This book is yet another example of what she has made possible through her tireless contributions as the family muse. It is dedicated to her and will hopefully serve as one tangible record of her countless efforts. NOTE TO THE INSTRUCTOR If you should feel, as I myself do, that it is not possible to cover all the material in the book in one semester, here are some recommendations. • To begin with, you can skip any topic in fine print.

References to this book

About the author (1995)

Ramamurti Shankar is the John Randolph Huffman Professor of Physics at Yale University, USA. 

Bibliographic information