# Basic Training in Mathematics: A Fitness Program for Science Students

Springer Science & Business Media, 1995 M04 30 - 366 pages
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.

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Later after I study

### 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

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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.