Description
CBS Publishers & Distributors Pharmaceutical Mathematics with Applications 1st Edition 2022 by Pundir and Sudhir Kumar
Pharmaceutical Mathematics with Applications is meant for the students of BPharm, DPharm, MPharm and other related courses in the field of pharmaceutical sciences as per PCI regulations. The present text is designed to introduce students about the methods and applications of mathematics in industrial pharmacy and pharmacokinetics. The author has attempted to give as many illustrations as possible in order to make the students to understand various methods in solving or deriving pharmaceutical problems. Each chapter deals with an introduction, clear statement of definitions, objective and principles supplemented by solved examples and ends with a set of exercises. Collection of objective type questions from different examinations is given at the end of each chapter. The language of the book has been kept very simple.
About Editor
Sudhir Kumar Pundir PhD is currently Professor and Principal (Ex-Head, Department of Mathematics), SD (PG) College, Muzaffarnagar, UP. Formerly, he was Head, Department of Mathematics, Government (PG) College, Rishikesh, UK. Dr Pundir has been a recipient of JRF and SRF of CSIR, New Delhi, during his research work. He has been teaching undegraduate and postgraduate classes for well over two decades. He also organized and attended a number of national and international conferences. Six students have been awarded PhD degree under his supervision. He has to his credit more than 100 books for undergraduate, postgraduate and engineering students which are widely used by the students of various universities.
TABLE OF CONTENTS:-
Ch. 1. PARTIAL FRACTIONS 1-14
1.1 Introduction 1
1.2 Basic Definitions 1
1.3 Partial Fractions 2
1.4 Methods of Resolution into Partial Fractions 2
1.5 Applications of Partial Fractions in Chemical Kinetic and Pharmacokinetics 9
Ch. 2. LOGARITHMS 15-32
2.1 Introduction 15
2.2 Properties of Logarithms 15
2.3 System of Logarithms 16
2.4 Standard Form of Decimal 16
2.5 Characteristic and Mantissa 17
2.6 Method to determine the Characteristic and Mantissa 19
2.7 Antilogarithm 22
2.8 Application of Logarithms in Pharmaceutical Problems 23
Ch. 3. FUNCTIONS 33-44
3.1 Introduction 33
3.2 Type of Functions 34
3.3 Some Special Mapping or Functions 37
Ch. 4. LIMIT AND CONTINUITY 45-60
4.1 Introduction 45
4.2 Limit of the Function 46
4.3 Theorems related to Limits 46
4.4 Method of finding the Limit of a Function 46
4.5 Right and Left Hand Limit of a Function 49
4.6 Existence of the Limit of a Function 50
4.7 Concepts of Continuity 53
4.8 Continuity of a Function at a point 54
Ch. 5. DETERMINANTS 61-84
5.1 Introduction 61
5.2 Determinant of Order Two 61
5.3 Determinant of Order Three 61
5.4 Co–factors and Minors of an Element 63
5.5 Properties of Determinants 65
5.6 Applications of Determinants 77
5.7 Cramer’s Rule 78
5.8 Product of Determinants 82
Ch. 6. MATRICES 85-136
6.1 Introduction 85
6.2 Matrix 85
6.3 Types of Matrices 85
6.4 Operations on Matrices 88
6.5 Properties of Matrices Addition 88
6.6 Multiplication of a Matrix by a Scalar 89
6.7 Multiplication of Matrices 92
6.8 Properties of Matrix Multiplication 93
6.9 Transpose of a Matrix 98
6.10 Symmetric, Skew-Symmetric and Orthogonal Matrices 98
6.11 Elementary Operations (or Transformation) on Matrices 102
6.12 Equivalent Matrices and Elementary Matrix 102
6.13 Singular and Non-Singular Matrix 103
6.14 Inverse Matrix or Inverse of a Matrix 103
6.15 Inverse of a Matrix by Elementary Operations 103
6.16 Adjoint of a Matrix 106
6.17 Homogeneous Linear Equations 112
6.18 Nature of the Solution of the Equation AX = O 113
6.19 Non-Homogeneous Equations 117
6.20 Condition for Consistency 118
6.21 Eigenvalue and Eigenvectors of a Matrix 123
6.22 The Characteristic Equation of a Matrix 123
6.23 The Cayley-Hamilton Theorem 124
6.24 Applications of Matrices in solving Pharmacokinetics Equations 129
Ch. 7. DIFFERENTIATIONS 137-178
7.1 Introduction 137
7.2 Method for Finding the Derivative using First Principles 137
7.3 Derivative of the Sum of Two Functions 141
7.4 Derivative of the Difference of Two Functions 141
7.5 Derivative of the Product of Two Functions 144
7.6 Derivative of the Quotient of Two Functions 144
7.7 Derivative of Functions of a Function (Chain Rule) 147
7.8 Differentiation of Implicit Functions 149
7.9 Logarithmic Differentiation 153
7.10 Differentiation of a Function w.r.t. another Function 161
7.11 Second and Higher Order Derivatives : Successive Differentiation 165
7.12 Maxima and Minima 169
Ch. 8. ANALYTICAL GEOMETRY 179-188
8.1 Introduction 179
8.2 Distance between Two Points 181
8.3 Collinear Points 184
8.4 Section Formula 185
8.5 Mid Point Formula 186
Ch. 9. STRAIGHT LINES 189-212
9.1 Introduction 189
9.2 Slope or Gradient of a Line 189
9.3 Slope of a Line through Two Points 189
9.4 Equation of Lines in Standard Form 193
9.5 Transformation of General Equation in Different Standard Forms 203
9.6 Point of Intersection of Two Lines 205
9.7 Angle between Two Intersecting Lines 206
Ch. 10. INTEGRATIONS 213-258
10.1 Introduction 213
10.2 Indefinite Integral 213
10.3 Method of Integration 216
10.4 Integration by Parts 223
10.5 Integration by Partial Fractions 226
10.6 More Problems based on Integration by Substitution 230
10.7 Definite Integral 239
10.8 Properties of Definite Integrals 240
10.9 Some More Solved Problems Related to Definite Integrals 247
10.10 Definite Integral as the Limit of the Sum 249
10.11 Summation of Series with the help of Definite Integral 251
10.12 Applications of Integrations 254
Ch. 11. DIFFERENTIAL EQUATIONS 259-306
11.1 Introduction 259
11.2 Differential Equation 259
11.3 Types of Differential Equations 259
11.4 Order of a Differential Equation 260
11.5 Solution of a Differential Equation 260
11.6 Formation of a Differential Equation 260
11.7 Method of forming a Differential Equation 261
11.8 General and Particular Solutions of a Differential Equation 261
11.9 Solution of Differential Equations: Variable Separable Method 263
11.10 Homogeneous Differential Equations 272
11.11 Equation Reducible to the Homogeneous Form 284
11.12 Linear Differential Equations 286
11.13 Equation Reducible to Linear Form (Bernoulli's Equation) 294
11.14 Exact Differential Equation 297
11.15 Applications of Differential Equations in Solving Pharmacokinetics Problems300
Ch. 12. THE LAPLACE TRANSFORMS 307-342
12.1 Introduction 307
12.2 Linearity Property 307
12.3 Existence of Laplace Transform 308
12.4 Laplace Transform of Some Elementary Functions 308
12.5 Translation or Shifting Theorems 312
12.6 Laplace Transform of Derivatives 314
12.7 The Inverse Laplace Transforms 319
12.8 Some Inverse Laplace Transforms 320
12.9 Important Properties of Inverse Laplace Transform 320
12.10 Inverse Laplace Transforms of Derivatives 326
12.11 Division By p 326
12.12 Multiplication by Powers of p 327
12.13 Inverse Laplace Transforms of Integrals 327
12.14 Solution of Ordinary Differential Equation with Constant Coefficients 330
12.15 Solution of Ordinary Differential Equation with Variable Coefficients 335
12.16 Applications of Laplace Transforms in Chemical Kinetics and Pharmacokinetics 336
APPENDIX: SELECTED TABLES 343-348
BIBLIOGRAPHY 349-350
INDEX 351-352