Basic Applied Mathematics For The Physical Sciences : Based On The Syllabus Of The University Of Delhi

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Cover Contents Preface to the Third Edition Preface Reviewers Syllabus for B.Sc. (Physical Sciences) Part I Chapter 1: Matrices 1.1 Introduction to Matrices 1.1.1 Types of Matrices 1.1.2 Operations on Matrices 1.1.3 Properties of Matrix Addition 1.1.4 Properties of Scalar Multiplication 1.2 Elementary Row Operations 1.3 Inverse of a Matrix 1.4 Rank of a Matrix 1.5 Systems of Linear Equations Chapter 2: Vectors in R2 and R3 2.1 Introduction 2.2 Vector Operations 2.2.1 Standard Basis for R2 and R3 2.3 Linear Combination of Vectors 2.4 Linear Independence 2.5 Basis and Dimension 2.6 Subspaces Chapter 3: Linear Transformations 3.1 Introduction 3.2 Some Special Transformations 3.2.1 Projection 3.2.2 Dilation and Contraction 3.2.3 Reflection 3.2.4 Rotation 3.2.5 Shear 3.2.6 Translation 3.3 Matrix Representation of a Linear Transformation 3.3.1. Composition of Two Transformations 3.3.2. Geometric Effect of Multiplication by a Matrix Chapter 4: Eigenvalues and Eigenvectors 4.1 Eigenvalues and Eigenvectors 4.2 Eigen Space 4.3 Diagonalization Part II Chapter 5: Sequences 5.1 What is a Sequence? 5.2 Recursion Formula for Sequences 5.2.1 Fibonacci Sequence 5.2.2 Tower of Hanoi Game (Tower of Brahma) 5.3 Difference Equation 5.4 Types of Sequences 5.4.1. Subsequences 5.4.2 Other Important Types of Sequences 5.5 Convergent Sequences 5.5.1 Convergence of Sequences 5.5.2 Algebra of Convergent Sequences 5.5.3 More on Convergence of Sequences 5.5.4. Some Important Limits Chapter 6: Functions and their Graphs 6.1 Introduction 6.1.1 Graph of a Function 6.1.2 Some Useful Graphs 6.1.3 Logarithmic Functions 6.1.4. Trigonometric Functions 6.1.5. Inverse Trigonometric Functions 6.1.6 Hyperbolic Functions Chapter 7: Differential Equations in Mathematical Modelling 7.1 Introduction 7.1.1 Exponential Growth Model 7.2 Exponential Decay Model 7.3 Population Growth with Logistic Growth Model Chapter 8: Successive Differentiation 8.1 Higher Order Derivatives 8.2 The nth Derivatives of Some Important Functions 8.3 Leibnitz’s Theorem Chapter 9: Polynomial Approximation of Functions 9.1 Taylor Polynomial and Maclaurin Polynomial 9.2 Polynomial Approximations of Functions and Error Estimation 9.3 Series Expansion of Functions 9.3.1 Taylor and Maclaurin Series 9.4 Convergence of Taylor Series Chapter 10: Functions of two Variables 10.1 Functions of Two or More Variables 10.1.1 Graphs and Level Curves of Functions of Two Variables 10.2 Partial Derivatives 10.3 Applications of Partial Derivatives 10.3.1 The Wave Equation 10.3.2. Laplace’s Equation 10.3.3 Diffusion Equation 10.3.4. Heat Equation Part III Chapter 11: Geometry of Complex Numbers 11.1 Introduction 11.1.1 Geometrical Representation of Sum, Difference, Product and Quotient of Complex Numbers 11.1.2 Point Dividing a Line Segment in a Given Ratio 11.1.3 Regarding Angles in the Argand Plane 11.2 Straight Lines in Argand Plane 11.2.1 General Equation of a Straight Line 11.2.2 Parametric Equation of a Straight Line 11.2.3 Half-planes 11.3 Circles in the Argand Plane 11.3.1 Equation of a Circle with Given Centre and Radius 11.3.2 The General Equation of a Circle 11.3.3 Equation of a Circle with Given Endpoints of a Diameter 11.3.4 Discs in a Plane 11.4 Fundamental Theorem of Algebra Chapter 12: De Moivre’s Theorem 12.1 De Moivre’s Theorem for a rational index 12.2 Roots of Complex Numbers and Solution of Equations Answers to Exercises Appendix Question Paper 2007–08 Question Paper 2008–09 Question Paper 2009–10 Question Paper 2010–11 Solution of Examination Paper 2010-11 Index