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

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