Mathematics for Computer and Information Science For KTU B. Tech Semester 1 (Group A)
ISBN: 9789363860421
356 pages
For more information write to us at: acadmktg@wiley.com
Description
This book is a refined adaptation of the best-selling titles Advanced Engineering Mathematics by Erwin Kreyszig and Calculus: Early Transcendentals, 12th Edition by Howard Anton. Renowned for its expository style and clarity of presentation, this text offers an elementary exploration of the subject, addressing the evolving needs of today’s students. Our aim is to elucidate the fundamentals of subject in the most comprehensible way, with pedagogy as our primary focus. It covers topics of:
- Continuity and Derivatives
- Functions of Several Variables and Partial Derivatives
- Directional Derivatives, Gradient and Local Extreme Values
- Constrained Maxima and Minima and Linear Programming
1. LIMITS, CONTINUITY AND DERIVATIVES
1.1 Limit of a Function Values
Sampling Pitfalls
One-Sided Limits
The Relationship Between One-Sided Limits and Two-Sided Limits
Computing Limits
Limits of Polynomials and Rational Functions as x → a
Limits Involving Radicals
Limits of Piecewise-Defined Functions
The sandwich Theorem [Squeeze Principle]
Solved Examples
Quick Check Problem 1.1
Problem Set 1.1
Answer Key
1.2 Continuity
Definition of Continuity
Continuity in Applications
Continuity on an Interval
Some Properties of Continuous Functions
Continuity of Polynomials and Rational Functions
Continuity of Compositions
Continuity of Inverse Functions
The Intermediate-Value Theorem
Approximating Roots Using the Intermediate-Value Theorem
Continuity of Trigonometric Functions
Obtaining Limits by Squeezing
Solved Examples
Quick Check Problem 1.2
Problem Set 1.2
Answer Key
1.3 Tangent Lines and Rates of Change
Tangent Lines
Velocity
Slopes and Rates of Change
Rates of Change in Applications
Quick Check Problem 1.3
Problem Set 1.3
Answer Key
1.4 The Derivative Function
Definition of the Derivative Function
Computing Instantaneous Velocity
Differentiability
The Relationship Between Differentiability and Continuity
Derivatives at the Endpoints of an Interval
Other Derivative Notations
Geometrical Interpretation of Derivative
Solved Examples
Quick Check Problem 1.4
Problem Set 1.4
Answer Key
1.5 Differentiation Rules
Derivative of a Constant
Derivatives of Power Functions
Derivative of a Constant Times a Function
Derivatives of Sums and Differences
Higher Derivatives
The Product and Quotient Rules
Derivative of a Quotient
Summary of Differentiation Rules
Quick Check Problem 1.5
Problem Set 1.5
Answer Key
Obtaining Limits by Squeezing
Solved Examples
Quick Check Problem 1.2
Problem Set 1.2
Answer Key
1.3 Tangent Lines and Rates of Change
Tangent Lines
Velocity
Slopes and Rates of Change
Rates of Change in Applications
Quick Check Problem 1.3
Problem Set 1.3
Answer Key
1.4 The Derivative Function
Definition of the Derivative Function
Computing Instantaneous Velocity
Differentiability
The Relationship Between Differentiability and Continuity
Derivatives at the Endpoints of an Interval
Other Derivative Notations
Geometrical Interpretation of Derivative
Solved Examples
Quick Check Problem 1.4
Problem Set 1.4
Answer Key
1.5 Differentiation Rules
Derivative of a Constant
Derivatives of Power Functions
Derivative of a Constant Times a Function
Derivatives of Sums and Differences
Higher Derivatives
The Product and Quotient Rules
Derivative of a Quotient
Summary of Differentiation Rules
Quick Check Problem 1.5
Problem Set 1.5
Answer Key
1.6 Instantaneous Rates of Change
Motion on a Straight Line – Displacement Velocity, Speed and Acceleration
Definition Velocity (Instantaneous Velocity)
Derivatives in Economics
Problem Set 1.6
Answer Key
1.7 The Chain Rule
Derivatives of Compositions
An Alternative Version of the Chain Rule
Generalized Derivative Formulas
Differentiating Using Computer Algebra Systems
Quick Check Problem 1.7
Problem Set 1.7
Answer Key
1.8 Implicit Differentiation
Functions Defined Explicitly and Implicitly
Implicit Differentiation
Necessary Conditions for Implicit Differentiation
Tangent and Normal Lines
Quick Check Problem 1.8
Problem Set 1.8
Answer Key
1.9 Local Linear Approximation; Differentials
Error in Local Linear Approximations
Differentials
Local Linear Approximation from the Differential Point of View
Error Propagation
More Notation; Differential Formulas
Quick Check Problem 1.9
Problem Set 1.9
Answer Key
1.10 Analysis of Functions: Increase, Decrease and Concavity
Increasing and Decreasing Functions
Concavity
Inflection Points
Inflection Points in Applications
Logistic Curves
Quick Check Problem 1.10
Problem Set 1.10
Answer Key
2. FUNCTIONS OF SEVERAL VARIABLES AND PARTIAL DERIVATIVES
2.1 Functions of Two or More Variables
Notation and Terminology
Functions Described by Tables
Graphs of Functions of Two Variables
Level Curves
Contour Plots Using Technology
Level Surfaces
Graphing Functions of Two Variables Using Technology
Quick Check Problem 2.1
Problem Set 2.1
Answer Key
2.2 Limits and Continuity
Limits Along Curves
Open and Closed Sets
General Limits of Functions of Two Variables
Relationships Between General Limits and Limits Along Smooth Curves
Repeated Limits
Algebra of Limits
Continuity
Limits at Discontinuities
Continuity at Boundary Points
Extensions to Three Variables
Solved Examples
Quick Check Problem 2.2
Problem Set 2.2
Answer Key
2.3 Partial Derivatives
Partial Derivatives of Functions of Two Variables
The Partial Derivative Functions
Partial Derivative Notation
Partial Derivatives Viewed as Rates of Change and Slopes
Estimating Partial Derivatives from Tabular Data
Implicit Partial Differentiation
Partial Derivatives and Continuity
Partial Derivatives of Functions with More Than Two Variables
Higher-order Partial Derivatives
Equality of Mixed Partials
The Wave Equation
Differentiability
Differentiability and Continuity
Differentials
Solved Examples
Quick Check Problem 2.3
Problem Set 2.3
Answer Key
2.4 The Chain Rule
Chain Rules for Derivatives
Chain Rules for Partial Derivatives
Other Versions of the Chain Rule
Implicit Differentiation
Solved Examples
Quick Check Problem 2.4
Problem Set 2.4
Answer Key
3. Directional Derivatives, Gradient and Local Extreme Values
3.1 Directional Derivatives and Gradients
Directional Derivatives
The Gradient
Properties of the Gradient
Gradients are Normal to Level Curves
An Application of Gradients
Properties of the Directional Derivative
Solved Examples
Quick Check Problem 3.1
Problem Set 3.1
Answer Key
3.2 Maxima and Minima of Functions of Two Variables
Extrema
Bounded Sets
The Extreme-value Theorem
Finding Relative Extrema
The Second Partials Test
Finding Absolute Extrema on Closed and Bounded Sets
Solved Examples
Quick Check Problem 3.2
Problem Set 3.2
Answer Key
4. Constrained Maxima and Minima and Linear Programming
4.1 Lagrange Multipliers
Extremum Problems with Constraints
Lagrange Multipliers
Three Variables and One Constraint
Lagrange’s Multipliers with Two Constraints
Quick Check Problem 4.1
Problem Set 4.1
Answer Key
4.2 Basic Concepts. Unconstrained Optimization: Method of Steepest Descent
Quick Check Problem 4.2
Problem Set 4.2
Answer Key
4.3 Linear Programming Formation
General LPP
Normal Form of a Linear Programming Problem
Formation of LPP
Graphical Solution Method
Problem Set 4.3
Answer Key