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Problems in Calculus of one Variable
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Problems in Calculus of one Variable

Rs.160.00

160 INR
    ISBN: 9789385966583
    Author: I.A.MARON
    Edition: 2016
    Pages: 456
  • Shipping Weight: 388gms
  • Classes: Class 11, Class 12
  • Exams: School Books
  • Subjects: Mathematics
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Product Description
Content
 
1. Introduction to Mathematical Analysis
 § 1.1. Real Numbers. The Absolute Value of a Real Number
 § 1.2. Function. Domain of Definition 
 § 1.3. Investigation of Functions 
 § 1.4. Inverse Functions
 § 1.5. Graphical Representation of Functions 
 § 1.6. Number Sequences. Limit of a Sequence 
 § 1.7. Evaluation of Limits of Sequences
 § 1.8. Testing Sequences for Convergence 
 § 1.9. The Limit of a Function 
 § 1.10. Calculation of Limits of Functions 
 § 1.11. Infinitesimal and Infinite Functions. Their Definition
 and Comparison
 § 1.12. Equivalent Infinitesimals. Application to Finding 
 Limits 
 § 1.13. One-Sided Limits 
 § 1.14. Continuity of a Function. Points of Discontinuity and
 Their Classification 
 § 1.15. Arithmetical Operations on Continuous Functions.
 Continuity of a Composite Function
 § 1.16. The Properties of a Function Continuous on a Closed
 Interval. Continuity of an Inverse Function
 § 1.17. Additional Problems 
 
2. Differentiation of Functions 
 § 2.1. Definition of the Derivative 
 § 2.2. Differentiation of Explicit Functions 
 CHAPTERS
 § 2.3. Successive Differentiation of Explicit Functions.Leibniz
 Formula 
 § 2.4. Differentiation of Inverse, Implicit and Parametrically
 Represented Functions 
 § 2.5. Applications of the Derivative 
 § 2.6. The Differential of a Function. Application to
 Approximate Computations 
 § 2.7. Additional Problems 
 
3. Application of Differential Calculus to Investigation of 
 Functions
 § 3.1. Basic Theorems on Differentiable Functions
 § 3.2. Evaluation of Indeterminate Forms.L’Hospital’s Rule
 § 3.3. Taylor’s Formula. Application to Approximate
 Calculations
 § 3.4. Application of Taylor’s Formula to Evaluation of 
 Limits 
 § 3.5. Testing a Function for Monotonicity 
 § 3.6. Maxima and Minima of a Function 
 § 3.7. Finding the Greatest and the Least Values of a 
 Function 
 § 3.8. Solving Problems in Geometry and Physics 
 § 3.9. Convexity and Concavity of a Curve. Points of 
 Inflection 
 § 3.10. Asymptotes 
 § 3.11. General Plan for Investigating Functions and Sketching
 Graphs 
 § 3.12. Approximate Solution of Algebraic and
 Transcendental Equations
 § 3.13. Additional Problems
 
4. Indefinite Integrals. Basic Methods of Integration
 § 4.1. Direct lntegration and the Method of Expansion
 § 4.2. Integration by Substitution
 § 4.3. Integration by Parts
 § 4.4. Reduction Formulas
 CHAPTERS
 
5. Basic Classes of Integrable Functions
 § 5.1. Integration of Rational Functions
 § 5.2. Integration of Certain Irrational Expressions 
 § 5.3. Euler’s Substitutions
 § 5.4. Other Methods of Integrating Irrational Expressions
 § 5.5. Integration of a Binomial Differential 
 § 5.6. Integration of Trigonometric and Hyperbolic Functions
 § 5.7. Integration of Certain Irrational Functions with the Aid
 of Trigonometric or Hyperbolic Substitutions
 § 5.8. Integration of Other Transcendental Functions
 § 5.9. Methods of Integration (List of Basic Forms of 
 Integrals) 
 
6. The Definite Integral 
 § 6.1. Statement of the Problem. The Lower and Upper 
 Integral Sums 
 § 6.2. Evaluating Definite Integrals by the Newton-Leibniz 
 Formula 
 § 6.3. Estimating an Integral. The Definite Integral as a  
 Function of Its Limits 
 § 6.4. Changing the Variable in a Definite Integral 
 § 6.5. Simplification of Integrals Based on the Properties of 
 Symmetry of Integrands 
 § 6.6. Integration by Parts. Reduction Formulas 
 § 6.7. Approximating Definite Integrals 
 § 6.8. Additional Problems 
 
7. Applications of the Definite Integral 
 § 7.1. Computing the Limits of Sums with the Aid of 
 Definite Integrals 
 § 7.2. Finding Average Values of a Function 
 § 7.3. Computing Areas in Rectangular Coordinates 
 CHAPTERS
 § 7.4. Computing Areas with Parametrically Represented 
 Boundaries 
 § 7.5. The Area of a Curvilinear Sector in Polar Coordinates
 § 7.6. Computing the Volume of a Solid
 § 7.7. The Arc Length of a Plane Curve in Rectangular 
 Coordinates 
 § 7.8. The Arc Length of a Curve Represented
 Parametrically
 § 7.9. The Arc Length of a Curve in Polar Coordinates
 § 7.10. Area of Surface of Revolution 
 § 7.11. Geometrical Applications of the Definite Integral.
 § 7.12. Computing Pressure, Work and Other Physical
 Quantities by the Definite Integrals
 § 7.13. Computing Static Moments and Moments of Inertia.
 Determining Coordinates of the Centre of Gravity
 § 7.14. Additional Problems 
 
8. Improper Integrals
 § 8.1. Improper Integrals with Infinite Limits
 § 8.2. Improper Integrals of Unbounded Functions
 § 8.3. Geometric and Physical Applications of Improper
 Integrals
 § 8.4. Additional Problems
 
 Answers and Hints 
 


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