Problems in Calculus of one Variable

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The book consists of principal definition, theorems and formulas followed by solved examples and problems for practice. Answers are given in the end of the book.

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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
ISBN11 9789385966583
Author I.A.MARON
Edition 2016
Pages 456
Classes Class 11, Class 12
Exams School Books
Subjects Mathematics
Weight 388gm

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